Page 82 - Instant notes

Physical Chemistry 68

K in concentrations

The activity, a i, given by:

−3
where c i is the concentration of a species, i, in mol dm (see Topic D1), is the
−3
standard concentration of 1 mol dm and γ i is the activity coefficient of the species. The
activity therefore depends on the species concentration, but this is modified by the
activity coefficient γ i, which takes account of the (usually attractive) interactions
between species, which can stabilize them by reducing their free energy. The activity
coefficient itself depends on concentration, as at a higher concentration, species are closer
together and tend to interact more. This is an extra complication when determining an
equilibrium constant from the concentrations of reagents and products. In many cases this
complication can be avoided, as for neutral molecules, both in the gas phase and in
solution, the intermolecular forces are relatively weak and short-range, and can be
neglected at all practical concentrations. This is also the case for ions (which are charged
chemical species, see Topic E1) at low solution concentrations (typically of the order of
−4
−3
10 mol dm and below), when the ions are sufficiently separated in solution that the
electrostatic interactions between them can be neglected (see Topics E1 and E2).
Under these conditions of negligible interaction, γ i can be assumed to be unity for all
species and by substituting concentration for activities, the equilibrium constant for the
reaction:

where c i is the concentration of species i (see Topic D1). In this general case, the value
of the equilibrium constant for the reaction is therefore simply found by combining the
−3
concentrations of the reactants and products (in units of mol dm ) at equilibrium,
producing a dimensionless equilibrium constant.
However, the activity coefficients cannot be approximated to unity for ions at higher
concentrations, as the electrostatic forces between them become important (see Topics E1
to E4 and C5).

Gases, solids and pure liquids

When the equilibrium reaction involves gases, it is more convenient to measure the
amount of these species by their partial pressures (see Topic D2). The activity of a gas, i
(often called its fugacity) is given by: