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ION–SOLVENT INTERACTIONS 129
where is the free volume available to the ion in solution described in Section
2.15.11. Therefore, the entropy of translation is
Also,
where and are the free volumes of solution, salt, and water,
respectively, and is the mole fraction of the salt. Equation (2.94) can be rearranged
as
and a plot of vs. can then be used to calculate
The can be calculated from the velocity of sound by the expression
where is the velocity in the gas phase given by kinetic theory,
is the velocity of sound in solution, is the molar volume of the solution,
and M is the molecular weight. Equation (2.96) at 298.16 K becomes upon
substitution of appropriate values:
The molar volume of a binary solution is given by
where and are the weight fraction and molar weight of the ith component,
respectively, and is the density of the solution. For example, for NaCl, Eq. (2.98)
reduces to
