Topics in Thermodynamics of Solutions and Liquid Mixtures

1.2: Acquisitive Convention

This convention refers to the sign associated with communication between a system and its surroundings. The convention describes changes as seen from the standpoint of the system. The convention guides chemists concerning the ‘sign’ of changes in thermodynamic variables

00for a given system. For example, if heat q flows from the surroundings into a system, q is positive. If thermodynamic energy U is lost by a system to the surroundings, ΔU is negative. In fact this convention is intuitively attractive to chemists. For example, when told that the volume of a system increases during a given process, then chemists conclude that the volume of the surroundings (i.e. the rest of the universe!) decreases.

Classically, the colligative properties of non-ionic solutions were used to determine the molar mass of solutes. For example, the depression of the freezing point of water at a given molalilty of solute- yields an estimate of the relative molar mass of the solute . Key thermodynamic assumptions require that (a) on cooling only pure solvent separates out as the solid phase and (b) the thermodynamic properties of the solution are ideal. The key relationship emerges from the Schroder- van Laar equation [1]. The common assumption is that the thermodynamic properties of the solution are ideal. If the properties of a given aqueous solutions are determined to a significant extent by solute-solute interactions, a measured relative molar mass will be in error. Indeed McGlashan[2] was dismissive of the procedures based on Beckmann’s apparatus for the determination of the relative molar mass of solute using freezing point measurements. The chemical potential of water in an aqueous solution, at temperature and pressure (assumed to be close to the standard pressure, ) is related to the molality of solute , using equation (a) where is the gas constant, is the practical osmotic coefficient and is the molar mass of water, where is the chemical potential of water( ) at the same T and P.

Hence for a solution having thermodynamic properties which are ideal, is a linear function of molality , the plot having slope, . Equation (d) forms a reference for a consideration of the properties of real solutions. For a solution having thermodynamic properties which are ideal, the solvent, water in an aqueous solution is at a lower chemical potential than the pure liquid. This observation is at the heart of the terms ‘depression of freezing point’ and ‘elevation of boiling point’. In the event that the thermodynamic properties of a given solution are not ideal then the form of the plot showing as a function of molality is determined by which is, in turn, a function of . The dependence of on for a given solute in aqueous solutions (at fixed and ) is not defined ‘a priori’.