# The heterogeneous equilibrium

## A vapour in contact with the pure solid (or liquid)

### Experiment

Two test tubes contain different quantities of iodine .
We have a solid phase where iodine is pure and a gas phase. The system is heterogeneous.
The two tubes are put at the same temperature:

The intensity of coloration in the gas phase (therefore the partial pressure of iodine) seams to be the same.

### Interpretation

As iodine is alone in the lower solid phase, its concentration $c=[I_2(s)]$ is constant therein.
We apply the law of mass action:
$\frac{[I_2(g)]}{[I_2(s)]}$ $=$ $K$
$\frac{[I_2(g)]}{c}$ $=$ $K$
$[I_2(g)]$ = $K\cdot c $
Using the ideal gas law, let us examine the partial pressures of iodine in the gas phase :
$P_{I_2(g)}$ $= $ $[I_2(g)]\cdot R\cdot T$
$P_{I_2(g)}$ $= $ $K \cdot c \cdot R\cdot T$
A new constant is found as a product of four constants:
$P_{I_2(g)}$ $= $ $K_{sat}$

### Generalization

When a substance $X$ is in equilibrium between gaseous phase and a pure liquid or solid phase , and when it stays pure in the last phase, its partial pressure in the gaseous phase is constant at a given temperature when equilibrium is attained:
$P_X(g)$ $=$ $K_{sat}$
$K_{sat}$ is a constant at a given temperature called ** saturation vapour pressure** of substance X in the gaseous phase.