Equations for testing Onsager's reciprocal relations for isothermal diffusion depend on the frame of reference chosen for the flows. This subject is considered for certain frames of reference, as is the problem of measuring diffusion coefficients when there is a change of volume on mixing. Frames of reference discussed are those moving with the local center of mass, the local center of volume, the local velocity of the solvent (or of any single component), and that fixed on the diffusion cell. Multicomponent systems, both of strong electrolytes and nonelectrolytes, are considered. An expression is derived which relates the flow of a component in the cell‐fixed frame of reference to the flows in any other frame of reference when there is a change of volume on mixing. This relation is used to show that a flow relative to the cell becomes identical to that in the volume‐fixed frame as the initial differences in concentration within the diffusion cell are made sufficiently small. Throughout this article a special effort has been made to present derivations and final equations in a form well adapted for use in experimental work.

## REFERENCES

*Thermodynamics of Irreversible Processes*(Interscience Publishers, Inc., New York, 1951);

*S*relative to the diffusion cell and the velocity, $uRC,$ of frame

*R*relative to the cell by

*N*,

*i*relative to the cell. Because $(ui)C$ must be the same for every component when all the concentration gradients are zero, the equations are readily simplified by using Eqs. (5) and (6) and lead to $uMC\u2009=\u2009u0C\u2009=\u2009uVC\u2009=\u2009(ui)C.$

*T*on $\u2202\mu j/\u2202x$ in Eq. (11a) indicates that these new derivatives are taken at constant temperature but not at constant pressure). To eliminate $X0$ from this revised Eq. (15) the generalized form of Eq. (18) (with the pressure term retained),

*may*be specified in a way so that Eqs. (13) are satisfied (see footnote references 4 and 18).

*necessary*for the $(\Omega ij)M$ to be defined so that they satisfy Eq. (13); it is sufficient that they

*may*be defined so that Eq. (13) is satisfied. This may be shown by starting with the $(\Omega ij)M$ defined so that they satisfy Eq. (13) and then adding $\sigma i$ (footnote 16) to each Eq. (12), using values of $Ki$ such that the $(\Omega \u0302ij)M$ do not exhibit reciprocal relations. After repeating the derivation with these $(\Omega \u0302ij)M$ one finds that in the equation corresponding to Eq. (21) the coefficients of $Ki$ and $K0$ are zero, again giving Eq. (22) as a consequence of $(\Omega ij)M\u2009=\u2009(\Omega ji)M.$

*j*can be expressed in terms of the concentration, $cj,$ and molecular weight, $Mj,$ of that component and an activity coefficient, $yj,$ (which may be a function of all solute concentrations)

*R*is the gas constant per mole and

*T*is the absolute temperature. This activity coefficient, $yj,$ is identical with the activity coefficient associated with the molarity scale of concentration; it is customary to let each $yj$ approach unity as

*all*the solute concentrations approach zero. For a given solvent each reference chemical potential, $\mu jo,$ is a function only of temperature and pressure. By differentiation of Eq. (23a) we see that

*s*, except when all of the salts have a common ionic species.

*M*and 0. Then terms in this relation are summed over all components and Eq. (2) applied to obtain $u0M.$ Substitution of this expression back into Eq. (1) for frames

*M*and 0 gives the relation

*M*could be omitted from the $Rik$ and reciprocal relations for the $(Rik)M$ would correspond directly to Eq. (33). To avoid any uncertainty the subscripts 0 are retained on the $Rik$ in the text.

*The Mathematics of Diffusion*(Oxford University Press, New York, 1956), p. 236 ff.

*The Principles of Chemical Equilibrium*(Cambridge University Press, New York, 1955), Eq. (2.114).