Question

How come the higher the value of Henry’s Law constant, the lower is the solubility of a gas in a liquid?

Answer 1

Hint: It is given that the higher the value of Henry’s Law constant, the lower is the solubility of the gas. This can be explained by using the equation of the Henry’s Law standard state of the binary mixture where the activity of the solute is related with the mole fraction.

Complete step by step answer:
The relation between the Henry’s Law constant and the solubility of the gas in a liquid is given by Henry's law.
The Henry’s Law is given by English physician and chemist, William Henry.
The Henry’s law is given as shown below
$C = k_P$
Where,
C is the concentration of the dissolved gas at the equilibrium
K is the Henry’s law constant
P is the partial pressure of the gas
The unit of Henry’s law constant is mol/(L.atm)
The Henry’s Law standard state of the binary mixture is given by the equation shown below.
${a_{2x}} = \dfrac{{{P_2}}}{{{K_H},x}}$
Where,
${a_{2x}}$ is the activity of the solute related to the mole fraction.
The mole fraction is given as
${x_2} = \dfrac{{{n_2}}}{{{n_1} + {n_2}}}$
Where,
${x_2}$ is the mole fraction of solvent
${n_1}$ is the number of moles of solute
${n_2}$ is the number of moles of solvent
As, ${x_2} \to 0$, ${a_{2X}} \to {x_2}$ which means that the smaller is the amount of solute, the mole fraction is used instead of activity to explain the amount of solute in the solution.
${P_2}$ is the vapour pressure of the solute
${K_{H,x}}$ is the Henry’s Law constant on the mole fraction scale ${x_2} \to 0$ also we know ${P_2} \to {K_{H,x}}{x_2}$
We know that for a specific solute, the vapour pressure ${P_2}$ is specific for the solute’s identity at a particular temperature. When we’ll have the same solute at the same temperature, the ${P_2}$ will not change.
As the mole fraction is the amount of solute dissolved in the solution, as ${x_2} \to 0$, so ${a_{2x}} \to {x_2}$ which means $a_{2x} \to 0$. Therefore, the solubility decreases as the Henry’s law constant increases.

Note:
There are many applications of Henry’s Law of constant in daily life. The Henry’s Law is applied when we open the bottle of carbonated drink and as a result the bubbles are formed. This is due to the fact that when the bottle is opened the pressure of the carbon dioxide above the solution drops and the dissolved gas escapes in the form of bubbles.