Intermolecular Interactions in Ternary Glycerol–Sample–H2O: Towards Understanding the Hofmeister Series (V)

Partial molar quantity of an intensive mother function

A new formal definition is given to the partial molar quantity of a component i for an intensive mother function. We perturb the entire system by increasing the amount of the target component by δn(i) keeping others constant and measure the response of the system in terms of an intensive mother function, Φ, δΦ. We then define its partial molar quantity of the ith component, φ(i), as φ(i) = [δΦ∕{δn(i)∕(N + δn(i))]] in the limit of δn(i) → 0. Thus, the physical meaning of φ(i) is the effect of the ith component (only) on Φ of the system, just as the partial molar quantity for an extensive mother function. This new formal definition could serve as a starting point for statistical mechanics development of a microscopic connection to the third derivatives of G. We show a number of examples such as an enthalpic inter-solute interaction, a partial molar S-V cross fluctuation density of solute, their analogues, and an excess partial molar absorptivity of solute. These examples were used for studying the nature of aqueous solutions without realizing their formal definition and were instrumental in advancing our understandings.