1.10 Henry's law
Let's have a look again at the pressure-composition diagram for binary systems.
As we said before, in real systems (e.g the green curves in the above figure) we can still use Raoult's law, but only at the higher range of compositions, since the linear behaviour coincides with the tangent to the curve (see Raoult's law).
For xi << 1, Raoult's law is not valid anymore; in this case the Henry's law can be applied.
The Henry's law states that:
The partial pressure of component i in the gas phase is proportional to its mole fraction in the liquid phase. The constant of proportionality is the Henry's constant (H).
Pi = H xi
The Henry's constant can be seen as the vapor pressure of the pure compound at infinite dilution.
As shown in the diagram below, the real behaviour of a liquid-vapor system is well approximated with the linear correlation of Henry's law at very low concentration of solute A, when the Henry's line is tangent to the real curve.
Applying Dalton's law to the first member of Henry's law and rearranging leads to:
yi = [Hi / P] xi
[Hi / P] = mi
For binary systems, the x-y composition diagram is shown here below. m is the slope of the equilibrium line:
As examples, the equilibrium line for the most common gases which follow the Henry's law is here reported.
The Henry's constant depends on the temperature according to the following correlation:
Hi [T] = Ho exp [- E / (RT)]
E = activation energy
R = constant of ideal gas
T = temperature
(1) indicates that Hi increases as the temperature increases.
Just to give you an anticipation of how the thermodynamics strongly impact on the feasibility of the unit operations, we can make the following consideration:
Having small values of the slope mi of the equilibrium line means that the solute is thermodynamically more "willing" to stay in the liquid phase than in the vapor one. This is very important when, e.g. in the case of the Absorption operation, the purpose is to transfer the solute from the vapor into the liquid phase.
For this reason the absorption is favoured at low temperatures and high pressures.