Question

A mixture of carbon dioxide and hydrogen gases contains carbon dioxide at a partial pressure of 401 mm Hg and hydrogen at a partial pressure of 224 mm Hg. What is the mole fraction of each gas in the mixture?

Answer 1

Answer:

$X_{H_2}=\0.3584$

$X_{CO_2}=\0.6416$

Explanation:

According to the Dalton's law of partial pressure, the total pressure of the gaseous mixture is equal to the sum of the pressure of the individual gases.

Partial pressure of carbon dioxide = 401 mmHg

Partial pressure of hydrogen gas = 224 mmHg

Total pressure,P = sum of the partial pressure  of the gases = 401 + 224 mmHg = 625 mmHg

Also, the partial pressure of the gas is equal to the product of the mole fraction and total pressure.

So,

$P_{CO_2}=X_{CO_2}\times P$

$X_{CO_2}=\frac{P_{CO_2}}{P}$

$X_{CO_2}=\frac{401\ mmHg}{625\ mmHg}$

$X_{CO_2}=\0.6416$

Similarly,

$X_{H_2}=\frac{P_{H_2}}{P}$

$X_{H_2}=\frac{224\ mmHg}{625\ mmHg}$

$X_{H_2}=\0.3584$