Question

Henry’s law constant for solubility of ${CH_4}$ is 4.27x10 5 mmHg at constant temperature. Calculate the solubility of ${CH_4}$ at 760 mmHg pressure and at same temperature.

Answer 1

In the given question we have to find out the solubility of the methane gas at given temperature and pressure. We can use Henry's relation which provides a relation between pressure and solubility. As pressure and Henry's constant are given we can easily find solubility.

Complete Step by step answer: Henry's law is defined as the amount of dissolved gas is proportional to its partial pressure in the gas phase and the proportionality factor is called as the Henry's law constant. It is denoted by ${K_H}$.
Mathematically it is expressed as $P = {K_H} \times C$ where,
P =partial pressure of the gas
${K_H}$ =Henry’s law constant of the gas.
C =concentration of the dissolved gas.
It was given by the English chemist William Henry, that's why it is named after him and said as Henry law constant for solubility.
Given that
Pressure (P) =760 mmHg
Solubility?, ${K_H}$ = 4.27x105
According to Henry's Law $P = {K_H}C$
So, $760 = 4.27 \times {10^5} \times C$
$C = \dfrac{{760}}{{4.27 \times {{10}^5}}} = 178 \times {10^{ - 3}}$

So at 760 mmHg pressure and at the same temperature the solubility of ${CH_4}$ is $178 \times {10^{ - 3}}$.

Note: The value of the Henry’s law constant of a gas can vary depending on the following factors such as temperature and pressure, nature of the solvent and mainly the nature of the gas. Therefore we can say that different gases have different Henry’s laws constant values in the different solvents and temperature & pressure. Although the law has some limitations also like the Henry law constant of a gas is applicable only when the molecules of the system are in a state of equilibrium.