Page 112 - Instant notes

Physical chemistry 98

substance whose molecular mass is unknown. Addition of a given mass of this substance
as B to a solvent to form an ideal-dilute solution allows the determination of a colligative
property to obtain x B, molality m B or concentration c B. Using the number of moles,
volume or mass of the solvent (all of which are related) respectively then enables the
determination of the number of moles of B added. This, in conjunction with the added
mass of B, allows the molar mass (or mass of one mole) of B to be determined.

Depression of solvent freezing point

For the equilibrium corresponding to the physical transition of A between solid and
liquid:

the activity of the solvent A in the liquid is given by a A=x A (see Topic D1). This means
that the small amount of the solute, B, added in an ideal-dilute solution affects this
activity. Equilibrium is established only at the freezing temperature or freezing point
(which is the same as the melting temperature or melting point) of A. Below this
temperature, all of the liquid A has frozen and A is only present as solid; above this
temperature, all the solid A has melted and only liquid A is present. At the equilibrium
temperature, the change in Gibbs free energy and hence the equilibrium constant, K, for
the reaction is dominated by A (as there is a minute amount of B present) and is given by
K=x A, as pure solid A has an activity of 1 (see Topic C1).
The temperature variation of this equilibrium constant is given by the van’t Hoff
equation (see Topic C1):

where is the standard enthalpy of fusion (the enthalpy required to melt a mole of
solid A under standard conditions). For pure liquid A, K T2=x A=1 and , the
freezing point of pure liquid A, whereas when B is added, K T1=x A and T 1=T f, the new
freezing point. Therefore:

which gives