Question

Water undergoes electrolysis to produce hydrogen and oxygen gas at ${14}^{0}C$, with the products collected above water. The vapor pressure of water at ${14}^{0}C$ is $12mmHg$. The total pressure is $740mmHg$.
If the partial pressure of oxygen is $242.7mmHg$, what is the mole fraction of hydrogen gas?

• A. $0.56$
• B. $0.66$
• C. $0.96$
• D. $0.76$

Answer 1

The correct option is B $0.66$

Water undergoes electrolysis to produce hydrogen and oxygen which is given by the reaction-

$H_{2}O$$⟶$$H_2$$+$$O_2$

Dalton's law of partial pressure states that in a mixture of non-reacting gases, the total pressure exerted by the gases is equal to the sum of the partial pressures exerted by individual gases.

The total pressure of the system is $740mm$ $Hg$. The system is at ${14}^{o}C$. The vapor pressure of water is $12mm$ $Hg$

The partial pressure of oxygen is $242.7mm$ $Hg$.

Thus, the partial pressure of Hydrogen is $(740-12-242.7)$, that is $485.3mm$ $Hg$

We know that partial pressure of a gas depends on the mole fraction of the gas by the formula $n\ast P$$=$$p$, where $n$ is the mole fraction of the gas, $P$ is the total pressure and $p$ is the partial pressure of the gas.

Thus, $n\ast 740$$=$$485.3$

Or, $n$$=$$\frac{485.3}{740}$, that is $0.655$ or $0.66$

Thus, mole fraction of Hydrogen gas is $0.66$

Option B is the correct answer.