Gas-Phase Equilibria: Mixed-Phase Equilibria

James Richard Fromm

Mixed-phase equilibria are those in which solids, liquids, and gases may be involved. The gases in mixed-phase equilibria are treated just as they are in gaseous equilibria, with replacement of activities by partial pressures. Pure solids and liquids are treated differently, since their mass per unit volume is essentially constant, and it is usually replaced by unity. The value of unity is actually the ratio of the actual activity of the pure element or compound to its activity in its standard state at 25oC and one atmosphere pressure, which is very close to one.

Example. The equilibrium constant for the equilibrium:

NH3(g) + HCl(g) NH4Cl(s)

is K = 1/p(NH3)p(HCl), where K has the units kPa-2 or atm-2. The solid NH4Cl is taken as having an activity of unity, and as having no nominal units.

Example. The equilibrium constant for the reaction:

4Al(s) + 3O2(g) 2Al2O3(s)

is K = a2(Al2O3)/a4(Al)a3(O2), or K = 1/p3(O2). The activities of aluminum and aluminum (III) oxide are taken as unity since both are present as pure solids.

Example. The equilibrium constant for the reaction:

H3O+(aq) + HCO3-(aq) H2O + CO2(g)

is K = a(H2O)a(CO2) /a(H3O+)a(HCO3-). Here a(H2O) is approximately constant in a dilute solution of the ions in water, so we rearrange:

K/a(H2O) = K' = a(CO2(g))/a(H3O+)a(HCO3-)

K' = a(CO2(g))/a(H3O+)a(HCO3-); K' = p(CO2(g))/a(H3O+)a(HCO3-)

K' = p(CO2(g))/[H3O+][HCO3-]

In the last example, the square bracket notation is used to indicate the molar concentration of each of these ions. This is a common notation and one we shall be using frequently.