Question

For a given gas , predict the relationship between $K_{H_1},K_{H_2},K_{H_3}$ from the given graph.
(where $K_H$ is henry's law constant)

• A. $K_{H_1}>K_{H_2}>K_{H_3}$
• B. $K_{H_1}<K_{H_2}<K_{H_3}$
• C. $K_{H_1}<K_{H_2}>K_{H_3}$
• D. $K_{H_1}=K_{H_2}=K_{H_3}$

Answer 1

The correct option is A $K_{H_1}>K_{H_2}>K_{H_3}$

Henry's law states that the solubility of a gas in a liquid at a given temperature is directly proportional to its partial pressure of the gas present above the solution.

$P=K_H𝓧............\left(eq\right(i\left)\right)$

Where P is the partial pressure​ of gas over the solution, $K_H$ is Henry’s law constant​ and 𝓧 is mole fraction of the​ gas in the solution.


From the above graph we can see that at a given partial pressure, ${\chi }_3>{\chi }_2>{\chi }_1$
so, $T_1>T_2>T_3$
and
From equation (i) :
If mole fraction is more at a given partial pressure then, value of henry's law constant will be less.
So, at a given partial pressure
$\chi \propto \frac{1}{K_H}$
Hence,
$K_{H_1}>K_{H_2}>K_{H_3}$
The correct answer is option (c).

Alternatively,
The slope of the graph gives the value of Henry's law constant.
Slope for graph having $T_1$ temperature is greater than $T_2$ followed by $T_3$:
Hence,
$K_{H_1}>K_{H_2}>K_{H_3}$