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Physical Chemistry 70

since A is a pure liquid. Thus the vapor pressure of the gas, p A (in atmospheres), gives the
value of the equilibrium constant directly. This is also the case for a system which
sublimes (transforms directly from a pure solid to a gas). For a system where a species is
soluble in two immiscible liquid phases, i.e. where A partitions between
liquid 1 (l1) and liquid 2 (l2), the equilibrium constant for the partitioning process is:

where c A,l2 and c A,l1 are the concentrations of A in the liquids l2 and l1 respectively if
γ A,l1=γ A,l2. This equilibrium constant is termed a partition coefficient.

Thermodynamic data from K

Given that (see Topic B6).

then values can be determined at any T if can be obtained. Combining these

expressions, , and for a small change in temperature,
dT, both and can be assumed to be independent of T. Therefore at constant
pressure:

This equation is called the van’t Hoff equation and allows to be measured at any
temperature, T. This is done by using the small changes in the concentrations and
pressures of the species in equilibrium to calculate the small change in lnK, dlnK, when T
is changed by a small amount dT from T to (T+dT).
Often, and show little variation over a much wider temperature range. In
this case the equation:

can be used to determine , where K T1 and K T2 are the equilibrium constants
measured at any two temperatures, T 1 and T 2 respectively, within this range.