# When do you use Henry's law and when do you use Raoult's law?

Feb 3, 2016

$C = K P$

#### Explanation:

Henry's law gives a relationship between the solubility of gases in liquids and their corresponding pressure above the solution. It is given by:

$C = K P$,

where $C$ is the concentration of gas in the liquid,

$P$ is the pressure of the gas above the liquid and

$K$ is Henry's constant.

Therefore, the solubility of the gas is proportional to its pressure above the liquid. When the pressure increases, the solubility increases and vice versa.

$\textcolor{g r e y}{\text{Image source: Zumdahl textbook}}$

Feb 3, 2016

Henry's law and Raoult's law generally are associated with the vapor pressures of the pure solution, of the solution with stuff in it, and of the mole fraction of stuff in the would-be pure solution.

• Henry's law works best at low concentration of the solute (close to 5% or less).
• Raoult's law works best at non-low concentration of the solute (10 - 50% or so).

This is all in the context of a liquid-vapor equilibrium, i.e. the process of vaporization.

For ideal binary mixtures, it helps to compare Henry's law with Raoult's law.

For Raoult's law, the vapor pressure ${P}_{j}$ above the solution is related to the mole fraction ${\chi}_{j}$ of component $j$ at the liquid-vapor interface, and the vapor pressure of the pure solution (as if no minor component is in the major component), ${P}_{j}^{\text{*}}$:

$\setminus m a t h b f \left({P}_{j} = {\chi}_{j} {P}_{j}^{\text{*}}\right)$

$\textcolor{b l u e}{{\lim}_{{\chi}_{j} \to 1} \frac{{P}_{j}}{{\chi}_{j}} = {P}_{j}^{\text{*}}}$

As ${\chi}_{j}$ approaches $1$, there is more of the minor component at the liquid-vapor interface, the minor component vaporizes more easily out of solution, and the solution becomes more and more pure (as if the mixture is comprised of ONE component only).

For Henry's law, the vapor pressure ${P}_{j}$ above the solution is related to the mole fraction ${\chi}_{j}$ of component $j$ at the liquid-vapor interface, and the Henry's Law constant ${k}_{H , j}$:

$\setminus m a t h b f \left({P}_{j} = {\chi}_{j} {k}_{H , j}\right)$

$\textcolor{b l u e}{{\lim}_{{\chi}_{j} \to 0} \frac{{P}_{j}}{{\chi}_{j}} = {k}_{H , j}}$

So as ${\chi}_{j}$ approaches $0$, the mole fraction of $j$ at the liquid-vapor interface is low, so the minor component is not reaching the surface well and the Henry's law constant is high.

Therefore, a low mole fraction ${\chi}_{j}$ of component $j$ at the liquid-vapor interface means a higher Henry's law constant, which means that the major component is greatly surrounding the minor component, and the minor component is having a hard time vaporizing.