The literature database for the ionization constant of water, pKw, has been critically reevaluated to include new accurate flow conductivity data recently reported at near-critical and supercritical conditions. Recently published equations to express the limiting conductivity of fully ionized water were used to correct the conductivity data and yield more accurate pKw values at water densities below 0.6 g cm−3. The ability of the functional forms adopted by the 1980 and 2006 International Association for the Properties of Water and Steam releases to fit the near-critical and supercritical data was tested. Revised parameters for the 2006 “simple” function were derived to improve the accuracy of the model under these conditions. The data fitting procedure made use of estimated standard uncertainties as well as a weighting parameter for each dataset to minimize potential bias due to the very large amount of flow conductivity data now available. Calculations based on the revised formulation were found to be consistent with independent high-temperature data measured using calorimetry and density methods. The revised equation is accurate to within the estimated standard uncertainty limits over the range 0–1000 °C, p = 0–1000 MPa.

a w

activity of water

a 1 –a 4

adjustable parameters in Marshall–Franck model

b 1 –b 3

adjustable parameters in Marshall–Franck model

K

equilibrium constant

K a,H

ionization constant of an acid

K b,OH

ionization constant of a base

M w

molar mass of water, g mol−1 (Mw = 18.015 268 g mol−1)

n

ion coordination number parameter in Bandura–Lvov model

p

pressure, MPa

pK

−log10K

p sat

saturation vapor pressure, MPa

R

gas constant (8.314 462 618 J mol−1 K−1)

t

temperature, °C

T

temperature, K

u

estimated IUPAC type B standard uncertainty

Z

empirical function in Bandura–Lvov model

ΔrG°

standard molar Gibbs free energy of reaction

ΔrH°

standard molar enthalpy of reaction

ΔrS°

standard molar entropy of reaction

Δ r C p

standard molar heat capacity of reaction

ΔrV°

standard molar volume of reaction

Λ

molar conductivity, S cm2 mol−1

Λ°

limiting molar conductivity, S cm2 mol−1

α 1 –α 3

adjustable parameters in Bandura–Lvov model

α w

thermal expansion coefficient of water

β 1 –β 3

adjustable parameters in Bandura–Lvov model

β w

compressibility coefficient of water

κ

electrical conductivity, S cm−1

λ°

limiting molar ionic conductivity, S cm2 mol−1

ρ

density, g cm−3

Subscripts and superscripts
exp.

experimental

fit

fitted

G

gas

r

reaction

w

water

The ionization constant of water (pKw) is an important parameter for modeling the chemistry of aqueous systems. Several formulations have been developed based on critical reviews of the literature data.1–7 The current generation of chemistry software and industrial codes predominantly use three formulations to calculate the ionization constant of water at high temperatures and pressures: (i) the 2006 International Association for the Properties of Water and Steam (IAPWS)8 model developed by Bandura and Lvov (B–L),7 (ii) the 1980 IAPWS “density” model reported by Marshall and Franck (M–F),3 which is still widely used in the power industry; (iii) and the revised Tanger–Helgeson–Kirkham–Flowers (HKF) model.4 Briefly, the current IAPWS model7 is based on a critically evaluated database comprising about 300 data points spanning temperature and density conditions from 0 to 800 °C and 0.08 to 1.2 g cm−3; the 1980 model considered only a subset of these data together with a few derivative properties (ΔrCp°, ΔrV°);2 and the HKF model4,9 makes use of high-temperature standard partial molar heat capacity and volume data for OH, published in the 1970s and 1980s.

Recently, a large number of flow conductivity-based pKw values (about 330 datapoints) have been reported between 100 and 400 °C and 0.2 and 0.9 g cm−3.10 These new data provide the opportunity to extend the range of chemical equilibrium models/software (e.g., EPRI MULTEQ11,12) to the higher temperatures required to model advanced reactor designs more accurately. In Ref. 10, the conductivity data were used, together with pKw values from other literature sources, to derive provisional revised parameters for the M–F and B–L equations, based on an unweighted fit of the selected data with a strong emphasis on the flow conductivity data. Two issues were identified with this approach. First, the un-weighted fitting procedure may have resulted in a bias in favor of the flow conductivity data due to their very large number relative to data from other methods in the overall database. Second, systematic uncertainties were observed in the calculated high-temperature limiting conductivity of fully ionized water below 0.6 g cm−3, resulting in large uncertainties in the new flow conductivity-based Kw values above 330 °C.13 This study addresses both issues. The flow conductivity derived equilibrium constant data reported in Ref. 10 have been revised using more accurate equations to represent the limiting conductivity of H+ and OH in high-temperature water.13 The revised data were critically evaluated together with the pre-existing database following similar methods and assumptions used in previous work.13,14 The ability of the 2006 B–L and 1980 M–F IAPWS models to represent the temperature and density dependences of pKw was tested, especially at near-critical and supercritical conditions. The results indicated that the functional form of the B–L equation gives a better fit to the data over a complete range of conditions and revised B–L parameters were derived. The data fitting procedure made use of estimated standard uncertainties as well as a weighting parameter for each dataset to minimize potential bias due to the very large amount of flow conductivity data. The fit results were compared to a set of independent high-temperature heat capacity and volume data, indicating that the revised B–L parameters lead to more accurate calculations of the derivative properties at high temperatures. The revised formulation can reproduce most of the literature data measured from 0 to 1000 °C and p = 0–1000 MPa to within their assigned error limits, and is expected to be much more accurate than the existing formulae for near-critical and supercritical conditions.

Electrical conductivity methods have been used to determine the ionization constant of water, pKw. The methods are well suited to measure thermodynamic ionization constants because the measurements can be made under dilute conditions where the Debye–Hückel limiting law applies. Besides the results published by Bignold et al.15 and Arcis et al.,10 most of the reported pKw studies are based on indirect measurements of acid and base conductivities where the ionization constants of an acid, pKa,H, and its conjugate base, pKb,OH, are well-known and used to solve for pKw. The first high-temperature conductivity pKw data were measured up to ∼300 °C along the steam saturation line by Noyes et al.,16 who studied the change in conductivity associated with ionization in aqueous solutions of ammonium acetate, and its variation with excess ammonia or acetic acid. Holzapfel and Franck,17 Quist,18 Fisher and Barnes,19 and Svistunov et al.20,21 used similar approaches to extend the measurements to higher temperatures and pressures. It is also possible to use conductivity methods to directly determine the ionization constant of water if the measurements are made on very pure water samples and the technique does not produce any ionic impurities that would affect the results.10 A description of all the different conductivity methods can be found in Corti’s 2008 review.22 

The very low conductivity values that can be measured with Wood-type conductivity flow cells23 are achieved using flow to carry away minute concentrations of contaminants from previous runs, and a diamond frit to prevent back-flow of corrosion products from downstream insulators and pressure seal materials. The power of the technique is illustrated by Arcis’ recent results for pKw10 which are based on very accurate flow conductivity measurements of very pure water samples.24–43 A review13 showed systematic errors in Arcis’ calculations10 above 330 °C because of the extrapolations used to estimate the limiting conductivity of fully ionized water, Λw°, which is defined by:
Λw=λ°H3O++λ°OH=Λ°HCl+Λ°KOHΛ°KCl.
(1)
Λw° can be calculated using the limiting conductivity of H3O+ and OH (Method 1) or that of HCl, KOH, and KCl (Method 2), which ought to yield the same results based on Kohlrausch’s law of independent ion migration. In practice, however, inconsistencies can arise when extrapolating empirical equations adjusted to fit data for a limited range of conditions. Arcis et al. have reported revised correlations for H3O+ and OH, HCl, KOH, and KCl,13,14 and these were used to calculate revised Λw° values for the experimental conductivity data reported in Ref. 10 using both methods. While both calculation methods yield results consistent with experimental data to within the experimental uncertainties between 0.5 and 1.0 g cm−3, the extrapolations diverge significantly below 0.5 g cm−3, up to about 1.2 pK difference for the lowest density considered. This is illustrated in Fig. 1, where Method 2 yields unphysical values below 0.3 g cm−3 whereas Method 1 gives results consistent with Marshall’s reduced relationship and his extrapolated limiting value of 1850 S cm2 mol−1 at zero density between 400 and 800 °C.44 
FIG. 1.

Limiting molar conductivity of fully ionized water calculated using Method 1 and Method 2.

FIG. 1.

Limiting molar conductivity of fully ionized water calculated using Method 1 and Method 2.

Close modal
To correct this error, the data treatment from Ref. 10 has been replicated using Method 1 together with the new expressions for λ°(H3O+) and λ°(OH) reported in Ref. 13, using pKw values calculated from the expression:
pKw=2log10106κwexp.ρwλ°H3O++λ°OH,
(2)
where κwexp. and ρw are the electrical conductivity and density of water. Experimental values for κwexp. were taken from Ref. 10 and ρw values were calculated from Ref. 45. The estimated IUPAC Type B46 standard uncertainties of the revised results10 are u(pKw) = 0.04 for ρw ≥ 0.7 g cm3; u(pKw) = 0.1 for 0.7 > ρw ≥ 0.5 g cm−3; u(pKw) = 0.3 for 0.5 > ρw ≥ 0.3 g cm−3; u(pKw) = 0.8 for ρw < 0.3 g cm−3.

Potentiometry techniques have been widely used to determine the ionization constant of water, Kw, and details of the different reported methods and apparatus can be found in Refs. 47 and 48. Several studies have reported water ionization quotients, Qw.1,49–56 To date the best tool to carry out isothermal potentiometric titrations under hydrothermal conditions is the hydrogen-electrode concentration cell designed by Mesmer et al.57 at Oak Ridge National Laboratory (ORNL). The method can yield experimental ionization quotient values for simple acids and bases to an accuracy within ±0.01 pK with the use of thermally stable electrodes. With this technique, Sweeton et al.1 reported what are considered to be the most accurate Kw data between 50 and 300 °C. No high-temperature pKw data have been reported since 1980.

Hamman et al.58,59 have studied the ionization constant of water up to 800 MPa by potentiometry and conductivity using a shock wave technique, with very large uncertainties associated to their results. Chau et al.60 have measured the electrical conductivity of water at high pressures up to 180 GPa using a reverberating shock wave technique, but the lack of data on the limiting conductivity of H+ and OH under these extreme conditions (and of any formulation to compute the water density up to 180 GPa) makes it too difficult to derive accurate pKw values, hence these results were not considered in this assessment.

Calorimetry has also been used to measure the degree of ionization of water at elevated temperatures.61,62 The method relies on the use of very accurate measurements of the enthalpies of reaction of H+(aq) and OH(aq), or their apparent molar heat capacities and volumes, both of which were made possible by the development of flow calorimeters capable of operating under hydrothermal conditions. These data and methods have been reviewed by Chen et al.6 and Tremaine and Arcis.63 

The current literature database for pKw includes more than 600 data points with temperature, pressure, and density conditions from t = 0 °C to t = 1200 °C, p = 0.1 MPa to p = 1000 MPa, and ρw = 0.08 g cm−3 to ρw = 1.65 g cm−3, respectively. The flow conductivity data10 have addressed the previous gap for high-temperature low-density at near-critical conditions; except for the results from Ref. 21 the earlier studies did not extend below 0.4 g cm−3 due to the formidable experimental challenges that arise when approaching the critical point of water. 487 datapoints from static conductivity (seven sources), potentiometric (nine sources), calorimetry (two sources), high-pressure shock wave measurements (two sources), and flow conductivity (12 sources) studies make up the final dataset used in this work. All the reported data points were used except for the flow conductivity studies, where we followed previous work10 and considered only 177 data points out of 366 possible.10 The temperature-density profile of the retained experimental data is shown in Fig. 2. The estimated uncertainty for each of the data points was assigned based on the authors’ reported (or highest) uncertainties, or reassessed (i) for Ref. 16 based on previous work,14 (ii) for Ref. 59 to account for expected large uncertainties with the shock wave method, and (iii) for the flow conductivity data24,25,28,30–32,35–38,40–43 (see Sec. 2.2). The pKw datasets considered in this work are shown in Fig. 3. References and conditions are listed in Table 1, and numerical values are tabulated together with the estimated IUPAC Type B46 standard uncertainties, u(pKw), in the Appendix.

FIG. 2.

A temperature-density profile of the 487 selected data points. Top, full experimental range; bottom, zoom illustrating knowledge gap filled at near-critical conditions.

FIG. 2.

A temperature-density profile of the 487 selected data points. Top, full experimental range; bottom, zoom illustrating knowledge gap filled at near-critical conditions.

Close modal
FIG. 3.

The selected pKw database versus temperature.

FIG. 3.

The selected pKw database versus temperature.

Close modal
TABLE 1.

References and data considered in this work

Source Data selected/total Reported uncertainty (pK unit) Assigned experimental uncertainty (pK unit)
Potentiometry studies 
Harned and Robinson (1940)49   13/13  0.001  Same as reported uncertainty 
Perkovets and Kryukov (1969)50   6/6  0.02  Same as reported uncertainty 
Linov and Kryukov (1972)52,a  32/32  0.02–0.03  Upper limit of reported uncertainty 
Whitfield (1972)51,a  50/50  0.005–0.015  Upper limit of reported uncertainty 
MacDonald et al. (1973)53   8/8  0.01–0.03  Upper limit of reported uncertainty 
Sweeton et al. (1974)1,a  13/13  0.006–0.045  Same as reported uncertainty 
Busey and Mesmer (1978)54,b  13/13  0.006–0.045  Same as reported uncertainty 
Kryukov et al. (1980)55   31/31  0.01–0.04  Same as reported uncertainty 
Palmer and Drummond (1988)56   6/6  0.01  Same as reported uncertainty 
Static conductivity studies 
Noyes et al. (1910)16,b  7/7  NA  0.1 
Holzapfel and Franck (1966)17,b  6/6  0.7  Same as reported uncertainty 
Quist (1970)18,a  31/31  0.3–0.5  Upper limit of reported uncertainty 
Bignold et al. (1971)15   24/24  0.008–0.04  Upper limit of reported uncertainty 
Fisher and Barnes (1972)19   6/6  0.2  Same as reported uncertainty 
Svistunov et al. (1977)20   4/4  0.5–1.0  Upper limit of reported uncertainty 
Svistunov et al. (1978)21   12/12  0.1–0.4  Upper limit of reported uncertainty 
Calorimetry studies 
Ackermann (1958)61   15/15  0.005  Same as reported uncertainty 
Chen et al. (1994)62   15/15  0.005–0.1  Same as reported uncertainty 
High-pressure shock wave studies 
Hamann (1963)58,a  9/9  0.01–0.03  Upper limit of reported uncertainty 
Hamann and Linton (1969)59,b  9/9  ≤0.5  3.0 
Chau et al. (2001)60,b  0/10  NA  NA 
Flow conductivity studiesb 
Zimmerman et al. (2012)33   0/7  NA  NA 
Arcis et al. (2014)34   0/14  NA  NA 
Arcis et al. (2016)35   16/18  NA  0.04–0.1 
Arcis et al. (2017)36   8/10  NA  0.04–0.1 
Ferguson et al. (2017)37   12/15  NA  0.04–0.1 
Ferguson et al. (2019)40   6/11  NA  0.04–0.1 
Ferguson (2018)39   3/6  NA  0.04–0.1 
Arcis et al. (2022)42   0/8  NA  NA 
Conrad et al. (2023)41   0/6  NA  NA 
Arcis et al. (2023)43   0/15  NA  NA 
Zimmerman et al. (1995)23   0/37  NA  NA 
Gruszkiewicz and Wood (1997)24   38/38  NA  0.04–0.8 
Sharygin et al. (2001)29   0/4  NA  NA 
Sharygin et al. (2002)30   29/29  NA  0.04–0.8 
Zimmerman and Wood (2002)31   9/9  NA  0.04–0.8 
Hnedkovsky et al. (2005)25   9/10  NA  0.04–0.8 
Sharygin et al. (2006)32   13/13  NA  0.04–0.8 
Balashov et al. (2017)38   9/9  NA  0.04–0.8 
Ho et al. (2000)26   0/23  NA  NA 
Ho et al. (2000)27   0/28  NA  NA 
Ho et al. (2001)28   27/27  NA  0.04–0.8 
Source Data selected/total Reported uncertainty (pK unit) Assigned experimental uncertainty (pK unit)
Potentiometry studies 
Harned and Robinson (1940)49   13/13  0.001  Same as reported uncertainty 
Perkovets and Kryukov (1969)50   6/6  0.02  Same as reported uncertainty 
Linov and Kryukov (1972)52,a  32/32  0.02–0.03  Upper limit of reported uncertainty 
Whitfield (1972)51,a  50/50  0.005–0.015  Upper limit of reported uncertainty 
MacDonald et al. (1973)53   8/8  0.01–0.03  Upper limit of reported uncertainty 
Sweeton et al. (1974)1,a  13/13  0.006–0.045  Same as reported uncertainty 
Busey and Mesmer (1978)54,b  13/13  0.006–0.045  Same as reported uncertainty 
Kryukov et al. (1980)55   31/31  0.01–0.04  Same as reported uncertainty 
Palmer and Drummond (1988)56   6/6  0.01  Same as reported uncertainty 
Static conductivity studies 
Noyes et al. (1910)16,b  7/7  NA  0.1 
Holzapfel and Franck (1966)17,b  6/6  0.7  Same as reported uncertainty 
Quist (1970)18,a  31/31  0.3–0.5  Upper limit of reported uncertainty 
Bignold et al. (1971)15   24/24  0.008–0.04  Upper limit of reported uncertainty 
Fisher and Barnes (1972)19   6/6  0.2  Same as reported uncertainty 
Svistunov et al. (1977)20   4/4  0.5–1.0  Upper limit of reported uncertainty 
Svistunov et al. (1978)21   12/12  0.1–0.4  Upper limit of reported uncertainty 
Calorimetry studies 
Ackermann (1958)61   15/15  0.005  Same as reported uncertainty 
Chen et al. (1994)62   15/15  0.005–0.1  Same as reported uncertainty 
High-pressure shock wave studies 
Hamann (1963)58,a  9/9  0.01–0.03  Upper limit of reported uncertainty 
Hamann and Linton (1969)59,b  9/9  ≤0.5  3.0 
Chau et al. (2001)60,b  0/10  NA  NA 
Flow conductivity studiesb 
Zimmerman et al. (2012)33   0/7  NA  NA 
Arcis et al. (2014)34   0/14  NA  NA 
Arcis et al. (2016)35   16/18  NA  0.04–0.1 
Arcis et al. (2017)36   8/10  NA  0.04–0.1 
Ferguson et al. (2017)37   12/15  NA  0.04–0.1 
Ferguson et al. (2019)40   6/11  NA  0.04–0.1 
Ferguson (2018)39   3/6  NA  0.04–0.1 
Arcis et al. (2022)42   0/8  NA  NA 
Conrad et al. (2023)41   0/6  NA  NA 
Arcis et al. (2023)43   0/15  NA  NA 
Zimmerman et al. (1995)23   0/37  NA  NA 
Gruszkiewicz and Wood (1997)24   38/38  NA  0.04–0.8 
Sharygin et al. (2001)29   0/4  NA  NA 
Sharygin et al. (2002)30   29/29  NA  0.04–0.8 
Zimmerman and Wood (2002)31   9/9  NA  0.04–0.8 
Hnedkovsky et al. (2005)25   9/10  NA  0.04–0.8 
Sharygin et al. (2006)32   13/13  NA  0.04–0.8 
Balashov et al. (2017)38   9/9  NA  0.04–0.8 
Ho et al. (2000)26   0/23  NA  NA 
Ho et al. (2000)27   0/28  NA  NA 
Ho et al. (2001)28   27/27  NA  0.04–0.8 
a

Considered by Marshall and Franck in their data regression.3 

b

Not considered by Bandura and Lvov in their data regression.7 

A number of semi-empirical models have been proposed1–4,6,7 to correlate and/or predict thermodynamic ionization constants over an extended range of temperatures and pressures/densities, and several reviews of the models can be found in the literature (e.g., Refs. 63–66). In this work, the models tested have been restricted to the two latest IAPWS releases. While it is widely used for geochemical67 and industrial68 applications because of its extensive database, the revised HKF (Tanger–Helgeson–Kirkham–Flowers) model4,9 was not considered as part of this work, mainly because the model framework starts to collapse at near-critical conditions due to the limited data available for the dielectric constant of water. Calculations based on the HKF model are expected to give similar results to the M–F and B–L models discussed below between 25 and 250 °C (above this temperature, the results could be affected by the choice of the dielectric constant model used69).

The 1980 IAPWS pKw formulation is based on Franck and Marshall’s density model,3 which was developed following Franck’s high-temperature and high-pressure measurements70,71 that showed clear correlations between log K and log ρw. The model expression3,72 takes the form
lnK=ΔrGoRT=i=14aiT1i+lnρwj=13bjT1j,
(3)
where ai and bj are empirical parameters adjusted to experimental data, T is the temperature in K, and ρw is the density of water in g cm−3. In its original form, the model considers four ai and three bj parameters. The first series of terms (ai) seeks to represent short-range hydration effects with the solute that dominate at low temperature, whereas the second series (bj) accounts for long-range polarization effects and standard-state terms which are more important at high temperatures. The density term in the equation is consistent with the limiting near-critical behavior of ions and non-electrolytes as described by the Krichevskii equation.73,74 One of the attractive features of the density model resides in the simplicity with which it can be used to calculate thermodynamic standard-state derivative properties (ΔrH°, ΔrS°, ΔrCp°, ΔrV°), as defined by Mesmer et al.:72 
ΔrHo=Rln10a2+2a3T+3a4T2+b2+2b3Tlog10ρwRT2b1+b2T+b3T2αw
(4)
ΔrSo=Rln10a1a3T22a4T3+b1b3T2log10ρwRTb1+b2T+b3T2αw
(5)
ΔrCpo=Rln102a3T26a4T32b3T2log10ρwR2b1T2b3TαwRT2b1+b2T+b3T2αwTp
(6)
ΔVo=RTb1+b2T+b3T2βw,
(7)
where αw = −(1/ρw)(∂ρw/∂T)p and βw = (1/ρw)(∂ρw/∂p)T are the thermal expansion coefficient and isothermal compressibility of water, respectively.

Marshall and Franck adjusted their model parameters based on data from Refs. 1, 2, 18, 51, 52, and 58. Briefly, they regressed their three bj density terms from least-squares fitting using the data reported in these references and constrained their fit at 25 °C using an average value from Refs. 2, 51, and 58. In order to derive their four ai parameters, Marshall and Franck recalculated Sweeton et al.’s1 data points at a hypothetical water density of 1.0 g cm−3 and performed a least-squares fitting of the recalculated data.

The B–L model7 combines formulations for the contributions to the standard-state chemical potential of the ionic hydration process based on statistical thermodynamics considerations and uses a sorption model to calculate the inner-shell term. Unlike the M–F model, it includes a term for the temperature-dependent ionization constant of water in the ideal gas state to predict the theoretically correct zero-density limit of pKw. Bandura and Lvov also reported a simplified analytical expression, given by Eqs. (8) and (9), which performs as well as the full model (which has nine adjustable parameters, with eight regressed and one fixed):
pKwT,ρw=2nlog10(1+Z)ZZ+1ρwβ0+β1T+β2ρw+pKwG(T)+2log10Mw1000,
(8)
where T is the temperature in K, ρw is the water density in g cm−3, n = 6 is the ion coordination number, Z=ρwexpα0+α1T+α2T2ρw2/3 is an empirical function of temperature and water density, Mw is the molar mass of water in g mol−1, and αi and βi are fit parameters adjusted to literature data. The gas-phase pKw term, pKwG(T), which is an important feature of the model, is defined using reference thermodynamic data:75,
pKwG(T)=0.61415+48251.33T67707.93T2+10102100T3.
(9)
The other major difference with M–F arises from the choices in the critically compiled datasets used to adjust the model parameters. The B–L database includes Svistunov et al. data20,21 (Marshall and Franck did not) and consideration of the four data points at very low water densities20 in the model regression has a significant effect on the pKw calculations for water densities below 0.5 g cm−3, where very few data had been reported. There are no significant differences in the pKw values calculated using the M–F and B–L formulations between room temperature and 250 °C; differences at higher temperatures are briefly discussed below.

In this work, we followed a similar data fitting procedure to that described in Ref. 7 and associated two parameters with each data point: an estimated uncertainty and a weight. In most cases, the standard uncertainty was defined as the experimental uncertainty or error limit reported in the original studies except for Refs. 15, 18, 20, 21, 5153, and 58 where it was set to the highest reported uncertainty. The error limits for the flow conductivity data (see Sec. 2.2) and the data reported in Refs. 16 and 59 were re-estimated based on the uncertainties on the limiting conductivity of fully ionized water under hydrothermal conditions.13 The data regression method used a non-linear weighted least-squares technique (Levenberg–Marquardt algorithm), where each data point was weighted inversely to its estimated uncertainty. A second weight parameter (w) was introduced to minimize potential bias in the fitting that would result from the large amount of flow conductivity data. These were assigned using a scale from 0 to 1 with w = 1 for Sweeton et al.1 and Harned and Stokes,49 and w = 0.5 for the other potentiometry sources; w = 0.6 for the calorimetry studies; w = 0.4 for the (flow and static) conductivity studies; and w = 0.05 for the high-pressure shock wave measurements. Both M–F and B–L equations were fitted to the selected dataset following this procedure. A visual comparison of both fits suggested that the B–L functional form was more adequate than M–F to represent the selected dataset, especially at high-density conditions. The M–F model was not considered further in this work.

Revised parameters for Eq. (8) were derived from the regression to the selected dataset, whereas parameters for Eq. (9) based on JANAF98 data for the species in the ideal gas reference state75 were unchanged. Results are reported in Table 2 together with the original B–L fit parameters. The revised model parameters listed in Table 2 were regressed to the same selection of data as described in Sec. 2.6 with a standard deviation SD = 0.276. This corresponds to a standard uncertainty u(pKw) = 0.013. The revised model yields significant improvement relative to the original B–L and M–F equations. The deviation plots between experimental data used for the regression and the fitted Eq. (8) are shown in Figs. 47. Numerical values for (i) the deviations between the literature and fitted values, ΔpKw = pKw(exp.) − pKw(calc.), and (ii) the differences between the estimated IUPAC Type B46 standard uncertainties and the absolute values of these deviations, u[δpKw(exp.)] − |ΔpKw|, are tabulated in the Appendix. As illustrated in Fig. 8, the revised parameters for Eq. (8) greatly improve the accuracy of the original B–L model for the ionization of water for densities below 0.45 g cm−3. Overall, the revised model can represent most of the experimental pKw data to within the estimated errors, as illustrated by the large number of positive values listed in the last columns of the Table in the Appendix. Some negative values are observed for some of the results from Noyes et al.16 below 25 °C and above 300 °C, Quist18 at low densities for 600 and 700 °C, Holzapfel and Franck17 and Linov and Kryukov,52 Fisher and Barnes,19 Hnedkovsky et al.,25 Zimmerman and Wood,31 Ho et al.,28 Sharygin et al.,32 and Chen et al.62 suggesting that these data could be less accurate than reported or estimated here. Calculated values of pKw using Eq. (8) together with the parameters listed in Table 2 are tabulated in Table 3 between 0 and 1000 °C and 0.1 or psat and 1000 MPa.

TABLE 2.

Original and revised model parameters for Eq. (8)

Source α 0 α1 (K) α2 [K2 (g cm−3)−2/3] β0 (cm3 g−1) β1 (K cm3 g−1) β2 (cm6 g−2)
Reference 7   −0.864 671  8659.19  −22 786.2  0.642 044  −56.8534  −0.375 754 
This work  −0.702 132  8681.05  −24 145.1  0.813 876  −51.4471  −0.469 920 
Source α 0 α1 (K) α2 [K2 (g cm−3)−2/3] β0 (cm3 g−1) β1 (K cm3 g−1) β2 (cm6 g−2)
Reference 7   −0.864 671  8659.19  −22 786.2  0.642 044  −56.8534  −0.375 754 
This work  −0.702 132  8681.05  −24 145.1  0.813 876  −51.4471  −0.469 920 
FIG. 4.

Deviation between model and static conductivity data. Top, full experimental range; bottom, zoom for pKw between 10 and 15.

FIG. 4.

Deviation between model and static conductivity data. Top, full experimental range; bottom, zoom for pKw between 10 and 15.

Close modal
FIG. 5.

Deviation between model and potentiometry data. Top, full experimental range; bottom, zoom for pKw between 11.5 and 13.5.

FIG. 5.

Deviation between model and potentiometry data. Top, full experimental range; bottom, zoom for pKw between 11.5 and 13.5.

Close modal
FIG. 6.

Deviation between model and calorimetry data.

FIG. 6.

Deviation between model and calorimetry data.

Close modal
FIG. 7.

Deviation between model and flow conductivity data.

FIG. 7.

Deviation between model and flow conductivity data.

Close modal
FIG. 8.

Model performance with original (red symbols) and revised (blue symbols) B–L parameters against experimental data. Top, full experimental range; bottom, zoom for ρw between 200 and 480 kg m−3: circles, Wood’s flow conductivity data; squares, Palmer’s flow conductivity data; dashed lines, experimental uncertainties [see Sec. 2.2, u(pKw) = 0.3 for 500 > ρw ≥ 300 kg m−3; u(pKw) = 0.8 for ρw < 300 kg m−3].

FIG. 8.

Model performance with original (red symbols) and revised (blue symbols) B–L parameters against experimental data. Top, full experimental range; bottom, zoom for ρw between 200 and 480 kg m−3: circles, Wood’s flow conductivity data; squares, Palmer’s flow conductivity data; dashed lines, experimental uncertainties [see Sec. 2.2, u(pKw) = 0.3 for 500 > ρw ≥ 300 kg m−3; u(pKw) = 0.8 for ρw < 300 kg m−3].

Close modal
TABLE 3.

Calculated values of pKw using Eq. (8) with revised parameters from this work

t (°C)
Pressure (MPa) 0a 25 50 75 100 150 200 250 300 350 400 450 500 600 700 800 900 1000
p sat b   14.95  13.99  13.26  12.70  12.25  11.64  11.31  11.19  11.29  11.77  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯ 
15  14.89  13.94  13.21  12.65  12.20  11.59  11.24  11.11  11.20  18.99  20.07  20.54  20.85  21.28  21.58  21.80  21.94  21.97 
25  14.85  13.91  13.18  12.61  12.17  11.55  11.19  11.04  11.09  11.45  15.88  17.35  17.95  18.60  18.99  19.28  19.49  19.61 
50  14.76  13.83  13.10  12.54  12.09  11.46  11.08  10.90  10.87  11.02  11.42  12.40  13.68  14.97  15.58  15.97  16.25  16.45 
75  14.67  13.75  13.03  12.46  12.01  11.37  10.98  10.77  10.71  10.77  10.97  11.33  11.89  13.03  13.73  14.17  14.48  14.71 
100  14.58  13.67  12.95  12.39  11.94  11.29  10.89  10.66  10.57  10.58  10.69  10.91  11.21  11.96  12.59  13.03  13.34  13.57 
150  14.42  13.52  12.82  12.25  11.80  11.14  10.72  10.47  10.34  10.29  10.32  10.42  10.56  10.94  11.34  11.67  11.94  12.15 
200  14.28  13.39  12.69  12.12  11.67  11.01  10.58  10.30  10.15  10.07  10.06  10.10  10.18  10.41  10.67  10.92  11.13  11.31 
250  14.14  13.26  12.56  12.00  11.55  10.88  10.44  10.16  9.98  9.88  9.85  9.86  9.90  10.05  10.24  10.43  10.60  10.75 
300  14.02  13.14  12.45  11.89  11.44  10.77  10.32  10.02  9.83  9.72  9.67  9.66  9.68  9.78  9.92  10.08  10.22  10.34 
350  13.90  13.03  12.34  11.78  11.33  10.66  10.20  9.90  9.70  9.58  9.51  9.48  9.49  9.55  9.67  9.79  9.91  10.02 
400  13.79  12.92  12.23  11.68  11.23  10.55  10.09  9.78  9.58  9.44  9.37  9.33  9.32  9.36  9.45  9.56  9.66  9.75 
500  13.58  12.72  12.04  11.48  11.03  10.36  9.89  9.57  9.35  9.21  9.11  9.06  9.04  9.04  9.10  9.17  9.26  9.33 
600  13.39  12.54  11.86  11.30  10.85  10.17  9.71  9.38  9.15  9.00  8.90  8.83  8.79  8.78  8.81  8.87  8.93  9.00 
700  ⋯  12.36  11.68  11.14  10.69  10.01  9.53  9.20  8.97  8.81  8.70  8.63  8.58  8.55  8.57  8.61  8.66  8.72 
800  ⋯  12.20  11.52  10.98  10.53  9.85  9.37  9.04  8.80  8.64  8.52  8.44  8.39  8.35  8.35  8.39  8.43  8.48 
900  ⋯  12.04  11.37  10.82  10.38  9.70  9.22  8.89  8.64  8.47  8.35  8.27  8.21  8.16  8.16  8.19  8.22  8.27 
1000  ⋯  11.90  11.23  10.68  10.23  9.55  9.08  8.74  8.50  8.32  8.20  8.11  8.05  7.99  7.98  8.00  8.04  8.08 
t (°C)
Pressure (MPa) 0a 25 50 75 100 150 200 250 300 350 400 450 500 600 700 800 900 1000
p sat b   14.95  13.99  13.26  12.70  12.25  11.64  11.31  11.19  11.29  11.77  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯  ⋯ 
15  14.89  13.94  13.21  12.65  12.20  11.59  11.24  11.11  11.20  18.99  20.07  20.54  20.85  21.28  21.58  21.80  21.94  21.97 
25  14.85  13.91  13.18  12.61  12.17  11.55  11.19  11.04  11.09  11.45  15.88  17.35  17.95  18.60  18.99  19.28  19.49  19.61 
50  14.76  13.83  13.10  12.54  12.09  11.46  11.08  10.90  10.87  11.02  11.42  12.40  13.68  14.97  15.58  15.97  16.25  16.45 
75  14.67  13.75  13.03  12.46  12.01  11.37  10.98  10.77  10.71  10.77  10.97  11.33  11.89  13.03  13.73  14.17  14.48  14.71 
100  14.58  13.67  12.95  12.39  11.94  11.29  10.89  10.66  10.57  10.58  10.69  10.91  11.21  11.96  12.59  13.03  13.34  13.57 
150  14.42  13.52  12.82  12.25  11.80  11.14  10.72  10.47  10.34  10.29  10.32  10.42  10.56  10.94  11.34  11.67  11.94  12.15 
200  14.28  13.39  12.69  12.12  11.67  11.01  10.58  10.30  10.15  10.07  10.06  10.10  10.18  10.41  10.67  10.92  11.13  11.31 
250  14.14  13.26  12.56  12.00  11.55  10.88  10.44  10.16  9.98  9.88  9.85  9.86  9.90  10.05  10.24  10.43  10.60  10.75 
300  14.02  13.14  12.45  11.89  11.44  10.77  10.32  10.02  9.83  9.72  9.67  9.66  9.68  9.78  9.92  10.08  10.22  10.34 
350  13.90  13.03  12.34  11.78  11.33  10.66  10.20  9.90  9.70  9.58  9.51  9.48  9.49  9.55  9.67  9.79  9.91  10.02 
400  13.79  12.92  12.23  11.68  11.23  10.55  10.09  9.78  9.58  9.44  9.37  9.33  9.32  9.36  9.45  9.56  9.66  9.75 
500  13.58  12.72  12.04  11.48  11.03  10.36  9.89  9.57  9.35  9.21  9.11  9.06  9.04  9.04  9.10  9.17  9.26  9.33 
600  13.39  12.54  11.86  11.30  10.85  10.17  9.71  9.38  9.15  9.00  8.90  8.83  8.79  8.78  8.81  8.87  8.93  9.00 
700  ⋯  12.36  11.68  11.14  10.69  10.01  9.53  9.20  8.97  8.81  8.70  8.63  8.58  8.55  8.57  8.61  8.66  8.72 
800  ⋯  12.20  11.52  10.98  10.53  9.85  9.37  9.04  8.80  8.64  8.52  8.44  8.39  8.35  8.35  8.39  8.43  8.48 
900  ⋯  12.04  11.37  10.82  10.38  9.70  9.22  8.89  8.64  8.47  8.35  8.27  8.21  8.16  8.16  8.19  8.22  8.27 
1000  ⋯  11.90  11.23  10.68  10.23  9.55  9.08  8.74  8.50  8.32  8.20  8.11  8.05  7.99  7.98  8.00  8.04  8.08 
a

Above p ∼ 629 MPa, water at 0 °C is solid.

b

Values generated using the density of the liquid at 0.1 MPa below 100 °C, or the density of the saturated liquid at and above 100 °C.

Equation (8) together with the revised parameters listed in Table 2 is expected to be valid for computation of the ionization constant of water for all thermodynamically stable fluid states in the following ranges: 0°C ≤ t ≤ 1000 °C; 0 ≤ p ≤ 1000 MPa. For general and scientific applications, the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use45 should be used to determine the densities as input to Eq. (8) when the state point under consideration is defined by pressure and temperature instead of density and temperature. In addition, Eq. (8) can be used to provide reasonable extrapolation behavior for densities up to 1.69 g cm−3 at temperatures up to 1273 K. However, the recommended range of validity of the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use45 only extends up to ∼1.24 g cm−3. For stable fluid states outside the range of validity of Eq. (8), but within the range of validity of the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,45 the extrapolation behavior of Eq. (8) should be physically reasonable.

As for the original B–L equation,7 in the liquid-phase region and at temperatures and pressures below 200 °C and 200 MPa, the deviations of the experimental data from the calculated values of pKw do not generally exceed 0.05. Most of the available experimental data do not differ from those calculated by Eq. (8) by more than the reported experimental uncertainties or errors, as shown in the Appendix. At near-critical conditions, only a few deviations between the calculated values and the experimental data are observed outside of the combined uncertainties, up to 0.77 pK units. The very high-pressure pKw data up to 13 000 MPa and density of 1.69 g cm−3, which are well outside range of validity of the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use,45 are reproduced within less than the expected experimental error of 3.0 pK units. The revised model is expected to be more accurate at near-critical and supercritical conditions due to the inclusion in the regression of flow conductivity data that filled the knowledge gap around the critical point. The uncertainty of the calculated pKwG, the ionization constant of water at ρw = 0 (ideal-gas state), remains less than 0.005 up to 800 °C. For densities between the limit of experimental data (about 0.1 g cm−3) and the ideal-gas limit, the physical basis for the interpolation provided by Eq. (8) is not rigorous. Therefore, quantitative accuracy cannot be expected in this region.

Calculated values for pKw generated along the saturation line, and at p = 30, 100, and 200 MPa, using the 1980 and 2006 IAPWS release are compared to the results from this work in Figs. 9 and 10, where water densities were calculated using the IAPWS 1995 formulation.45  Figure 9 shows that differences between the different formulations at saturation pressure are within the expected experimental uncertainties below 290 °C. Deviations start to show at about 295 °C with ΔpKw differences between the revised fit from this work and the IAPWS B–L (M–F) model of −0.05 (−0.10), −0.07 (−0.19), −0.11 (−0.34), −0.13 (−0.45), and −0.27 (−1.12) at 295, 315, 335, 345, and 370 °C, respectively. Whereas the observed differences are consistent with the larger uncertainties associated with hydrothermal measurements, the present results confirm that the IAPWS 2006 formulation is more accurate than the 1980 model at near-critical and supercritical conditions, and it should be evident that the revised parameters listed in Table 2 provide even better accuracy under these conditions (Fig. 8). For ρw ≥ 0.45 g cm−3, the difference between the revised and original B–L model is generally within the experimental uncertainty. Figure 10 shows that differences between the original and revised B–L models remain within less than about 0.8 pK unit between 0 to 800 °C at 30 MPa, whereas between the M–F and revised B–L models they reach about 4.7 pK unit (Fig. 10); the magnitude of those differences decrease with increasing pressure.

FIG. 9.

Water ionization constant at saturation pressure versus temperature between 0 and 370 °C. Top, comparison between formulations: Blue plain line, pKw(revised B–L model); large dotted red line, pKw(B–L model); small dotted black line, pKw(M–F model). Bottom, deviation within ±0.1 pK unit between formulations: Plain black line, pKw(revised B–L model) − pKw(B–L model); large dotted black line, pKw(revised B–L model) − pKw(M–F model).

FIG. 9.

Water ionization constant at saturation pressure versus temperature between 0 and 370 °C. Top, comparison between formulations: Blue plain line, pKw(revised B–L model); large dotted red line, pKw(B–L model); small dotted black line, pKw(M–F model). Bottom, deviation within ±0.1 pK unit between formulations: Plain black line, pKw(revised B–L model) − pKw(B–L model); large dotted black line, pKw(revised B–L model) − pKw(M–F model).

Close modal
FIG. 10.

Water ionization constant versus temperature between 0 and 800 °C. Plain line, 30 MPa; small dotted line, 100 MPa; large dotted line, 200 MPa. Top, comparison between formulations: Blue lines, pKw(revised B–L model); red lines, pKw(B–L model); black lines, pKw(M–F model). Bottom, deviation in pK unit between formulations: Red lines, pKw(revised B–L model) − pKw(B–L model); black lines, pKw(revised B–L model) − pKw(M–F model).

FIG. 10.

Water ionization constant versus temperature between 0 and 800 °C. Plain line, 30 MPa; small dotted line, 100 MPa; large dotted line, 200 MPa. Top, comparison between formulations: Blue lines, pKw(revised B–L model); red lines, pKw(B–L model); black lines, pKw(M–F model). Bottom, deviation in pK unit between formulations: Red lines, pKw(revised B–L model) − pKw(B–L model); black lines, pKw(revised B–L model) − pKw(M–F model).

Close modal

The thermodynamic equilibrium constant log10K(T, p) is directly related to standard molar enthalpy (ΔrH°), heat capacity (ΔrCp°), and volume (ΔrV°) of reaction as briefly discussed in Sec. 3.1. To test the performance of the new model against the two previous IAPWS releases, comparisons were made with independent sources of high-temperature heat capacity and volume data.76–81 The techniques used in these studies have been reviewed by Tremaine and Arcis63 and therefore will not be discussed here. For M–F, Eqs. (6) and (7) were used together with the water coefficient of thermal expansion (αw), its partial derivative (∂αw/∂T)p, and the water compressibility (βw) based on IAPWS 199545 to calculate the standard partial molar heat capacities and volumes, ΔrCp and ΔrV°, associated with the water ionization equilibrium. For the B–L type equations, the log10Kw expression was differentiated numerically with respect to temperature and pressure using δT = 10−4 K and δp = 10−8 MPa. Results are plotted in Figs. 11 and 12. Recently Plyasunov and Bugaev82 have critically reviewed the enthalpy, heat capacity, and volume data for the ionization of water and discussed the associated experimental uncertainties. These authors considered a larger dataset compared to what is plotted in Figs. 11 and 12, but their results do not change the general conclusions of the present work. For the heat capacity, all models were in reasonable agreement with the data to within the combined experimental uncertainties below 200 °C (Fig. 11). Above this temperature, differences start to show in which the B–L type equations are consistent with the studies from the University of Delaware78 and Murdoch University79,81 while the M–F model is in better agreement with the results from San Diego State University.80 The reason for the discrepancies between the datasets is unclear. Djamali suggested the differences observed between his results80 and those of Sharygin and Wood78 may be due to extrapolation errors, but the NaOH79 and KOH81 measurements from Hefter and co-workers suggest otherwise, confirming the Sharygin and Wood results. Similar conclusions can be drawn from the volume data comparisons, with reasonable agreement between all models below 100 °C and more scatter above this temperature (Fig. 12), where the new model calculates a value at the highest temperature for which data are available that is within the reported experimental uncertainty (±20 cm3 mol−1) at this temperature. Below 100 °C, the ability of the three models to reproduce the data appears consistent with the experimental scatter for both heat capacity (±10 J K−1 mol−1) and volume data (±2 cm3 mol−1). In general, the new model agrees better than the previous IAPWS releases with the high-temperature experimental data.

FIG. 11.

Deviation between experimental standard partial molar heat capacity of reaction and calculated values (in J K−1 mol−1) from the M–F (black symbols), B–L (red symbols) and revised B–L (blue symbols) pKw model. ♦, Simonson et al.;76 ◼, Patterson et al.;77 ▴, Sharygin and Wood;78 ×, Shrödel et al.;79 ●, Djamali;80 ▾, Hnedkovsky et al.81 Top, full experimental range (the M–F calculations for the highest temperature from Refs. 79 and 81 are off the top of the scale); bottom, zoom between 0 and 125 °C.

FIG. 11.

Deviation between experimental standard partial molar heat capacity of reaction and calculated values (in J K−1 mol−1) from the M–F (black symbols), B–L (red symbols) and revised B–L (blue symbols) pKw model. ♦, Simonson et al.;76 ◼, Patterson et al.;77 ▴, Sharygin and Wood;78 ×, Shrödel et al.;79 ●, Djamali;80 ▾, Hnedkovsky et al.81 Top, full experimental range (the M–F calculations for the highest temperature from Refs. 79 and 81 are off the top of the scale); bottom, zoom between 0 and 125 °C.

Close modal
FIG. 12.

Deviation between experimental standard partial molar volume of reaction and calculated values (in cm3 mol−1) from the M–F (black symbols), B–L (red symbols) and revised B–L (blue symbols) revised pKw model. ◼, Patterson et al.;77 ●, Sharygin and Wood;78 ▾, Hnedkovsky et al.81 Top, full experimental range (the M–F calculation for the highest temperature from Ref. 81 is off the top of the scale); bottom, zoom between 0 and 125 °C.

FIG. 12.

Deviation between experimental standard partial molar volume of reaction and calculated values (in cm3 mol−1) from the M–F (black symbols), B–L (red symbols) and revised B–L (blue symbols) revised pKw model. ◼, Patterson et al.;77 ●, Sharygin and Wood;78 ▾, Hnedkovsky et al.81 Top, full experimental range (the M–F calculation for the highest temperature from Ref. 81 is off the top of the scale); bottom, zoom between 0 and 125 °C.

Close modal

Recent near-critical and supercritical data10 derived from experimental results performed using flow AC conductivity techniques, based on Wood’s design, at the University of Guelph, the University of Delaware, and Oak Ridge National Laboratory have been reassessed using more accurate models to calculate the limiting conductivity of fully ionized water at high temperature.13 The corrected pKw data together with previously reported results at high temperatures and pressures were critically evaluated to yield a selected dataset which, in turn, was used to regress revised parameters for the semi-empirical formulation proposed by Bandura and Lvov7 that forms the basis of the 2006 IAPWS formulation.8 The revised set of parameters significantly improves the accuracy of the model at conditions approaching the critical point of water. The revised model is accurate to within the estimated standard uncertainty limits over the range 0–1000 °C, p = 0–1000 MPa. Comparisons with independent high-temperature standard partial molar heat capacities and volumes, ΔrCp and ΔrV°, for the ionization of water provided an independent confirmation the accuracy of the revised model at high temperatures.

The work was funded by the Electric Power Research Institute (EPRI, Agreement No. 10016176) and the National Nuclear Laboratory’s Science and Technology program (Reactor Chemistry and Corrosion Core Science theme). Hugues Arcis and Peter Tremaine express deep gratitude to Professor R. H. Wood for donating his AC conductance cell to the Hydrothermal Chemistry Laboratory at the University of Guelph and for many fruitful discussions, and to Professor Greg Zimmerman for providing them with the benefit of his extensive operating experience with the instrument during his one-year appointment as a Fulbright Chair (2009–2010) and for his collaboration in several of the papers cited here. Hugues Arcis thanks Natasha Gotham (UK Atomic Energy Authority) for useful discussion on data fitting methods during the early stages of the project.

The authors have no conflicts to disclose.

Dr. Arcis was the principal investigator in this study. He proposed the project and carried out the detailed data analysis, regressions and interpretation of the results. Dr. Lee contributed to the development of the Mathematica spreadsheets used in this work. Professor Tremaine contributed to the protocols for selecting and weighing of data, during early stages of the project. The manuscript was written by Dr. Arcis with contributions from Dr. Bachet, Mr. Duncanson, Dr. Eaker, Dr. Jarvis, Mr. Johnson, Dr. Lee, Mr. Lord, Dr. Marks, Professor Tremaine, and was independently reviewed by Dr. Dickinson.

Table 4 presents experimental values of pKw used in this work along with calculated values at the same conditions.

TABLE 4.

Experimental and correlated values for the ionization constant of water of the selected dataset

Source t (°C) ρw (g cm−3) pKw(exp.) u[pKw(exp.)]a pKw(fit) ΔpKwb Diff.c
Noyes et al. (1910)16   0.0  0.9998  15.050  0.100  14.947  0.104  −0.004 
Noyes et al. (1910)16   18.0  0.9986  14.336  0.100  14.235  0.101  −0.001 
Noyes et al. (1910)16   25.0  0.9970  14.084  0.100  13.994  0.089  0.011 
Noyes et al. (1910)16   100.0  0.9583  12.282  0.100  12.254  0.028  0.072 
Noyes et al. (1910)16   156.0  0.9113  11.571  0.100  11.590  −0.019  0.081 
Noyes et al. (1910)16   218.0  0.8428  11.188  0.100  11.241  −0.053  0.047 
Noyes et al. (1910)16   306.0  0.6995  11.464  0.100  11.317  0.148  −0.048 
Holzapfel and Franck (1966)17   500.0  1.3460  4.058  0.700  5.149  −1.091  −0.391 
Holzapfel and Franck (1966)17   500.0  1.5134  2.960  0.700  3.361  −0.401  0.299 
Holzapfel and Franck (1966)17   750.0  1.3638  3.069  0.700  4.208  −1.138  −0.438 
Holzapfel and Franck (1966)17   750.0  1.5067  2.056  0.700  2.696  −0.640  0.060 
Holzapfel and Franck (1966)17   1000.0  1.3837  2.382  0.700  3.551  −1.169  −0.469 
Holzapfel and Franck (1966)17   1000.0  1.5601  1.386  0.700  1.645  −0.259  0.441 
Quist (1970)18   300.0  1.0000  9.000  0.500  9.317  −0.317  0.183 
Quist (1970)18   300.0  0.9500  9.255  0.500  9.687  −0.431  0.069 
Quist (1970)18   400.0  0.9500  8.655  0.500  8.993  −0.337  0.163 
Quist (1970)18   400.0  0.9000  9.008  0.500  9.344  −0.336  0.164 
Quist (1970)18   400.0  0.8500  9.259  0.500  9.683  −0.425  0.075 
Quist (1970)18   400.0  0.8000  9.606  0.500  10.012  −0.406  0.094 
Quist (1970)18   400.0  0.7500  9.850  0.500  10.333  −0.483  0.017 
Quist (1970)18   400.0  0.7000  10.390  0.500  10.649  −0.258  0.242 
Quist (1970)18   400.0  0.6500  11.326  0.500  10.962  0.363  0.137 
Quist (1970)18   400.0  0.6000  11.656  0.500  11.279  0.378  0.122 
Quist (1970)18   500.0  0.8500  8.859  0.500  9.170  −0.311  0.189 
Quist (1970)18   500.0  0.8000  9.206  0.500  9.496  −0.289  0.211 
Quist (1970)18   500.0  0.7500  9.650  0.500  9.813  −0.163  0.337 
Quist (1970)18   500.0  0.5500  11.381  0.500  11.069  0.312  0.188 
Quist (1970)18   500.0  0.5000  11.898  0.500  11.405  0.493  0.007 
Quist (1970)18   500.0  0.4500  12.706  0.500  11.764  0.942  −0.442 
Quist (1970)18   600.0  0.7500  9.350  0.500  9.415  −0.065  0.435 
Quist (1970)18   600.0  0.6000  10.556  0.500  10.342  0.215  0.285 
Quist (1970)18   600.0  0.5500  11.081  0.500  10.660  0.421  0.079 
Quist (1970)18   600.0  0.5000  11.798  0.500  10.993  0.805  −0.305 
Quist (1970)18   600.0  0.4500  12.406  0.500  11.349  1.057  −0.557 
Quist (1970)18   700.0  0.7000  9.290  0.500  9.406  −0.116  0.384 
Quist (1970)18   700.0  0.6500  9.826  0.500  9.711  0.115  0.385 
Quist (1970)18   700.0  0.6000  10.056  0.500  10.019  0.037  0.463 
Quist (1970)18   700.0  0.5500  10.781  0.500  10.334  0.446  0.054 
Quist (1970)18   700.0  0.5000  11.398  0.500  10.665  0.733  −0.233 
Quist (1970)18   700.0  0.4500  12.006  0.500  11.019  0.987  −0.487 
Quist (1970)18   800.0  0.6500  9.326  0.500  9.449  −0.123  0.377 
Quist (1970)18   800.0  0.6000  9.856  0.500  9.754  0.102  0.398 
Quist (1970)18   800.0  0.5500  10.481  0.500  10.067  0.414  0.086 
Quist (1970)18   800.0  0.5000  11.098  0.500  10.395  0.703  −0.203 
Bignold et al. (1971)15   51.0  0.9876  13.241  0.100  13.239  0.002  0.098 
Bignold et al. (1971)15   60.9  0.9827  12.992  0.100  13.000  −0.008  0.092 
Bignold et al. (1971)15   70.5  0.9775  12.802  0.100  12.789  0.012  0.088 
Bignold et al. (1971)15   80.2  0.9717  12.642  0.100  12.596  0.046  0.054 
Bignold et al. (1971)15   89.9  0.9654  12.490  0.100  12.420  0.070  0.030 
Bignold et al. (1971)15   99.3  0.9589  12.234  0.100  12.265  −0.031  0.069 
Bignold et al. (1971)15   108.6  0.9520  12.074  0.100  12.125  −0.051  0.049 
Bignold et al. (1971)15   118.0  0.9447  11.986  0.100  11.997  −0.010  0.090 
Bignold et al. (1971)15   127.3  0.9371  11.870  0.100  11.881  −0.011  0.089 
Bignold et al. (1971)15   136.7  0.9291  11.767  0.100  11.775  −0.008  0.092 
Bignold et al. (1971)15   146.0  0.9207  11.721  0.100  11.681  0.040  0.060 
Bignold et al. (1971)15   155.4  0.9119  11.608  0.100  11.596  0.012  0.088 
Bignold et al. (1971)15   164.7  0.9028  11.548  0.100  11.520  0.028  0.072 
Bignold et al. (1971)15   174.2  0.8931  11.473  0.100  11.451  0.021  0.079 
Bignold et al. (1971)15   183.6  0.8831  11.393  0.100  11.392  0.001  0.099 
Bignold et al. (1971)15   193.0  0.8727  11.333  0.100  11.341  −0.008  0.092 
Bignold et al. (1971)15   202.5  0.8617  11.279  0.100  11.296  −0.017  0.083 
Bignold et al. (1971)15   212.1  0.8501  11.259  0.100  11.259  −0.001  0.099 
Bignold et al. (1971)15   221.7  0.8380  11.228  0.100  11.230  −0.002  0.098 
Bignold et al. (1971)15   231.4  0.8252  11.215  0.100  11.208  0.007  0.093 
Bignold et al. (1971)15   241.2  0.8117  11.202  0.100  11.194  0.008  0.092 
Bignold et al. (1971)15   251.0  0.7974  11.195  0.100  11.187  0.008  0.092 
Bignold et al. (1971)15   261.0  0.7821  11.203  0.100  11.189  0.014  0.086 
Bignold et al. (1971)15   271.0  0.7658  11.219  0.100  11.199  0.020  0.080 
Fisher and Barnes (1972)19   100.0  0.9583  12.193  0.200  12.254  −0.061  0.139 
Fisher and Barnes (1972)19   150.0  0.9170  11.145  0.200  11.644  −0.499  −0.299 
Fisher and Barnes (1972)19   200.0  0.8647  11.074  0.200  11.307  −0.234  −0.034 
Fisher and Barnes (1972)19   250.0  0.7989  11.035  0.200  11.188  −0.153  0.047 
Fisher and Barnes (1972)19   300.0  0.7121  11.035  0.200  11.286  −0.251  −0.051 
Fisher and Barnes (1972)19   350.0  0.5747  11.419  0.200  11.773  −0.355  −0.155 
Svistunov et al. (1977)20   332.1  0.0800  20.444  1.000  19.509  0.936  0.064 
Svistunov et al. (1977)20   343.8  0.1000  18.921  1.000  18.419  0.502  0.498 
Svistunov et al. (1977)20   357.8  0.1360  17.496  1.000  16.997  0.499  0.501 
Svistunov et al. (1977)20   371.3  0.2170  16.311  1.000  15.047  1.264  −0.264 
Svistunov et al. (1978)21   299.6  0.7130  11.406  0.400  11.284  0.122  0.278 
Svistunov et al. (1978)21   309.4  0.6920  11.480  0.400  11.336  0.144  0.256 
Svistunov et al. (1978)21   320.0  0.6670  11.548  0.400  11.409  0.139  0.261 
Svistunov et al. (1978)21   329.6  0.6420  11.615  0.400  11.494  0.121  0.279 
Svistunov et al. (1978)21   340.2  0.6100  11.871  0.400  11.617  0.253  0.147 
Svistunov et al. (1978)21   343.2  0.6000  11.856  0.400  11.659  0.197  0.203 
Svistunov et al. (1978)21   395.0  0.4000  13.004  0.400  12.734  0.270  0.130 
Svistunov et al. (1978)21   395.0  0.5070  12.210  0.400  11.924  0.286  0.114 
Svistunov et al. (1978)21   395.0  0.5500  11.881  0.400  11.634  0.247  0.153 
Svistunov et al. (1978)21   395.0  0.5800  11.727  0.400  11.438  0.289  0.111 
Svistunov et al. (1978)21   395.0  0.6020  11.559  0.400  11.297  0.262  0.138 
Svistunov et al. (1978)21   395.0  0.6200  11.385  0.400  11.182  0.202  0.198 
Harned and Robinson (1940)49   0.0  0.9998  14.944  0.001  14.947  −0.003  −0.002 
Harned and Robinson (1940)49   5.0  1.0000  14.734  0.001  14.734  0.000  0.001 
Harned and Robinson (1940)49   10.0  0.9997  14.535  0.001  14.534  0.001  0.000 
Harned and Robinson (1940)49   15.0  0.9991  14.346  0.001  14.344  0.002  −0.001 
Harned and Robinson (1940)49   20.0  0.9982  14.167  0.001  14.165  0.002  −0.001 
Harned and Robinson (1940)49   25.0  0.9970  13.997  0.001  13.994  0.002  −0.001 
Harned and Robinson (1940)49   30.0  0.9956  13.833  0.001  13.833  0.000  0.001 
Harned and Robinson (1940)49   35.0  0.9940  13.680  0.001  13.680  0.000  0.001 
Harned and Robinson (1940)49   40.0  0.9922  13.535  0.001  13.534  0.000  0.001 
Harned and Robinson (1940)49   45.0  0.9902  13.396  0.001  13.396  0.000  0.001 
Harned and Robinson (1940)49   50.0  0.9880  13.262  0.001  13.265  −0.003  −0.002 
Harned and Robinson (1940)49   55.0  0.9857  13.137  0.001  13.140  −0.003  −0.002 
Harned and Robinson (1940)49   60.0  0.9832  13.017  0.001  13.021  −0.004  −0.003 
Perkovets and Kryukov (1969)50   25.0  0.9970  13.990  0.020  13.994  −0.004  0.016 
Perkovets and Kryukov (1969)50   60.0  0.9832  13.000  0.020  13.021  −0.021  −0.001 
Perkovets and Kryukov (1969)50   90.0  0.9653  12.400  0.020  12.418  −0.018  0.002 
Perkovets and Kryukov (1969)50   100.0  0.9583  12.290  0.020  12.254  0.036  −0.016 
Perkovets and Kryukov (1969)50   125.0  0.9390  11.920  0.020  11.909  0.011  0.009 
Perkovets and Kryukov (1969)50   150.0  0.9170  11.660  0.020  11.644  0.016  0.004 
Linov and Kryukov (1972)52   18.0  1.0396  13.864  0.030  13.908  −0.044  −0.014 
Linov and Kryukov (1972)52   18.0  1.0737  13.547  0.030  13.628  −0.080  −0.050 
Linov and Kryukov (1972)52   18.0  1.1027  13.265  0.030  13.382  −0.117  −0.087 
Linov and Kryukov (1972)52   18.0  1.1282  13.034  0.030  13.162  −0.128  −0.098 
Linov and Kryukov (1972)52   18.0  1.1509  12.840  0.030  12.961  −0.121  −0.091 
Linov and Kryukov (1972)52   18.0  1.1714  12.664  0.030  12.776  −0.112  −0.082 
Linov and Kryukov (1972)52   18.0  1.1903  12.508  0.030  12.604  −0.096  −0.066 
Linov and Kryukov (1972)52   18.0  1.2077  12.372  0.030  12.442  −0.070  −0.040 
Linov and Kryukov (1972)52   25.0  1.0372  13.640  0.030  13.675  −0.036  −0.006 
Linov and Kryukov (1972)52   25.0  1.0707  13.359  0.030  13.400  −0.041  −0.011 
Linov and Kryukov (1972)52   25.0  1.0995  13.120  0.030  13.157  −0.038  −0.008 
Linov and Kryukov (1972)52   25.0  1.1247  12.901  0.030  12.940  −0.039  −0.009 
Linov and Kryukov (1972)52   25.0  1.1473  12.710  0.030  12.741  −0.031  −0.001 
Linov and Kryukov (1972)52   25.0  1.1678  12.540  0.030  12.557  −0.017  0.013 
Linov and Kryukov (1972)52   25.0  1.1867  12.390  0.030  12.385  0.005  0.025 
Linov and Kryukov (1972)52   25.0  1.2041  12.270  0.030  12.224  0.046  −0.016 
Linov and Kryukov (1972)52   50.0  1.0267  12.986  0.030  12.960  0.027  0.003 
Linov and Kryukov (1972)52   50.0  1.0592  12.741  0.030  12.696  0.045  −0.015 
Linov and Kryukov (1972)52   50.0  1.0873  12.516  0.030  12.462  0.054  −0.024 
Linov and Kryukov (1972)52   50.0  1.1122  12.308  0.030  12.251  0.057  −0.027 
Linov and Kryukov (1972)52   50.0  1.1346  12.124  0.030  12.056  0.068  −0.038 
Linov and Kryukov (1972)52   50.0  1.1550  11.962  0.030  11.876  0.086  −0.056 
Linov and Kryukov (1972)52   50.0  1.1738  11.815  0.030  11.707  0.108  −0.078 
Linov and Kryukov (1972)52   50.0  1.1912  11.688  0.030  11.548  0.140  −0.110 
Linov and Kryukov (1972)52   75.0  1.0139  12.381  0.030  12.394  −0.013  0.017 
Linov and Kryukov (1972)52   75.0  1.0464  12.123  0.030  12.134  −0.010  0.020 
Linov and Kryukov (1972)52   75.0  1.0745  11.888  0.030  11.903  −0.016  0.014 
Linov and Kryukov (1972)52   75.0  1.0994  11.675  0.030  11.695  −0.020  0.010 
Linov and Kryukov (1972)52   75.0  1.1218  11.485  0.030  11.503  −0.018  0.012 
Linov and Kryukov (1972)52   75.0  1.1422  11.319  0.030  11.325  −0.006  0.024 
Linov and Kryukov (1972)52   75.0  1.1611  11.172  0.030  11.158  0.015  0.015 
Linov and Kryukov (1972)52   75.0  1.1786  11.046  0.030  11.000  0.046  −0.016 
Whitfield (1972)51   5.0  1.0095  14.660  0.015  14.659  0.001  0.014 
Whitfield (1972)51   5.0  1.0187  14.588  0.015  14.585  0.003  0.012 
Whitfield (1972)51   5.0  1.0276  14.521  0.015  14.515  0.006  0.009 
Whitfield (1972)51   5.0  1.0360  14.454  0.015  14.447  0.008  0.007 
Whitfield (1972)51   5.0  1.0441  14.390  0.015  14.381  0.009  0.006 
Whitfield (1972)51   5.0  1.0519  14.327  0.015  14.317  0.010  0.005 
Whitfield (1972)51   5.0  1.0593  14.265  0.015  14.256  0.009  0.006 
Whitfield (1972)51   5.0  1.0665  14.206  0.015  14.197  0.009  0.006 
Whitfield (1972)51   5.0  1.0734  14.146  0.015  14.139  0.007  0.008 
Whitfield (1972)51   5.0  1.0801  14.089  0.015  14.083  0.006  0.009 
Whitfield (1972)51   15.0  1.0082  14.275  0.015  14.272  0.002  0.013 
Whitfield (1972)51   15.0  1.0170  14.205  0.015  14.203  0.002  0.013 
Whitfield (1972)51   15.0  1.0254  14.137  0.015  14.135  0.002  0.013 
Whitfield (1972)51   15.0  1.0335  14.072  0.015  14.070  0.001  0.014 
Whitfield (1972)51   15.0  1.0413  14.010  0.015  14.007  0.003  0.012 
Whitfield (1972)51   15.0  1.0487  13.949  0.015  13.946  0.003  0.012 
Whitfield (1972)51   15.0  1.0560  13.890  0.015  13.887  0.003  0.012 
Whitfield (1972)51   15.0  1.0629  13.834  0.015  13.830  0.005  0.010 
Whitfield (197251   15.0  1.0696  13.782  0.015  13.774  0.008  0.007 
Whitfield (1972)51   15.0  1.0761  13.733  0.015  13.720  0.013  0.002 
Whitfield (1972)51   25.0  1.0058  13.927  0.015  13.925  0.002  0.013 
Whitfield (1972)51   25.0  1.0143  13.859  0.015  13.858  0.001  0.014 
Whitfield (1972)51   25.0  1.0225  13.793  0.015  13.793  0.000  0.015 
Whitfield (1972)51   25.0  1.0303  13.730  0.015  13.730  0.000  0.015 
Whitfield (1972)51   25.0  1.0379  13.668  0.015  13.669  −0.001  0.014 
Whitfield (1972)51   25.0  1.0452  13.611  0.015  13.610  0.000  0.015 
Whitfield (1972)51   25.0  1.0522  13.555  0.015  13.553  0.002  0.013 
Whitfield (1972)51   25.0  1.0590  13.499  0.015  13.497  0.002  0.013 
Whitfield (1972)51   25.0  1.0655  13.445  0.015  13.443  0.002  0.013 
Whitfield (1972)51   25.0  1.0719  13.392  0.015  13.390  0.002  0.013 
Whitfield (1972)51   25.0  1.0058  13.928  0.015  13.925  0.002  0.013 
Whitfield (1972)51   25.0  1.0143  13.859  0.015  13.858  0.001  0.014 
Whitfield (1972)51   25.0  1.0225  13.795  0.015  13.793  0.002  0.013 
Whitfield (1972)51   25.0  1.0303  13.731  0.015  13.730  0.000  0.015 
Whitfield (1972)51   25.0  1.0379  13.670  0.015  13.669  0.000  0.015 
Whitfield (1972)51   25.0  1.0452  13.607  0.015  13.610  −0.003  0.012 
Whitfield (1972)51   25.0  1.0522  13.553  0.015  13.553  0.000  0.015 
Whitfield (197251   25.0  1.0590  13.499  0.015  13.497  0.002  0.013 
Whitfield (1972)51   25.0  1.0655  13.450  0.015  13.443  0.007  0.008 
Whitfield (1972)51   25.0  1.0719  13.404  0.015  13.390  0.014  0.001 
Whitfield (1972)51   35.0  1.0026  13.613  0.015  13.612  0.000  0.015 
Whitfield (1972)51   35.0  1.0109  13.546  0.015  13.547  −0.001  0.014 
Whitfield (1972)51   35.0  1.0189  13.482  0.015  13.484  −0.001  0.014 
Whitfield (1972)51   35.0  1.0266  13.422  0.015  13.422  −0.001  0.014 
Whitfield (1972)51   35.0  1.0340  13.363  0.015  13.363  0.000  0.015 
Whitfield (1972)51   35.0  1.0412  13.306  0.015  13.305  0.001  0.014 
Whitfield (1972)51   35.0  1.0481  13.250  0.015  13.249  0.001  0.014 
Whitfield (1972)51   35.0  1.0547  13.198  0.015  13.194  0.004  0.011 
Whitfield (1972)51   35.0  1.0612  13.148  0.015  13.141  0.007  0.008 
Whitfield (1972)51   35.0  1.0675  13.101  0.015  13.089  0.012  0.003 
MacDonald et al. (1973)53   25.0  0.9970  13.990  0.030  13.994  −0.004  0.026 
MacDonald et al. (1973)53   50.0  0.9880  13.240  0.030  13.265  −0.025  0.005 
MacDonald et al. (1973)53   75.0  0.9748  12.680  0.030  12.697  −0.017  0.013 
MacDonald et al. (1973)53   100.0  0.9583  12.240  0.030  12.254  −0.014  0.016 
MacDonald et al. (1973)53   125.0  0.9390  11.880  0.030  11.909  −0.029  0.001 
MacDonald et al. (1973)53   150.0  0.9170  11.640  0.030  11.644  −0.004  0.026 
MacDonald et al. (1973)53   175.0  0.8923  11.430  0.030  11.446  −0.016  0.014 
MacDonald et al. (1973)53   200.0  0.8647  11.260  0.030  11.307  −0.047  −0.017 
Sweeton et al. (1974)1   0.0  0.9998  14.941  0.009  14.947  −0.006  0.003 
Sweeton et al. (1974)1   25.0  0.9970  13.993  0.009  13.994  −0.001  0.008 
Sweeton et al. (1974)1   50.0  0.9880  13.272  0.006  13.265  0.007  −0.001 
Sweeton et al. (1974)1   75.0  0.9748  12.709  0.006  12.697  0.012  −0.006 
Sweeton et al. (1974)1   100.0  0.9583  12.264  0.009  12.254  0.010  −0.001 
Sweeton et al. (1974)1   125.0  0.9390  11.914  0.009  11.909  0.005  0.004 
Sweeton et al. (1974)1   150.0  0.9170  11.642  0.012  11.644  −0.002  0.010 
Sweeton et al. (1974)1   175.0  0.8923  11.441  0.012  11.446  −0.005  0.007 
Sweeton et al. (1974)1   200.0  0.8647  11.302  0.012  11.307  −0.005  0.007 
Sweeton et al. (1974)1   225.0  0.8337  11.222  0.012  11.222  0.000  0.012 
Sweeton et al. (1974)1   250.0  0.7989  11.196  0.015  11.188  0.008  0.007 
Sweeton et al. (1974)1   275.0  0.7590  11.224  0.027  11.206  0.018  0.009 
Sweeton et al. (1974)1   300.0  0.7121  11.301  0.045  11.286  0.015  0.030 
Busey and Mesmer (1978)54   0.0  0.9998  14.941  0.009  14.947  −0.006  0.003 
Busey and Mesmer (1978)54   25.0  0.9970  13.993  0.009  13.994  −0.001  0.008 
Busey and Mesmer (1978)54   50.0  0.9880  13.272  0.006  13.265  0.007  −0.001 
Busey and Mesmer (1978)54   75.0  0.9748  12.709  0.006  12.697  0.012  −0.006 
Busey and Mesmer (1978)54   100.0  0.9583  12.264  0.009  12.254  0.010  −0.001 
Busey and Mesmer (1978)54   125.0  0.9390  11.914  0.009  11.909  0.005  0.004 
Busey and Mesmer (1978)54   150.0  0.9170  11.642  0.012  11.644  −0.002  0.010 
Busey and Mesmer (1978)54   175.0  0.8923  11.441  0.012  11.446  −0.005  0.007 
Busey and Mesmer (1978)54   200.0  0.8647  11.302  0.012  11.307  −0.005  0.007 
Busey and Mesmer (1978)54   225.0  0.8337  11.222  0.012  11.222  0.000  0.012 
Busey and Mesmer (1978)54   250.0  0.7989  11.196  0.015  11.188  0.008  0.007 
Busey and Mesmer (1978)54   275.0  0.7590  11.224  0.027  11.206  0.018  0.009 
Busey and Mesmer (1978)54   300.0  0.7121  11.301  0.045  11.286  0.015  0.030 
Kryukov et al. (1980)55   25.0  1.0379  13.656  0.040  13.669  −0.013  0.027 
Kryukov et al. (1980)55   25.0  1.0719  13.372  0.040  13.390  −0.018  0.022 
Kryukov et al. (1980)55   25.0  1.1010  13.132  0.040  13.144  −0.012  0.028 
Kryukov et al. (1980)55   25.0  1.1266  12.914  0.040  12.923  −0.009  0.031 
Kryukov et al. (1980)55   25.0  1.1494  12.716  0.040  12.722  −0.006  0.034 
Kryukov et al. (1980)55   25.0  1.1701  12.530  0.040  12.536  −0.006  0.034 
Kryukov et al. (1980)55   50.0  1.0274  12.963  0.040  12.954  0.009  0.031 
Kryukov et al. (1980)55   50.0  1.0604  12.702  0.040  12.687  0.015  0.025 
Kryukov et al. (1980)55   50.0  1.0889  12.467  0.040  12.449  0.018  0.022 
Kryukov et al. (1980)55   50.0  1.1140  12.255  0.040  12.235  0.020  0.020 
Kryukov et al. (1980)55   50.0  1.1367  12.060  0.040  12.038  0.022  0.018 
Kryukov et al. (1980)55   50.0  1.1573  11.880  0.040  11.855  0.025  0.015 
Kryukov et al. (1980)55   75.0  1.0146  12.393  0.040  12.388  0.005  0.035 
Kryukov et al. (1980)55   75.0  1.0476  12.134  0.040  12.124  0.010  0.030 
Kryukov et al. (1980)55   75.0  1.0760  11.901  0.040  11.890  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1012  11.690  0.040  11.679  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1239  11.496  0.040  11.485  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1445  11.316  0.040  11.304  0.012  0.028 
Kryukov et al. (1980)55   100.0  0.9998  11.938  0.040  11.937  0.001  0.039 
Kryukov et al. (1980)55   100.0  1.0335  11.665  0.040  11.671  −0.006  0.034 
Kryukov et al. (1980)55   100.0  1.0624  11.433  0.040  11.437  −0.004  0.036 
Kryukov et al. (1980)55   100.0  1.0879  11.223  0.040  11.226  −0.003  0.037 
Kryukov et al. (1980)55   100.0  1.1108  11.040  0.040  11.033  0.007  0.033 
Kryukov et al. (1980)55   100.0  1.1317  10.865  0.040  10.854  0.011  0.029 
Kryukov et al. (1980)55   150.0  0.9170  11.630  0.040  11.644  −0.014  0.026 
Kryukov et al. (1980)55   150.0  0.9648  11.250  0.040  11.291  −0.041  −0.001 
Kryukov et al. (1980)55   150.0  1.0020  10.970  0.040  11.009  −0.039  0.001 
Kryukov et al. (1980)55   150.0  1.0329  10.720  0.040  10.767  −0.047  −0.007 
Kryukov et al. (1980)55   150.0  1.0598  10.560  0.040  10.551  0.009  0.031 
Kryukov et al. (1980)55   150.0  1.0837  10.350  0.040  10.355  −0.005  0.035 
Kryukov et al. (1980)55   150.0  1.1054  10.160  0.040  10.175  −0.015  0.025 
Palmer and Drummond (1988)56   25.0  0.9970  14.000  0.010  13.994  0.006  0.004 
Palmer and Drummond (1988)56   50.0  0.9880  13.280  0.010  13.265  0.015  −0.005 
Palmer and Drummond (1988)56   100.0  0.9583  12.270  0.010  12.254  0.016  −0.006 
Palmer and Drummond (1988)56   150.0  0.9170  11.640  0.010  11.644  −0.004  0.006 
Palmer and Drummond (1988)56   200.0  0.8647  11.290  0.010  11.307  −0.017  −0.007 
Palmer and Drummond (1988)56   250.0  0.7989  11.180  0.010  11.188  −0.008  0.002 
Ackermann (1958)61   0.0  0.9998  14.955  0.005  14.947  0.008  −0.003 
Ackermann (1958)61   10.0  0.9997  14.534  0.005  14.534  0.000  0.005 
Ackermann (1958)61   20.0  0.9982  14.161  0.005  14.165  −0.004  0.001 
Ackermann (1958)61   25.0  0.9970  13.999  0.005  13.994  0.005  0.000 
Ackermann (1958)61   30.0  0.9956  13.833  0.005  13.833  0.000  0.005 
Ackermann (1958)61   40.0  0.9922  13.533  0.005  13.534  −0.001  0.004 
Ackermann (1958)61   50.0  0.9880  13.263  0.005  13.265  −0.002  0.003 
Ackermann (1958)61   60.0  0.9832  13.015  0.005  13.021  −0.006  −0.001 
Ackermann (1958)61   70.0  0.9778  12.800  0.005  12.800  0.000  0.005 
Ackermann (1958)61   80.0  0.9718  12.598  0.005  12.600  −0.002  0.003 
Ackermann (1958)61   90.0  0.9653  12.422  0.005  12.418  0.004  0.001 
Ackermann (1958)61   100.0  0.9583  12.259  0.005  12.254  0.005  0.000 
Ackermann (1958)61   110.0  0.9509  12.126  0.005  12.105  0.021  −0.016 
Ackermann (1958)61   120.0  0.9431  12.002  0.005  11.971  0.031  −0.026 
Ackermann (1958)61   130.0  0.9348  11.907  0.005  11.850  0.057  −0.052 
Chen et al. (1994)62   0.0  0.9998  14.946  0.005  14.947  −0.001  0.004 
Chen et al. (1994)62   25.0  0.9970  13.999  0.005  13.994  0.005  0.000 
Chen et al. (1994)62   50.0  0.9880  13.276  0.005  13.265  0.011  −0.006 
Chen et al. (1994)62   75.0  0.9748  12.710  0.005  12.697  0.013  −0.008 
Chen et al. (1994)62   100.0  0.9583  12.264  0.005  12.254  0.010  −0.005 
Chen et al. (1994)62   125.0  0.9390  11.914  0.005  11.909  0.005  0.000 
Chen et al. (1994)62   150.0  0.9170  11.644  0.005  11.644  0.000  0.005 
Chen et al. (1994)62   175.0  0.8923  11.442  0.005  11.446  −0.004  0.001 
Chen et al. (1994)62   200.0  0.8647  11.303  0.005  11.307  −0.004  0.001 
Chen et al. (1994)62   225.0  0.8337  11.223  0.005  11.222  0.001  0.004 
Chen et al. (1994)62   250.0  0.7989  11.203  0.010  11.188  0.015  −0.005 
Chen et al. (1994)62   275.0  0.7590  11.251  0.020  11.206  0.045  −0.025 
Chen et al. (1994)62   300.0  0.7121  11.382  0.030  11.286  0.096  −0.066 
Chen et al. (1994)62   325.0  0.6543  11.638  0.050  11.451  0.187  −0.137 
Chen et al. (1994)62   350.0  0.5747  12.144  0.100  11.773  0.371  −0.271 
Hamann (1963)58   25.0  0.9970  13.997  0.030  13.994  0.002  0.028 
Hamann (1963)58   25.0  1.0081  13.907  0.030  13.907  −0.001  0.029 
Hamann (1963)58   25.0  1.0187  13.823  0.030  13.823  0.000  0.030 
Hamann (1963)58   25.0  1.0288  13.746  0.030  13.743  0.003  0.027 
Hamann (1963)58   25.0  1.0384  13.666  0.030  13.665  0.001  0.029 
Hamann (1963)58   25.0  1.0475  13.585  0.030  13.591  −0.006  0.024 
Hamann (1963)58   25.0  1.0563  13.524  0.030  13.519  0.005  0.025 
Hamann (1963)58   25.0  1.0647  13.449  0.030  13.450  −0.001  0.029 
Hamann (1963)58   25.0  1.0727  13.393  0.030  13.383  0.011  0.019 
Hamann and Linton (1969)59   20.0  0.9982  14.167  3.000  14.165  0.003  2.997 
Hamann and Linton (1969)59   45.0  1.1878  12.060  3.000  11.727  0.334  2.666 
Hamann and Linton (1969)59   240.0  1.4703  7.229  3.000  5.477  1.753  1.247 
Hamann and Linton (1969)59   304.0  1.5095  6.456  3.000  4.478  1.978  1.022 
Hamann and Linton (1969)59   373.0  1.5476  5.699  3.000  3.576  2.123  0.877 
Hamann and Linton (1969)59   444.0  1.5774  4.337  3.000  2.851  1.487  1.513 
Hamann and Linton (1969)59   527.0  1.6025  3.051  3.000  2.205  0.846  2.154 
Hamann and Linton (1969)59   670.0  1.6493  1.854  3.000  1.190  0.663  2.337 
Hamann and Linton (1969)59   804.0  1.6868  1.051  3.000  0.418  0.632  2.368 
Arcis et al. (2017)36   175.1  0.9038  11.317  0.040  11.363  −0.046  −0.006 
Arcis et al. (2017)36   250.2  0.8155  10.888  0.040  11.075  −0.187  −0.147 
Arcis et al. (2017)36   275.2  0.7778  11.056  0.040  11.082  −0.025  0.015 
Arcis et al. (2017)36   297.9  0.7377  11.145  0.040  11.140  0.005  0.035 
Arcis et al. (2017)36   274.0  0.7814  11.066  0.040  11.070  −0.004  0.036 
Arcis et al. (2017)36   299.6  0.7367  11.166  0.040  11.132  0.034  0.006 
Arcis et al. (2017)36   324.7  0.6823  11.407  0.100  11.276  0.131  −0.031 
Arcis et al. (2017)36   348.2  0.6116  11.858  0.100  11.549  0.309  −0.209 
Arcis et al. (2016)35   175.1  0.9039  11.346  0.040  11.363  −0.016  0.024 
Arcis et al. (2016)35   250.0  0.8158  11.027  0.040  11.075  −0.048  −0.008 
Arcis et al. (2016)35   275.0  0.7782  11.063  0.040  11.081  −0.018  0.022 
Arcis et al. (2016)35   297.9  0.7380  11.135  0.040  11.139  −0.004  0.036 
Arcis et al. (2016)35   274.0  0.7813  11.066  0.040  11.071  −0.005  0.035 
Arcis et al. (2016)35   299.6  0.7369  11.193  0.040  11.132  0.062  −0.022 
Arcis et al. (2016)35   324.8  0.6822  11.408  0.100  11.276  0.132  −0.032 
Arcis et al. (2016)35   348.9  0.6086  11.826  0.100  11.563  0.263  −0.163 
Arcis et al. (2016)35   175.1  0.9039  11.294  0.040  11.363  −0.069  −0.029 
Arcis et al. (2016)35   250.1  0.8156  11.059  0.040  11.076  −0.017  0.023 
Arcis et al. (2016)35   275.2  0.7779  11.057  0.040  11.082  −0.025  0.015 
Arcis et al. (2016)35   297.9  0.7380  11.142  0.040  11.139  0.003  0.037 
Arcis et al. (2016)35   275.0  0.7798  10.998  0.040  11.071  −0.073  −0.033 
Arcis et al. (2016)35   299.7  0.7366  11.146  0.040  11.133  0.014  0.026 
Arcis et al. (2016)35   324.9  0.6821  11.387  0.100  11.276  0.111  −0.011 
Arcis et al. (2016)35   348.0  0.6120  11.882  0.100  11.548  0.335  −0.235 
Ferguson et al. (2017)37   153.0  0.9172  11.527  0.040  11.595  −0.068  −0.028 
Ferguson et al. (2017)37   175.4  0.9040  11.295  0.040  11.357  −0.062  −0.022 
Ferguson et al. (2017)37   224.0  0.8503  11.067  0.040  11.121  −0.054  −0.014 
Ferguson et al. (2017)37   250.0  0.8165  11.022  0.040  11.071  −0.050  −0.010 
Ferguson et al. (2017)37   299.9  0.7354  11.218  0.040  11.139  0.080  −0.040 
Ferguson et al. (2017)37   325.8  0.6787  11.375  0.100  11.291  0.084  0.016 
Ferguson et al. (2017)37   175.0  0.9042  11.321  0.040  11.361  −0.040  0.000 
Ferguson et al. (2017)37   275.2  0.7785  11.094  0.040  11.078  0.016  0.024 
Ferguson et al. (2017)37   290.9  0.7517  11.137  0.040  11.111  0.027  0.013 
Ferguson et al. (2017)37   300.2  0.7344  11.175  0.040  11.142  0.032  0.008 
Ferguson et al. (2019)40   199.9  0.8727  11.216  0.040  11.253  −0.037  0.003 
Ferguson et al. (2019)40   253.8  0.8025  11.145  0.040  11.125  0.020  0.020 
Ferguson et al. (2019)40   250.0  0.8080  11.111  0.040  11.127  −0.017  0.023 
Ferguson et al. (2019)40   275.3  0.7675  11.121  0.040  11.148  −0.027  0.013 
Ferguson et al. (2019)40   298.4  0.7237  11.345  0.040  11.226  0.118  −0.078 
Ferguson et al. (2019)40   300.2  0.7192  11.360  0.040  11.240  0.120  −0.080 
Ferguson (2018)39   175.2  0.8992  11.362  0.040  11.394  −0.033  0.007 
Ferguson (2018)39   225.0  0.8423  11.085  0.040  11.164  −0.079  −0.039 
Ferguson (2018)39   275.0  0.7682  11.170  0.040  11.147  0.023  0.017 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.423  0.100  11.440  −0.016  0.084 
Gruszkiewicz and Wood (1997)24   343.1  0.6500  11.327  0.100  11.342  −0.015  0.085 
Gruszkiewicz and Wood (1997)24   347.3  0.5999  11.690  0.100  11.631  0.059  0.041 
Gruszkiewicz and Wood (1997)24   358.8  0.5999  11.620  0.100  11.549  0.071  0.029 
Gruszkiewicz and Wood (1997)24   361.8  0.5496  11.964  0.100  11.856  0.108  −0.008 
Gruszkiewicz and Wood (1997)24   371.0  0.4994  12.273  0.300  12.134  0.138  0.162 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.522  0.300  12.434  0.088  0.212 
Gruszkiewicz and Wood (1997)24   379.3  0.3973  13.045  0.300  12.860  0.185  0.115 
Gruszkiewicz and Wood (1997)24   379.5  0.3566  13.235  0.300  13.225  0.010  0.290 
Gruszkiewicz and Wood (1997)24   376.5  0.3086  13.580  0.300  13.741  −0.161  0.139 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.674  0.300  13.640  0.034  0.266 
Gruszkiewicz and Wood (1997)24   385.0  0.3207  13.745  0.300  13.551  0.194  0.106 
Gruszkiewicz and Wood (1997)24   379.4  0.2493  13.964  0.800  14.480  −0.515  0.285 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.407  0.800  14.438  −0.031  0.769 
Gruszkiewicz and Wood (1997)24   400.9  0.2498  13.956  0.800  14.331  −0.375  0.425 
Gruszkiewicz and Wood (1997)24   379.4  0.1999  14.449  0.800  15.303  −0.854  −0.054 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.451  0.100  11.440  0.011  0.089 
Gruszkiewicz and Wood (1997)24   343.1  0.6500  11.348  0.100  11.342  0.005  0.095 
Gruszkiewicz and Wood (1997)24   347.3  0.5999  11.706  0.100  11.631  0.076  0.024 
Gruszkiewicz and Wood (1997)24   358.8  0.5999  11.634  0.100  11.549  0.085  0.015 
Gruszkiewicz and Wood (1997)24   371.0  0.4994  12.373  0.300  12.134  0.239  0.061 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.628  0.300  12.434  0.194  0.106 
Gruszkiewicz and Wood (1997)24   379.3  0.3973  12.990  0.300  12.860  0.130  0.170 
Gruszkiewicz and Wood (1997)24   379.5  0.3566  13.241  0.300  13.225  0.016  0.284 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.839  0.300  13.640  0.199  0.101 
Gruszkiewicz and Wood (1997)24   385.0  0.3207  13.513  0.300  13.551  −0.038  0.262 
Gruszkiewicz and Wood (1997)24   379.4  0.2493  14.021  0.800  14.480  −0.458  0.342 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.377  0.800  14.438  −0.062  0.738 
Gruszkiewicz and Wood (1997)24   400.9  0.2498  14.122  0.800  14.331  −0.209  0.591 
Gruszkiewicz and Wood (1997)24   379.4  0.1999  14.685  0.800  15.303  −0.618  0.182 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.433  0.100  11.440  −0.006  0.094 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.723  0.300  12.434  0.289  0.011 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.707  0.300  13.640  0.067  0.233 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.291  0.800  14.438  −0.147  0.653 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.428  0.100  11.440  −0.011  0.089 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.575  0.300  12.434  0.140  0.160 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.777  0.300  13.640  0.137  0.163 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.407  0.800  14.438  −0.031  0.769 
Sharygin et al. (2002)30   378.1  0.5238  11.922  0.100  11.918  0.004  0.096 
Sharygin et al. (2002)30   378.1  0.5238  11.922  0.100  11.918  0.003  0.097 
Sharygin et al. (2002)30   378.1  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.1  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.1  0.5236  11.921  0.100  11.919  0.002  0.098 
Sharygin et al. (2002)30   378.1  0.5237  11.921  0.100  11.919  0.003  0.097 
Sharygin et al. (2002)30   378.2  0.5231  11.921  0.100  11.922  −0.002  0.098 
Sharygin et al. (2002)30   378.1  0.5236  11.921  0.100  11.919  0.002  0.098 
Sharygin et al. (2002)30   378.2  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.2  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.2  0.5238  11.922  0.100  11.917  0.004  0.096 
Sharygin et al. (2002)30   397.1  0.2968  13.268  0.800  13.742  −0.474  0.326 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   397.0  0.2982  13.271  0.800  13.726  −0.454  0.346 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   396.9  0.2999  13.276  0.800  13.707  −0.431  0.369 
Sharygin et al. (2002)30   396.9  0.2999  13.276  0.800  13.707  −0.431  0.369 
Sharygin et al. (2002)30   397.1  0.2974  13.111  0.800  13.735  −0.624  0.176 
Sharygin et al. (2002)30   397.1  0.2986  13.114  0.800  13.721  −0.607  0.193 
Sharygin et al. (2002)30   397.1  0.2986  13.114  0.800  13.721  −0.607  0.193 
Sharygin et al. (2002)30   397.1  0.2968  13.110  0.800  13.742  −0.632  0.168 
Sharygin et al. (2002)30   397.1  0.2992  13.115  0.800  13.714  −0.598  0.202 
Sharygin et al. (2002)30   397.2  0.2977  13.112  0.800  13.731  −0.620  0.180 
Sharygin et al. (2002)30   397.1  0.2956  13.107  0.800  13.756  −0.649  0.151 
Sharygin et al. (2002)30   397.1  0.2945  13.104  0.800  13.770  −0.666  0.134 
Sharygin et al. (2002)30   397.3  0.2932  13.100  0.800  13.783  −0.683  0.117 
Sharygin et al. (2002)30   397.2  0.2959  13.107  0.800  13.752  −0.645  0.155 
Sharygin et al. (2002)30   397.1  0.2956  13.107  0.800  13.756  −0.649  0.151 
Zimmerman and Wood (2002)31   195.8  0.8825  11.186  0.040  11.236  −0.050  −0.010 
Zimmerman and Wood (2002)31   195.8  0.8825  11.106  0.040  11.236  −0.129  −0.089 
Zimmerman and Wood (2002)31   195.8  0.8825  11.186  0.040  11.235  −0.050  −0.010 
Zimmerman and Wood (2002)31   195.8  0.8825  11.192  0.040  11.235  −0.044  −0.004 
Zimmerman and Wood (2002)31   275.0  0.7788  10.701  0.040  11.078  −0.377  −0.337 
Zimmerman and Wood (2002)31   275.0  0.7788  10.986  0.040  11.078  −0.092  −0.052 
Zimmerman and Wood (2002)31   275.0  0.7788  10.974  0.040  11.078  −0.104  −0.064 
Zimmerman and Wood (2002)31   195.9  0.8825  11.165  0.040  11.236  −0.070  −0.030 
Zimmerman and Wood (2002)31   275.0  0.7788  10.957  0.040  11.078  −0.122  −0.082 
Hnedkovsky et al. (2005)25   100.0  0.9641  11.962  0.040  12.210  −0.249  −0.209 
Hnedkovsky et al. (2005)25   200.0  0.8727  11.074  0.040  11.251  −0.177  −0.137 
Hnedkovsky et al. (2005)25   250.0  0.8083  11.025  0.040  11.125  −0.100  −0.060 
Hnedkovsky et al. (2005)25   300.1  0.7207  11.151  0.040  11.231  −0.080  −0.040 
Hnedkovsky et al. (2005)25   300.0  0.7478  10.949  0.040  11.058  −0.109  −0.069 
Hnedkovsky et al. (2005)25   350.0  0.6006  11.554  0.100  11.606  −0.052  0.048 
Hnedkovsky et al. (2005)25   350.0  0.6370  11.433  0.100  11.374  0.059  0.041 
Hnedkovsky et al. (2005)25   390.0  0.3785  12.671  0.300  12.953  −0.282  0.018 
Hnedkovsky et al. (2005)25   400.0  0.2299  13.206  0.800  14.641  −1.434  −0.634 
Sharygin et al. (2006)32   250.6  0.8153  10.945  0.040  11.072  −0.127  −0.087 
Sharygin et al. (2006)32   300.2  0.7344  11.044  0.040  11.142  −0.098  −0.058 
Sharygin et al. (2006)32   300.9  0.7431  10.993  0.040  11.081  −0.088  −0.048 
Sharygin et al. (2006)32   351.0  0.6261  11.453  0.100  11.436  0.017  0.083 
Sharygin et al. (2006)32   380.3  0.4698  12.070  0.300  12.283  −0.213  0.087 
Sharygin et al. (2006)32   400.2  0.3012  12.710  0.300  13.671  −0.960  −0.660 
Sharygin et al. (2006)32   250.8  0.8151  10.812  0.040  11.072  −0.260  −0.220 
Sharygin et al. (2006)32   296.9  0.7502  10.886  0.040  11.069  −0.183  −0.143 
Sharygin et al. (2006)32   299.6  0.7357  10.942  0.040  11.139  −0.197  −0.157 
Sharygin et al. (2006)32   303.1  0.7396  10.990  0.040  11.085  −0.094  −0.054 
Sharygin et al. (2006)32   351.0  0.6256  11.481  0.100  11.439  0.042  0.058 
Sharygin et al. (2006)32   380.8  0.4636  12.328  0.300  12.326  0.003  0.297 
Sharygin et al. (2006)32   399.5  0.3040  12.611  0.300  13.642  −1.031  −0.731 
Balashov et al. (2017)38   100.0  0.9641  12.208  0.040  12.210  −0.002  0.038 
Balashov et al. (2017)38   200.0  0.8727  11.236  0.040  11.251  −0.015  0.025 
Balashov et al. (2017)38   250.1  0.8084  11.128  0.040  11.124  0.004  0.036 
Balashov et al. (2017)38   300.0  0.7210  11.255  0.040  11.230  0.025  0.015 
Balashov et al. (2017)38   300.1  0.7477  11.075  0.040  11.058  0.017  0.023 
Balashov et al. (2017)38   350.0  0.6009  11.698  0.100  11.604  0.093  0.007 
Balashov et al. (2017)38   350.1  0.6370  11.443  0.100  11.374  0.069  0.031 
Balashov et al. (2017)38   389.9  0.3775  13.473  0.300  12.963  0.510  −0.210 
Balashov et al. (2017)38   400.1  0.2287  15.441  0.800  14.660  0.781  0.019 
Ho et al. (2001)28   200.0  0.8709  10.878  0.040  11.264  −0.386  −0.346 
Ho et al. (2001)28   300.0  0.7157  11.109  0.040  11.264  −0.155  −0.115 
Ho et al. (2001)28   300.0  0.7159  11.139  0.040  11.263  −0.123  −0.083 
Ho et al. (2001)28   350.0  0.6363  11.350  0.100  11.378  −0.029  0.071 
Ho et al. (2001)28   350.0  0.6302  11.375  0.100  11.418  −0.043  0.057 
Ho et al. (2001)28   370.0  0.5722  11.745  0.100  11.650  0.095  0.005 
Ho et al. (2001)28   370.0  0.5649  11.834  0.100  11.698  0.136  −0.036 
Ho et al. (2001)28   380.0  0.5439  11.904  0.100  11.770  0.133  −0.033 
Ho et al. (2001)28   380.0  0.5438  11.972  0.100  11.771  0.201  −0.101 
Ho et al. (2001)28   380.0  0.5194  12.006  0.100  11.935  0.070  0.030 
Ho et al. (2001)28   380.0  0.5062  11.895  0.100  12.026  −0.132  −0.032 
Ho et al. (2001)28   380.0  0.5067  12.264  0.100  12.022  0.242  −0.142 
Ho et al. (2001)28   390.0  0.4768  12.199  0.300  12.169  0.029  0.271 
Ho et al. (2001)28   390.0  0.4256  12.420  0.300  12.557  −0.136  0.164 
Ho et al. (2001)28   390.0  0.3810  12.270  0.300  12.931  −0.661  −0.361 
Ho et al. (2001)28   400.0  0.2987  12.524  0.800  13.700  −1.176  −0.376 
Ho et al. (2001)28   400.0  0.3003  12.779  0.300  13.682  −0.903  −0.603 
Ho et al. (2001)28   400.0  0.2993  12.460  0.800  13.694  −1.234  −0.434 
Ho et al. (2001)28   400.0  0.2993  12.633  0.800  13.694  −1.061  −0.261 
Ho et al. (2001)28   400.0  0.3369  12.206  0.300  13.285  −1.080  −0.780 
Ho et al. (2001)28   400.0  0.3354  12.502  0.300  13.300  −0.798  −0.498 
Ho et al. (2001)28   400.0  0.3364  12.568  0.300  13.290  −0.722  −0.422 
Ho et al. (2001)28   400.0  0.3369  12.424  0.300  13.285  −0.861  −0.561 
Ho et al. (2001)28   400.0  0.3866  12.858  0.300  12.818  0.039  0.261 
Ho et al. (2001)28   400.0  0.3866  12.753  0.300  12.818  −0.065  0.235 
Ho et al. (2001)28   410.0  0.2696  12.565  0.800  14.000  −1.436  −0.636 
Ho et al. (2001)28   410.0  0.2689  12.795  0.800  14.009  −1.215  −0.415 
Source t (°C) ρw (g cm−3) pKw(exp.) u[pKw(exp.)]a pKw(fit) ΔpKwb Diff.c
Noyes et al. (1910)16   0.0  0.9998  15.050  0.100  14.947  0.104  −0.004 
Noyes et al. (1910)16   18.0  0.9986  14.336  0.100  14.235  0.101  −0.001 
Noyes et al. (1910)16   25.0  0.9970  14.084  0.100  13.994  0.089  0.011 
Noyes et al. (1910)16   100.0  0.9583  12.282  0.100  12.254  0.028  0.072 
Noyes et al. (1910)16   156.0  0.9113  11.571  0.100  11.590  −0.019  0.081 
Noyes et al. (1910)16   218.0  0.8428  11.188  0.100  11.241  −0.053  0.047 
Noyes et al. (1910)16   306.0  0.6995  11.464  0.100  11.317  0.148  −0.048 
Holzapfel and Franck (1966)17   500.0  1.3460  4.058  0.700  5.149  −1.091  −0.391 
Holzapfel and Franck (1966)17   500.0  1.5134  2.960  0.700  3.361  −0.401  0.299 
Holzapfel and Franck (1966)17   750.0  1.3638  3.069  0.700  4.208  −1.138  −0.438 
Holzapfel and Franck (1966)17   750.0  1.5067  2.056  0.700  2.696  −0.640  0.060 
Holzapfel and Franck (1966)17   1000.0  1.3837  2.382  0.700  3.551  −1.169  −0.469 
Holzapfel and Franck (1966)17   1000.0  1.5601  1.386  0.700  1.645  −0.259  0.441 
Quist (1970)18   300.0  1.0000  9.000  0.500  9.317  −0.317  0.183 
Quist (1970)18   300.0  0.9500  9.255  0.500  9.687  −0.431  0.069 
Quist (1970)18   400.0  0.9500  8.655  0.500  8.993  −0.337  0.163 
Quist (1970)18   400.0  0.9000  9.008  0.500  9.344  −0.336  0.164 
Quist (1970)18   400.0  0.8500  9.259  0.500  9.683  −0.425  0.075 
Quist (1970)18   400.0  0.8000  9.606  0.500  10.012  −0.406  0.094 
Quist (1970)18   400.0  0.7500  9.850  0.500  10.333  −0.483  0.017 
Quist (1970)18   400.0  0.7000  10.390  0.500  10.649  −0.258  0.242 
Quist (1970)18   400.0  0.6500  11.326  0.500  10.962  0.363  0.137 
Quist (1970)18   400.0  0.6000  11.656  0.500  11.279  0.378  0.122 
Quist (1970)18   500.0  0.8500  8.859  0.500  9.170  −0.311  0.189 
Quist (1970)18   500.0  0.8000  9.206  0.500  9.496  −0.289  0.211 
Quist (1970)18   500.0  0.7500  9.650  0.500  9.813  −0.163  0.337 
Quist (1970)18   500.0  0.5500  11.381  0.500  11.069  0.312  0.188 
Quist (1970)18   500.0  0.5000  11.898  0.500  11.405  0.493  0.007 
Quist (1970)18   500.0  0.4500  12.706  0.500  11.764  0.942  −0.442 
Quist (1970)18   600.0  0.7500  9.350  0.500  9.415  −0.065  0.435 
Quist (1970)18   600.0  0.6000  10.556  0.500  10.342  0.215  0.285 
Quist (1970)18   600.0  0.5500  11.081  0.500  10.660  0.421  0.079 
Quist (1970)18   600.0  0.5000  11.798  0.500  10.993  0.805  −0.305 
Quist (1970)18   600.0  0.4500  12.406  0.500  11.349  1.057  −0.557 
Quist (1970)18   700.0  0.7000  9.290  0.500  9.406  −0.116  0.384 
Quist (1970)18   700.0  0.6500  9.826  0.500  9.711  0.115  0.385 
Quist (1970)18   700.0  0.6000  10.056  0.500  10.019  0.037  0.463 
Quist (1970)18   700.0  0.5500  10.781  0.500  10.334  0.446  0.054 
Quist (1970)18   700.0  0.5000  11.398  0.500  10.665  0.733  −0.233 
Quist (1970)18   700.0  0.4500  12.006  0.500  11.019  0.987  −0.487 
Quist (1970)18   800.0  0.6500  9.326  0.500  9.449  −0.123  0.377 
Quist (1970)18   800.0  0.6000  9.856  0.500  9.754  0.102  0.398 
Quist (1970)18   800.0  0.5500  10.481  0.500  10.067  0.414  0.086 
Quist (1970)18   800.0  0.5000  11.098  0.500  10.395  0.703  −0.203 
Bignold et al. (1971)15   51.0  0.9876  13.241  0.100  13.239  0.002  0.098 
Bignold et al. (1971)15   60.9  0.9827  12.992  0.100  13.000  −0.008  0.092 
Bignold et al. (1971)15   70.5  0.9775  12.802  0.100  12.789  0.012  0.088 
Bignold et al. (1971)15   80.2  0.9717  12.642  0.100  12.596  0.046  0.054 
Bignold et al. (1971)15   89.9  0.9654  12.490  0.100  12.420  0.070  0.030 
Bignold et al. (1971)15   99.3  0.9589  12.234  0.100  12.265  −0.031  0.069 
Bignold et al. (1971)15   108.6  0.9520  12.074  0.100  12.125  −0.051  0.049 
Bignold et al. (1971)15   118.0  0.9447  11.986  0.100  11.997  −0.010  0.090 
Bignold et al. (1971)15   127.3  0.9371  11.870  0.100  11.881  −0.011  0.089 
Bignold et al. (1971)15   136.7  0.9291  11.767  0.100  11.775  −0.008  0.092 
Bignold et al. (1971)15   146.0  0.9207  11.721  0.100  11.681  0.040  0.060 
Bignold et al. (1971)15   155.4  0.9119  11.608  0.100  11.596  0.012  0.088 
Bignold et al. (1971)15   164.7  0.9028  11.548  0.100  11.520  0.028  0.072 
Bignold et al. (1971)15   174.2  0.8931  11.473  0.100  11.451  0.021  0.079 
Bignold et al. (1971)15   183.6  0.8831  11.393  0.100  11.392  0.001  0.099 
Bignold et al. (1971)15   193.0  0.8727  11.333  0.100  11.341  −0.008  0.092 
Bignold et al. (1971)15   202.5  0.8617  11.279  0.100  11.296  −0.017  0.083 
Bignold et al. (1971)15   212.1  0.8501  11.259  0.100  11.259  −0.001  0.099 
Bignold et al. (1971)15   221.7  0.8380  11.228  0.100  11.230  −0.002  0.098 
Bignold et al. (1971)15   231.4  0.8252  11.215  0.100  11.208  0.007  0.093 
Bignold et al. (1971)15   241.2  0.8117  11.202  0.100  11.194  0.008  0.092 
Bignold et al. (1971)15   251.0  0.7974  11.195  0.100  11.187  0.008  0.092 
Bignold et al. (1971)15   261.0  0.7821  11.203  0.100  11.189  0.014  0.086 
Bignold et al. (1971)15   271.0  0.7658  11.219  0.100  11.199  0.020  0.080 
Fisher and Barnes (1972)19   100.0  0.9583  12.193  0.200  12.254  −0.061  0.139 
Fisher and Barnes (1972)19   150.0  0.9170  11.145  0.200  11.644  −0.499  −0.299 
Fisher and Barnes (1972)19   200.0  0.8647  11.074  0.200  11.307  −0.234  −0.034 
Fisher and Barnes (1972)19   250.0  0.7989  11.035  0.200  11.188  −0.153  0.047 
Fisher and Barnes (1972)19   300.0  0.7121  11.035  0.200  11.286  −0.251  −0.051 
Fisher and Barnes (1972)19   350.0  0.5747  11.419  0.200  11.773  −0.355  −0.155 
Svistunov et al. (1977)20   332.1  0.0800  20.444  1.000  19.509  0.936  0.064 
Svistunov et al. (1977)20   343.8  0.1000  18.921  1.000  18.419  0.502  0.498 
Svistunov et al. (1977)20   357.8  0.1360  17.496  1.000  16.997  0.499  0.501 
Svistunov et al. (1977)20   371.3  0.2170  16.311  1.000  15.047  1.264  −0.264 
Svistunov et al. (1978)21   299.6  0.7130  11.406  0.400  11.284  0.122  0.278 
Svistunov et al. (1978)21   309.4  0.6920  11.480  0.400  11.336  0.144  0.256 
Svistunov et al. (1978)21   320.0  0.6670  11.548  0.400  11.409  0.139  0.261 
Svistunov et al. (1978)21   329.6  0.6420  11.615  0.400  11.494  0.121  0.279 
Svistunov et al. (1978)21   340.2  0.6100  11.871  0.400  11.617  0.253  0.147 
Svistunov et al. (1978)21   343.2  0.6000  11.856  0.400  11.659  0.197  0.203 
Svistunov et al. (1978)21   395.0  0.4000  13.004  0.400  12.734  0.270  0.130 
Svistunov et al. (1978)21   395.0  0.5070  12.210  0.400  11.924  0.286  0.114 
Svistunov et al. (1978)21   395.0  0.5500  11.881  0.400  11.634  0.247  0.153 
Svistunov et al. (1978)21   395.0  0.5800  11.727  0.400  11.438  0.289  0.111 
Svistunov et al. (1978)21   395.0  0.6020  11.559  0.400  11.297  0.262  0.138 
Svistunov et al. (1978)21   395.0  0.6200  11.385  0.400  11.182  0.202  0.198 
Harned and Robinson (1940)49   0.0  0.9998  14.944  0.001  14.947  −0.003  −0.002 
Harned and Robinson (1940)49   5.0  1.0000  14.734  0.001  14.734  0.000  0.001 
Harned and Robinson (1940)49   10.0  0.9997  14.535  0.001  14.534  0.001  0.000 
Harned and Robinson (1940)49   15.0  0.9991  14.346  0.001  14.344  0.002  −0.001 
Harned and Robinson (1940)49   20.0  0.9982  14.167  0.001  14.165  0.002  −0.001 
Harned and Robinson (1940)49   25.0  0.9970  13.997  0.001  13.994  0.002  −0.001 
Harned and Robinson (1940)49   30.0  0.9956  13.833  0.001  13.833  0.000  0.001 
Harned and Robinson (1940)49   35.0  0.9940  13.680  0.001  13.680  0.000  0.001 
Harned and Robinson (1940)49   40.0  0.9922  13.535  0.001  13.534  0.000  0.001 
Harned and Robinson (1940)49   45.0  0.9902  13.396  0.001  13.396  0.000  0.001 
Harned and Robinson (1940)49   50.0  0.9880  13.262  0.001  13.265  −0.003  −0.002 
Harned and Robinson (1940)49   55.0  0.9857  13.137  0.001  13.140  −0.003  −0.002 
Harned and Robinson (1940)49   60.0  0.9832  13.017  0.001  13.021  −0.004  −0.003 
Perkovets and Kryukov (1969)50   25.0  0.9970  13.990  0.020  13.994  −0.004  0.016 
Perkovets and Kryukov (1969)50   60.0  0.9832  13.000  0.020  13.021  −0.021  −0.001 
Perkovets and Kryukov (1969)50   90.0  0.9653  12.400  0.020  12.418  −0.018  0.002 
Perkovets and Kryukov (1969)50   100.0  0.9583  12.290  0.020  12.254  0.036  −0.016 
Perkovets and Kryukov (1969)50   125.0  0.9390  11.920  0.020  11.909  0.011  0.009 
Perkovets and Kryukov (1969)50   150.0  0.9170  11.660  0.020  11.644  0.016  0.004 
Linov and Kryukov (1972)52   18.0  1.0396  13.864  0.030  13.908  −0.044  −0.014 
Linov and Kryukov (1972)52   18.0  1.0737  13.547  0.030  13.628  −0.080  −0.050 
Linov and Kryukov (1972)52   18.0  1.1027  13.265  0.030  13.382  −0.117  −0.087 
Linov and Kryukov (1972)52   18.0  1.1282  13.034  0.030  13.162  −0.128  −0.098 
Linov and Kryukov (1972)52   18.0  1.1509  12.840  0.030  12.961  −0.121  −0.091 
Linov and Kryukov (1972)52   18.0  1.1714  12.664  0.030  12.776  −0.112  −0.082 
Linov and Kryukov (1972)52   18.0  1.1903  12.508  0.030  12.604  −0.096  −0.066 
Linov and Kryukov (1972)52   18.0  1.2077  12.372  0.030  12.442  −0.070  −0.040 
Linov and Kryukov (1972)52   25.0  1.0372  13.640  0.030  13.675  −0.036  −0.006 
Linov and Kryukov (1972)52   25.0  1.0707  13.359  0.030  13.400  −0.041  −0.011 
Linov and Kryukov (1972)52   25.0  1.0995  13.120  0.030  13.157  −0.038  −0.008 
Linov and Kryukov (1972)52   25.0  1.1247  12.901  0.030  12.940  −0.039  −0.009 
Linov and Kryukov (1972)52   25.0  1.1473  12.710  0.030  12.741  −0.031  −0.001 
Linov and Kryukov (1972)52   25.0  1.1678  12.540  0.030  12.557  −0.017  0.013 
Linov and Kryukov (1972)52   25.0  1.1867  12.390  0.030  12.385  0.005  0.025 
Linov and Kryukov (1972)52   25.0  1.2041  12.270  0.030  12.224  0.046  −0.016 
Linov and Kryukov (1972)52   50.0  1.0267  12.986  0.030  12.960  0.027  0.003 
Linov and Kryukov (1972)52   50.0  1.0592  12.741  0.030  12.696  0.045  −0.015 
Linov and Kryukov (1972)52   50.0  1.0873  12.516  0.030  12.462  0.054  −0.024 
Linov and Kryukov (1972)52   50.0  1.1122  12.308  0.030  12.251  0.057  −0.027 
Linov and Kryukov (1972)52   50.0  1.1346  12.124  0.030  12.056  0.068  −0.038 
Linov and Kryukov (1972)52   50.0  1.1550  11.962  0.030  11.876  0.086  −0.056 
Linov and Kryukov (1972)52   50.0  1.1738  11.815  0.030  11.707  0.108  −0.078 
Linov and Kryukov (1972)52   50.0  1.1912  11.688  0.030  11.548  0.140  −0.110 
Linov and Kryukov (1972)52   75.0  1.0139  12.381  0.030  12.394  −0.013  0.017 
Linov and Kryukov (1972)52   75.0  1.0464  12.123  0.030  12.134  −0.010  0.020 
Linov and Kryukov (1972)52   75.0  1.0745  11.888  0.030  11.903  −0.016  0.014 
Linov and Kryukov (1972)52   75.0  1.0994  11.675  0.030  11.695  −0.020  0.010 
Linov and Kryukov (1972)52   75.0  1.1218  11.485  0.030  11.503  −0.018  0.012 
Linov and Kryukov (1972)52   75.0  1.1422  11.319  0.030  11.325  −0.006  0.024 
Linov and Kryukov (1972)52   75.0  1.1611  11.172  0.030  11.158  0.015  0.015 
Linov and Kryukov (1972)52   75.0  1.1786  11.046  0.030  11.000  0.046  −0.016 
Whitfield (1972)51   5.0  1.0095  14.660  0.015  14.659  0.001  0.014 
Whitfield (1972)51   5.0  1.0187  14.588  0.015  14.585  0.003  0.012 
Whitfield (1972)51   5.0  1.0276  14.521  0.015  14.515  0.006  0.009 
Whitfield (1972)51   5.0  1.0360  14.454  0.015  14.447  0.008  0.007 
Whitfield (1972)51   5.0  1.0441  14.390  0.015  14.381  0.009  0.006 
Whitfield (1972)51   5.0  1.0519  14.327  0.015  14.317  0.010  0.005 
Whitfield (1972)51   5.0  1.0593  14.265  0.015  14.256  0.009  0.006 
Whitfield (1972)51   5.0  1.0665  14.206  0.015  14.197  0.009  0.006 
Whitfield (1972)51   5.0  1.0734  14.146  0.015  14.139  0.007  0.008 
Whitfield (1972)51   5.0  1.0801  14.089  0.015  14.083  0.006  0.009 
Whitfield (1972)51   15.0  1.0082  14.275  0.015  14.272  0.002  0.013 
Whitfield (1972)51   15.0  1.0170  14.205  0.015  14.203  0.002  0.013 
Whitfield (1972)51   15.0  1.0254  14.137  0.015  14.135  0.002  0.013 
Whitfield (1972)51   15.0  1.0335  14.072  0.015  14.070  0.001  0.014 
Whitfield (1972)51   15.0  1.0413  14.010  0.015  14.007  0.003  0.012 
Whitfield (1972)51   15.0  1.0487  13.949  0.015  13.946  0.003  0.012 
Whitfield (1972)51   15.0  1.0560  13.890  0.015  13.887  0.003  0.012 
Whitfield (1972)51   15.0  1.0629  13.834  0.015  13.830  0.005  0.010 
Whitfield (197251   15.0  1.0696  13.782  0.015  13.774  0.008  0.007 
Whitfield (1972)51   15.0  1.0761  13.733  0.015  13.720  0.013  0.002 
Whitfield (1972)51   25.0  1.0058  13.927  0.015  13.925  0.002  0.013 
Whitfield (1972)51   25.0  1.0143  13.859  0.015  13.858  0.001  0.014 
Whitfield (1972)51   25.0  1.0225  13.793  0.015  13.793  0.000  0.015 
Whitfield (1972)51   25.0  1.0303  13.730  0.015  13.730  0.000  0.015 
Whitfield (1972)51   25.0  1.0379  13.668  0.015  13.669  −0.001  0.014 
Whitfield (1972)51   25.0  1.0452  13.611  0.015  13.610  0.000  0.015 
Whitfield (1972)51   25.0  1.0522  13.555  0.015  13.553  0.002  0.013 
Whitfield (1972)51   25.0  1.0590  13.499  0.015  13.497  0.002  0.013 
Whitfield (1972)51   25.0  1.0655  13.445  0.015  13.443  0.002  0.013 
Whitfield (1972)51   25.0  1.0719  13.392  0.015  13.390  0.002  0.013 
Whitfield (1972)51   25.0  1.0058  13.928  0.015  13.925  0.002  0.013 
Whitfield (1972)51   25.0  1.0143  13.859  0.015  13.858  0.001  0.014 
Whitfield (1972)51   25.0  1.0225  13.795  0.015  13.793  0.002  0.013 
Whitfield (1972)51   25.0  1.0303  13.731  0.015  13.730  0.000  0.015 
Whitfield (1972)51   25.0  1.0379  13.670  0.015  13.669  0.000  0.015 
Whitfield (1972)51   25.0  1.0452  13.607  0.015  13.610  −0.003  0.012 
Whitfield (1972)51   25.0  1.0522  13.553  0.015  13.553  0.000  0.015 
Whitfield (197251   25.0  1.0590  13.499  0.015  13.497  0.002  0.013 
Whitfield (1972)51   25.0  1.0655  13.450  0.015  13.443  0.007  0.008 
Whitfield (1972)51   25.0  1.0719  13.404  0.015  13.390  0.014  0.001 
Whitfield (1972)51   35.0  1.0026  13.613  0.015  13.612  0.000  0.015 
Whitfield (1972)51   35.0  1.0109  13.546  0.015  13.547  −0.001  0.014 
Whitfield (1972)51   35.0  1.0189  13.482  0.015  13.484  −0.001  0.014 
Whitfield (1972)51   35.0  1.0266  13.422  0.015  13.422  −0.001  0.014 
Whitfield (1972)51   35.0  1.0340  13.363  0.015  13.363  0.000  0.015 
Whitfield (1972)51   35.0  1.0412  13.306  0.015  13.305  0.001  0.014 
Whitfield (1972)51   35.0  1.0481  13.250  0.015  13.249  0.001  0.014 
Whitfield (1972)51   35.0  1.0547  13.198  0.015  13.194  0.004  0.011 
Whitfield (1972)51   35.0  1.0612  13.148  0.015  13.141  0.007  0.008 
Whitfield (1972)51   35.0  1.0675  13.101  0.015  13.089  0.012  0.003 
MacDonald et al. (1973)53   25.0  0.9970  13.990  0.030  13.994  −0.004  0.026 
MacDonald et al. (1973)53   50.0  0.9880  13.240  0.030  13.265  −0.025  0.005 
MacDonald et al. (1973)53   75.0  0.9748  12.680  0.030  12.697  −0.017  0.013 
MacDonald et al. (1973)53   100.0  0.9583  12.240  0.030  12.254  −0.014  0.016 
MacDonald et al. (1973)53   125.0  0.9390  11.880  0.030  11.909  −0.029  0.001 
MacDonald et al. (1973)53   150.0  0.9170  11.640  0.030  11.644  −0.004  0.026 
MacDonald et al. (1973)53   175.0  0.8923  11.430  0.030  11.446  −0.016  0.014 
MacDonald et al. (1973)53   200.0  0.8647  11.260  0.030  11.307  −0.047  −0.017 
Sweeton et al. (1974)1   0.0  0.9998  14.941  0.009  14.947  −0.006  0.003 
Sweeton et al. (1974)1   25.0  0.9970  13.993  0.009  13.994  −0.001  0.008 
Sweeton et al. (1974)1   50.0  0.9880  13.272  0.006  13.265  0.007  −0.001 
Sweeton et al. (1974)1   75.0  0.9748  12.709  0.006  12.697  0.012  −0.006 
Sweeton et al. (1974)1   100.0  0.9583  12.264  0.009  12.254  0.010  −0.001 
Sweeton et al. (1974)1   125.0  0.9390  11.914  0.009  11.909  0.005  0.004 
Sweeton et al. (1974)1   150.0  0.9170  11.642  0.012  11.644  −0.002  0.010 
Sweeton et al. (1974)1   175.0  0.8923  11.441  0.012  11.446  −0.005  0.007 
Sweeton et al. (1974)1   200.0  0.8647  11.302  0.012  11.307  −0.005  0.007 
Sweeton et al. (1974)1   225.0  0.8337  11.222  0.012  11.222  0.000  0.012 
Sweeton et al. (1974)1   250.0  0.7989  11.196  0.015  11.188  0.008  0.007 
Sweeton et al. (1974)1   275.0  0.7590  11.224  0.027  11.206  0.018  0.009 
Sweeton et al. (1974)1   300.0  0.7121  11.301  0.045  11.286  0.015  0.030 
Busey and Mesmer (1978)54   0.0  0.9998  14.941  0.009  14.947  −0.006  0.003 
Busey and Mesmer (1978)54   25.0  0.9970  13.993  0.009  13.994  −0.001  0.008 
Busey and Mesmer (1978)54   50.0  0.9880  13.272  0.006  13.265  0.007  −0.001 
Busey and Mesmer (1978)54   75.0  0.9748  12.709  0.006  12.697  0.012  −0.006 
Busey and Mesmer (1978)54   100.0  0.9583  12.264  0.009  12.254  0.010  −0.001 
Busey and Mesmer (1978)54   125.0  0.9390  11.914  0.009  11.909  0.005  0.004 
Busey and Mesmer (1978)54   150.0  0.9170  11.642  0.012  11.644  −0.002  0.010 
Busey and Mesmer (1978)54   175.0  0.8923  11.441  0.012  11.446  −0.005  0.007 
Busey and Mesmer (1978)54   200.0  0.8647  11.302  0.012  11.307  −0.005  0.007 
Busey and Mesmer (1978)54   225.0  0.8337  11.222  0.012  11.222  0.000  0.012 
Busey and Mesmer (1978)54   250.0  0.7989  11.196  0.015  11.188  0.008  0.007 
Busey and Mesmer (1978)54   275.0  0.7590  11.224  0.027  11.206  0.018  0.009 
Busey and Mesmer (1978)54   300.0  0.7121  11.301  0.045  11.286  0.015  0.030 
Kryukov et al. (1980)55   25.0  1.0379  13.656  0.040  13.669  −0.013  0.027 
Kryukov et al. (1980)55   25.0  1.0719  13.372  0.040  13.390  −0.018  0.022 
Kryukov et al. (1980)55   25.0  1.1010  13.132  0.040  13.144  −0.012  0.028 
Kryukov et al. (1980)55   25.0  1.1266  12.914  0.040  12.923  −0.009  0.031 
Kryukov et al. (1980)55   25.0  1.1494  12.716  0.040  12.722  −0.006  0.034 
Kryukov et al. (1980)55   25.0  1.1701  12.530  0.040  12.536  −0.006  0.034 
Kryukov et al. (1980)55   50.0  1.0274  12.963  0.040  12.954  0.009  0.031 
Kryukov et al. (1980)55   50.0  1.0604  12.702  0.040  12.687  0.015  0.025 
Kryukov et al. (1980)55   50.0  1.0889  12.467  0.040  12.449  0.018  0.022 
Kryukov et al. (1980)55   50.0  1.1140  12.255  0.040  12.235  0.020  0.020 
Kryukov et al. (1980)55   50.0  1.1367  12.060  0.040  12.038  0.022  0.018 
Kryukov et al. (1980)55   50.0  1.1573  11.880  0.040  11.855  0.025  0.015 
Kryukov et al. (1980)55   75.0  1.0146  12.393  0.040  12.388  0.005  0.035 
Kryukov et al. (1980)55   75.0  1.0476  12.134  0.040  12.124  0.010  0.030 
Kryukov et al. (1980)55   75.0  1.0760  11.901  0.040  11.890  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1012  11.690  0.040  11.679  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1239  11.496  0.040  11.485  0.011  0.029 
Kryukov et al. (1980)55   75.0  1.1445  11.316  0.040  11.304  0.012  0.028 
Kryukov et al. (1980)55   100.0  0.9998  11.938  0.040  11.937  0.001  0.039 
Kryukov et al. (1980)55   100.0  1.0335  11.665  0.040  11.671  −0.006  0.034 
Kryukov et al. (1980)55   100.0  1.0624  11.433  0.040  11.437  −0.004  0.036 
Kryukov et al. (1980)55   100.0  1.0879  11.223  0.040  11.226  −0.003  0.037 
Kryukov et al. (1980)55   100.0  1.1108  11.040  0.040  11.033  0.007  0.033 
Kryukov et al. (1980)55   100.0  1.1317  10.865  0.040  10.854  0.011  0.029 
Kryukov et al. (1980)55   150.0  0.9170  11.630  0.040  11.644  −0.014  0.026 
Kryukov et al. (1980)55   150.0  0.9648  11.250  0.040  11.291  −0.041  −0.001 
Kryukov et al. (1980)55   150.0  1.0020  10.970  0.040  11.009  −0.039  0.001 
Kryukov et al. (1980)55   150.0  1.0329  10.720  0.040  10.767  −0.047  −0.007 
Kryukov et al. (1980)55   150.0  1.0598  10.560  0.040  10.551  0.009  0.031 
Kryukov et al. (1980)55   150.0  1.0837  10.350  0.040  10.355  −0.005  0.035 
Kryukov et al. (1980)55   150.0  1.1054  10.160  0.040  10.175  −0.015  0.025 
Palmer and Drummond (1988)56   25.0  0.9970  14.000  0.010  13.994  0.006  0.004 
Palmer and Drummond (1988)56   50.0  0.9880  13.280  0.010  13.265  0.015  −0.005 
Palmer and Drummond (1988)56   100.0  0.9583  12.270  0.010  12.254  0.016  −0.006 
Palmer and Drummond (1988)56   150.0  0.9170  11.640  0.010  11.644  −0.004  0.006 
Palmer and Drummond (1988)56   200.0  0.8647  11.290  0.010  11.307  −0.017  −0.007 
Palmer and Drummond (1988)56   250.0  0.7989  11.180  0.010  11.188  −0.008  0.002 
Ackermann (1958)61   0.0  0.9998  14.955  0.005  14.947  0.008  −0.003 
Ackermann (1958)61   10.0  0.9997  14.534  0.005  14.534  0.000  0.005 
Ackermann (1958)61   20.0  0.9982  14.161  0.005  14.165  −0.004  0.001 
Ackermann (1958)61   25.0  0.9970  13.999  0.005  13.994  0.005  0.000 
Ackermann (1958)61   30.0  0.9956  13.833  0.005  13.833  0.000  0.005 
Ackermann (1958)61   40.0  0.9922  13.533  0.005  13.534  −0.001  0.004 
Ackermann (1958)61   50.0  0.9880  13.263  0.005  13.265  −0.002  0.003 
Ackermann (1958)61   60.0  0.9832  13.015  0.005  13.021  −0.006  −0.001 
Ackermann (1958)61   70.0  0.9778  12.800  0.005  12.800  0.000  0.005 
Ackermann (1958)61   80.0  0.9718  12.598  0.005  12.600  −0.002  0.003 
Ackermann (1958)61   90.0  0.9653  12.422  0.005  12.418  0.004  0.001 
Ackermann (1958)61   100.0  0.9583  12.259  0.005  12.254  0.005  0.000 
Ackermann (1958)61   110.0  0.9509  12.126  0.005  12.105  0.021  −0.016 
Ackermann (1958)61   120.0  0.9431  12.002  0.005  11.971  0.031  −0.026 
Ackermann (1958)61   130.0  0.9348  11.907  0.005  11.850  0.057  −0.052 
Chen et al. (1994)62   0.0  0.9998  14.946  0.005  14.947  −0.001  0.004 
Chen et al. (1994)62   25.0  0.9970  13.999  0.005  13.994  0.005  0.000 
Chen et al. (1994)62   50.0  0.9880  13.276  0.005  13.265  0.011  −0.006 
Chen et al. (1994)62   75.0  0.9748  12.710  0.005  12.697  0.013  −0.008 
Chen et al. (1994)62   100.0  0.9583  12.264  0.005  12.254  0.010  −0.005 
Chen et al. (1994)62   125.0  0.9390  11.914  0.005  11.909  0.005  0.000 
Chen et al. (1994)62   150.0  0.9170  11.644  0.005  11.644  0.000  0.005 
Chen et al. (1994)62   175.0  0.8923  11.442  0.005  11.446  −0.004  0.001 
Chen et al. (1994)62   200.0  0.8647  11.303  0.005  11.307  −0.004  0.001 
Chen et al. (1994)62   225.0  0.8337  11.223  0.005  11.222  0.001  0.004 
Chen et al. (1994)62   250.0  0.7989  11.203  0.010  11.188  0.015  −0.005 
Chen et al. (1994)62   275.0  0.7590  11.251  0.020  11.206  0.045  −0.025 
Chen et al. (1994)62   300.0  0.7121  11.382  0.030  11.286  0.096  −0.066 
Chen et al. (1994)62   325.0  0.6543  11.638  0.050  11.451  0.187  −0.137 
Chen et al. (1994)62   350.0  0.5747  12.144  0.100  11.773  0.371  −0.271 
Hamann (1963)58   25.0  0.9970  13.997  0.030  13.994  0.002  0.028 
Hamann (1963)58   25.0  1.0081  13.907  0.030  13.907  −0.001  0.029 
Hamann (1963)58   25.0  1.0187  13.823  0.030  13.823  0.000  0.030 
Hamann (1963)58   25.0  1.0288  13.746  0.030  13.743  0.003  0.027 
Hamann (1963)58   25.0  1.0384  13.666  0.030  13.665  0.001  0.029 
Hamann (1963)58   25.0  1.0475  13.585  0.030  13.591  −0.006  0.024 
Hamann (1963)58   25.0  1.0563  13.524  0.030  13.519  0.005  0.025 
Hamann (1963)58   25.0  1.0647  13.449  0.030  13.450  −0.001  0.029 
Hamann (1963)58   25.0  1.0727  13.393  0.030  13.383  0.011  0.019 
Hamann and Linton (1969)59   20.0  0.9982  14.167  3.000  14.165  0.003  2.997 
Hamann and Linton (1969)59   45.0  1.1878  12.060  3.000  11.727  0.334  2.666 
Hamann and Linton (1969)59   240.0  1.4703  7.229  3.000  5.477  1.753  1.247 
Hamann and Linton (1969)59   304.0  1.5095  6.456  3.000  4.478  1.978  1.022 
Hamann and Linton (1969)59   373.0  1.5476  5.699  3.000  3.576  2.123  0.877 
Hamann and Linton (1969)59   444.0  1.5774  4.337  3.000  2.851  1.487  1.513 
Hamann and Linton (1969)59   527.0  1.6025  3.051  3.000  2.205  0.846  2.154 
Hamann and Linton (1969)59   670.0  1.6493  1.854  3.000  1.190  0.663  2.337 
Hamann and Linton (1969)59   804.0  1.6868  1.051  3.000  0.418  0.632  2.368 
Arcis et al. (2017)36   175.1  0.9038  11.317  0.040  11.363  −0.046  −0.006 
Arcis et al. (2017)36   250.2  0.8155  10.888  0.040  11.075  −0.187  −0.147 
Arcis et al. (2017)36   275.2  0.7778  11.056  0.040  11.082  −0.025  0.015 
Arcis et al. (2017)36   297.9  0.7377  11.145  0.040  11.140  0.005  0.035 
Arcis et al. (2017)36   274.0  0.7814  11.066  0.040  11.070  −0.004  0.036 
Arcis et al. (2017)36   299.6  0.7367  11.166  0.040  11.132  0.034  0.006 
Arcis et al. (2017)36   324.7  0.6823  11.407  0.100  11.276  0.131  −0.031 
Arcis et al. (2017)36   348.2  0.6116  11.858  0.100  11.549  0.309  −0.209 
Arcis et al. (2016)35   175.1  0.9039  11.346  0.040  11.363  −0.016  0.024 
Arcis et al. (2016)35   250.0  0.8158  11.027  0.040  11.075  −0.048  −0.008 
Arcis et al. (2016)35   275.0  0.7782  11.063  0.040  11.081  −0.018  0.022 
Arcis et al. (2016)35   297.9  0.7380  11.135  0.040  11.139  −0.004  0.036 
Arcis et al. (2016)35   274.0  0.7813  11.066  0.040  11.071  −0.005  0.035 
Arcis et al. (2016)35   299.6  0.7369  11.193  0.040  11.132  0.062  −0.022 
Arcis et al. (2016)35   324.8  0.6822  11.408  0.100  11.276  0.132  −0.032 
Arcis et al. (2016)35   348.9  0.6086  11.826  0.100  11.563  0.263  −0.163 
Arcis et al. (2016)35   175.1  0.9039  11.294  0.040  11.363  −0.069  −0.029 
Arcis et al. (2016)35   250.1  0.8156  11.059  0.040  11.076  −0.017  0.023 
Arcis et al. (2016)35   275.2  0.7779  11.057  0.040  11.082  −0.025  0.015 
Arcis et al. (2016)35   297.9  0.7380  11.142  0.040  11.139  0.003  0.037 
Arcis et al. (2016)35   275.0  0.7798  10.998  0.040  11.071  −0.073  −0.033 
Arcis et al. (2016)35   299.7  0.7366  11.146  0.040  11.133  0.014  0.026 
Arcis et al. (2016)35   324.9  0.6821  11.387  0.100  11.276  0.111  −0.011 
Arcis et al. (2016)35   348.0  0.6120  11.882  0.100  11.548  0.335  −0.235 
Ferguson et al. (2017)37   153.0  0.9172  11.527  0.040  11.595  −0.068  −0.028 
Ferguson et al. (2017)37   175.4  0.9040  11.295  0.040  11.357  −0.062  −0.022 
Ferguson et al. (2017)37   224.0  0.8503  11.067  0.040  11.121  −0.054  −0.014 
Ferguson et al. (2017)37   250.0  0.8165  11.022  0.040  11.071  −0.050  −0.010 
Ferguson et al. (2017)37   299.9  0.7354  11.218  0.040  11.139  0.080  −0.040 
Ferguson et al. (2017)37   325.8  0.6787  11.375  0.100  11.291  0.084  0.016 
Ferguson et al. (2017)37   175.0  0.9042  11.321  0.040  11.361  −0.040  0.000 
Ferguson et al. (2017)37   275.2  0.7785  11.094  0.040  11.078  0.016  0.024 
Ferguson et al. (2017)37   290.9  0.7517  11.137  0.040  11.111  0.027  0.013 
Ferguson et al. (2017)37   300.2  0.7344  11.175  0.040  11.142  0.032  0.008 
Ferguson et al. (2019)40   199.9  0.8727  11.216  0.040  11.253  −0.037  0.003 
Ferguson et al. (2019)40   253.8  0.8025  11.145  0.040  11.125  0.020  0.020 
Ferguson et al. (2019)40   250.0  0.8080  11.111  0.040  11.127  −0.017  0.023 
Ferguson et al. (2019)40   275.3  0.7675  11.121  0.040  11.148  −0.027  0.013 
Ferguson et al. (2019)40   298.4  0.7237  11.345  0.040  11.226  0.118  −0.078 
Ferguson et al. (2019)40   300.2  0.7192  11.360  0.040  11.240  0.120  −0.080 
Ferguson (2018)39   175.2  0.8992  11.362  0.040  11.394  −0.033  0.007 
Ferguson (2018)39   225.0  0.8423  11.085  0.040  11.164  −0.079  −0.039 
Ferguson (2018)39   275.0  0.7682  11.170  0.040  11.147  0.023  0.017 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.423  0.100  11.440  −0.016  0.084 
Gruszkiewicz and Wood (1997)24   343.1  0.6500  11.327  0.100  11.342  −0.015  0.085 
Gruszkiewicz and Wood (1997)24   347.3  0.5999  11.690  0.100  11.631  0.059  0.041 
Gruszkiewicz and Wood (1997)24   358.8  0.5999  11.620  0.100  11.549  0.071  0.029 
Gruszkiewicz and Wood (1997)24   361.8  0.5496  11.964  0.100  11.856  0.108  −0.008 
Gruszkiewicz and Wood (1997)24   371.0  0.4994  12.273  0.300  12.134  0.138  0.162 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.522  0.300  12.434  0.088  0.212 
Gruszkiewicz and Wood (1997)24   379.3  0.3973  13.045  0.300  12.860  0.185  0.115 
Gruszkiewicz and Wood (1997)24   379.5  0.3566  13.235  0.300  13.225  0.010  0.290 
Gruszkiewicz and Wood (1997)24   376.5  0.3086  13.580  0.300  13.741  −0.161  0.139 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.674  0.300  13.640  0.034  0.266 
Gruszkiewicz and Wood (1997)24   385.0  0.3207  13.745  0.300  13.551  0.194  0.106 
Gruszkiewicz and Wood (1997)24   379.4  0.2493  13.964  0.800  14.480  −0.515  0.285 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.407  0.800  14.438  −0.031  0.769 
Gruszkiewicz and Wood (1997)24   400.9  0.2498  13.956  0.800  14.331  −0.375  0.425 
Gruszkiewicz and Wood (1997)24   379.4  0.1999  14.449  0.800  15.303  −0.854  −0.054 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.451  0.100  11.440  0.011  0.089 
Gruszkiewicz and Wood (1997)24   343.1  0.6500  11.348  0.100  11.342  0.005  0.095 
Gruszkiewicz and Wood (1997)24   347.3  0.5999  11.706  0.100  11.631  0.076  0.024 
Gruszkiewicz and Wood (1997)24   358.8  0.5999  11.634  0.100  11.549  0.085  0.015 
Gruszkiewicz and Wood (1997)24   371.0  0.4994  12.373  0.300  12.134  0.239  0.061 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.628  0.300  12.434  0.194  0.106 
Gruszkiewicz and Wood (1997)24   379.3  0.3973  12.990  0.300  12.860  0.130  0.170 
Gruszkiewicz and Wood (1997)24   379.5  0.3566  13.241  0.300  13.225  0.016  0.284 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.839  0.300  13.640  0.199  0.101 
Gruszkiewicz and Wood (1997)24   385.0  0.3207  13.513  0.300  13.551  −0.038  0.262 
Gruszkiewicz and Wood (1997)24   379.4  0.2493  14.021  0.800  14.480  −0.458  0.342 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.377  0.800  14.438  −0.062  0.738 
Gruszkiewicz and Wood (1997)24   400.9  0.2498  14.122  0.800  14.331  −0.209  0.591 
Gruszkiewicz and Wood (1997)24   379.4  0.1999  14.685  0.800  15.303  −0.618  0.182 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.433  0.100  11.440  −0.006  0.094 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.723  0.300  12.434  0.289  0.011 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.707  0.300  13.640  0.067  0.233 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.291  0.800  14.438  −0.147  0.653 
Gruszkiewicz and Wood (1997)24   330.2  0.6498  11.428  0.100  11.440  −0.011  0.089 
Gruszkiewicz and Wood (1997)24   379.6  0.4502  12.575  0.300  12.434  0.140  0.160 
Gruszkiewicz and Wood (1997)24   379.4  0.3159  13.777  0.300  13.640  0.137  0.163 
Gruszkiewicz and Wood (1997)24   385.0  0.2495  14.407  0.800  14.438  −0.031  0.769 
Sharygin et al. (2002)30   378.1  0.5238  11.922  0.100  11.918  0.004  0.096 
Sharygin et al. (2002)30   378.1  0.5238  11.922  0.100  11.918  0.003  0.097 
Sharygin et al. (2002)30   378.1  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.1  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.1  0.5236  11.921  0.100  11.919  0.002  0.098 
Sharygin et al. (2002)30   378.1  0.5237  11.921  0.100  11.919  0.003  0.097 
Sharygin et al. (2002)30   378.2  0.5231  11.921  0.100  11.922  −0.002  0.098 
Sharygin et al. (2002)30   378.1  0.5236  11.921  0.100  11.919  0.002  0.098 
Sharygin et al. (2002)30   378.2  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.2  0.5234  11.921  0.100  11.920  0.001  0.099 
Sharygin et al. (2002)30   378.2  0.5238  11.922  0.100  11.917  0.004  0.096 
Sharygin et al. (2002)30   397.1  0.2968  13.268  0.800  13.742  −0.474  0.326 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   397.0  0.2982  13.271  0.800  13.726  −0.454  0.346 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   397.0  0.2984  13.272  0.800  13.724  −0.452  0.348 
Sharygin et al. (2002)30   396.9  0.2999  13.276  0.800  13.707  −0.431  0.369 
Sharygin et al. (2002)30   396.9  0.2999  13.276  0.800  13.707  −0.431  0.369 
Sharygin et al. (2002)30   397.1  0.2974  13.111  0.800  13.735  −0.624  0.176 
Sharygin et al. (2002)30   397.1  0.2986  13.114  0.800  13.721  −0.607  0.193 
Sharygin et al. (2002)30   397.1  0.2986  13.114  0.800  13.721  −0.607  0.193 
Sharygin et al. (2002)30   397.1  0.2968  13.110  0.800  13.742  −0.632  0.168 
Sharygin et al. (2002)30   397.1  0.2992  13.115  0.800  13.714  −0.598  0.202 
Sharygin et al. (2002)30   397.2  0.2977  13.112  0.800  13.731  −0.620  0.180 
Sharygin et al. (2002)30   397.1  0.2956  13.107  0.800  13.756  −0.649  0.151 
Sharygin et al. (2002)30   397.1  0.2945  13.104  0.800  13.770  −0.666  0.134 
Sharygin et al. (2002)30   397.3  0.2932  13.100  0.800  13.783  −0.683  0.117 
Sharygin et al. (2002)30   397.2  0.2959  13.107  0.800  13.752  −0.645  0.155 
Sharygin et al. (2002)30   397.1  0.2956  13.107  0.800  13.756  −0.649  0.151 
Zimmerman and Wood (2002)31   195.8  0.8825  11.186  0.040  11.236  −0.050  −0.010 
Zimmerman and Wood (2002)31   195.8  0.8825  11.106  0.040  11.236  −0.129  −0.089 
Zimmerman and Wood (2002)31   195.8  0.8825  11.186  0.040  11.235  −0.050  −0.010 
Zimmerman and Wood (2002)31   195.8  0.8825  11.192  0.040  11.235  −0.044  −0.004 
Zimmerman and Wood (2002)31   275.0  0.7788  10.701  0.040  11.078  −0.377  −0.337 
Zimmerman and Wood (2002)31   275.0  0.7788  10.986  0.040  11.078  −0.092  −0.052 
Zimmerman and Wood (2002)31   275.0  0.7788  10.974  0.040  11.078  −0.104  −0.064 
Zimmerman and Wood (2002)31   195.9  0.8825  11.165  0.040  11.236  −0.070  −0.030 
Zimmerman and Wood (2002)31   275.0  0.7788  10.957  0.040  11.078  −0.122  −0.082 
Hnedkovsky et al. (2005)25   100.0  0.9641  11.962  0.040  12.210  −0.249  −0.209 
Hnedkovsky et al. (2005)25   200.0  0.8727  11.074  0.040  11.251  −0.177  −0.137 
Hnedkovsky et al. (2005)25   250.0  0.8083  11.025  0.040  11.125  −0.100  −0.060 
Hnedkovsky et al. (2005)25   300.1  0.7207  11.151  0.040  11.231  −0.080  −0.040 
Hnedkovsky et al. (2005)25   300.0  0.7478  10.949  0.040  11.058  −0.109  −0.069 
Hnedkovsky et al. (2005)25   350.0  0.6006  11.554  0.100  11.606  −0.052  0.048 
Hnedkovsky et al. (2005)25   350.0  0.6370  11.433  0.100  11.374  0.059  0.041 
Hnedkovsky et al. (2005)25   390.0  0.3785  12.671  0.300  12.953  −0.282  0.018 
Hnedkovsky et al. (2005)25   400.0  0.2299  13.206  0.800  14.641  −1.434  −0.634 
Sharygin et al. (2006)32   250.6  0.8153  10.945  0.040  11.072  −0.127  −0.087 
Sharygin et al. (2006)32   300.2  0.7344  11.044  0.040  11.142  −0.098  −0.058 
Sharygin et al. (2006)32   300.9  0.7431  10.993  0.040  11.081  −0.088  −0.048 
Sharygin et al. (2006)32   351.0  0.6261  11.453  0.100  11.436  0.017  0.083 
Sharygin et al. (2006)32   380.3  0.4698  12.070  0.300  12.283  −0.213  0.087 
Sharygin et al. (2006)32   400.2  0.3012  12.710  0.300  13.671  −0.960  −0.660 
Sharygin et al. (2006)32   250.8  0.8151  10.812  0.040  11.072  −0.260  −0.220 
Sharygin et al. (2006)32   296.9  0.7502  10.886  0.040  11.069  −0.183  −0.143 
Sharygin et al. (2006)32   299.6  0.7357  10.942  0.040  11.139  −0.197  −0.157 
Sharygin et al. (2006)32   303.1  0.7396  10.990  0.040  11.085  −0.094  −0.054 
Sharygin et al. (2006)32   351.0  0.6256  11.481  0.100  11.439  0.042  0.058 
Sharygin et al. (2006)32   380.8  0.4636  12.328  0.300  12.326  0.003  0.297 
Sharygin et al. (2006)32   399.5  0.3040  12.611  0.300  13.642  −1.031  −0.731 
Balashov et al. (2017)38   100.0  0.9641  12.208  0.040  12.210  −0.002  0.038 
Balashov et al. (2017)38   200.0  0.8727  11.236  0.040  11.251  −0.015  0.025 
Balashov et al. (2017)38   250.1  0.8084  11.128  0.040  11.124  0.004  0.036 
Balashov et al. (2017)38   300.0  0.7210  11.255  0.040  11.230  0.025  0.015 
Balashov et al. (2017)38   300.1  0.7477  11.075  0.040  11.058  0.017  0.023 
Balashov et al. (2017)38   350.0  0.6009  11.698  0.100  11.604  0.093  0.007 
Balashov et al. (2017)38   350.1  0.6370  11.443  0.100  11.374  0.069  0.031 
Balashov et al. (2017)38   389.9  0.3775  13.473  0.300  12.963  0.510  −0.210 
Balashov et al. (2017)38   400.1  0.2287  15.441  0.800  14.660  0.781  0.019 
Ho et al. (2001)28   200.0  0.8709  10.878  0.040  11.264  −0.386  −0.346 
Ho et al. (2001)28   300.0  0.7157  11.109  0.040  11.264  −0.155  −0.115 
Ho et al. (2001)28   300.0  0.7159  11.139  0.040  11.263  −0.123  −0.083 
Ho et al. (2001)28   350.0  0.6363  11.350  0.100  11.378  −0.029  0.071 
Ho et al. (2001)28   350.0  0.6302  11.375  0.100  11.418  −0.043  0.057 
Ho et al. (2001)28   370.0  0.5722  11.745  0.100  11.650  0.095  0.005 
Ho et al. (2001)28   370.0  0.5649  11.834  0.100  11.698  0.136  −0.036 
Ho et al. (2001)28   380.0  0.5439  11.904  0.100  11.770  0.133  −0.033 
Ho et al. (2001)28   380.0  0.5438  11.972  0.100  11.771  0.201  −0.101 
Ho et al. (2001)28   380.0  0.5194  12.006  0.100  11.935  0.070  0.030 
Ho et al. (2001)28   380.0  0.5062  11.895  0.100  12.026  −0.132  −0.032 
Ho et al. (2001)28   380.0  0.5067  12.264  0.100  12.022  0.242  −0.142 
Ho et al. (2001)28   390.0  0.4768  12.199  0.300  12.169  0.029  0.271 
Ho et al. (2001)28   390.0  0.4256  12.420  0.300  12.557  −0.136  0.164 
Ho et al. (2001)28   390.0  0.3810  12.270  0.300  12.931  −0.661  −0.361 
Ho et al. (2001)28   400.0  0.2987  12.524  0.800  13.700  −1.176  −0.376 
Ho et al. (2001)28   400.0  0.3003  12.779  0.300  13.682  −0.903  −0.603 
Ho et al. (2001)28   400.0  0.2993  12.460  0.800  13.694  −1.234  −0.434 
Ho et al. (2001)28   400.0  0.2993  12.633  0.800  13.694  −1.061  −0.261 
Ho et al. (2001)28   400.0  0.3369  12.206  0.300  13.285  −1.080  −0.780 
Ho et al. (2001)28   400.0  0.3354  12.502  0.300  13.300  −0.798  −0.498 
Ho et al. (2001)28   400.0  0.3364  12.568  0.300  13.290  −0.722  −0.422 
Ho et al. (2001)28   400.0  0.3369  12.424  0.300  13.285  −0.861  −0.561 
Ho et al. (2001)28   400.0  0.3866  12.858  0.300  12.818  0.039  0.261 
Ho et al. (2001)28   400.0  0.3866  12.753  0.300  12.818  −0.065  0.235 
Ho et al. (2001)28   410.0  0.2696  12.565  0.800  14.000  −1.436  −0.636 
Ho et al. (2001)28   410.0  0.2689  12.795  0.800  14.009  −1.215  −0.415 
a

Estimated IUPAC Type B46 standard uncertainty.

b

ΔpKw = pKw(exp.) − pKw [Eq. (8), this work].

c

Diff. = u[pKw(exp.)] − |ΔpKw|.

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