A rigid container holds a gas mixture containing 4.0\text{ g} of methane (\text{CH}_4) and… — JAMB UTME

A rigid container holds a gas mixture containing $4.0\text{ g}$ of methane ( $\text{CH}_4$ ) and $14.0\text{ g}$ of nitrogen ( $\text{N}_2$ ). If the partial pressure exerted by methane in the mixture is $125\text{ kPa}$ , what is the total pressure of the gas mixture in $\text{kPa}$ ? [Relative atomic masses: $\text{H} = 1$ , $\text{C} = 12$ , $\text{N} = 14$ ]

Answer: 375 kPa

Answer

The total pressure of the gas mixture is

375\text{ kPa}

The total pressure of

375\text{ kPa}

is determined by calculating the moles of methane (

0.25\text{ mol}

) and nitrogen (

0.50\text{ mol}

), giving a total of

0.75\text{ mol}

. Methane constitutes one-third (

1/3

) of the total moles, so its partial pressure is one-third of the total pressure. Dividing the partial pressure of methane (

125\text{ kPa}

) by its mole fraction (

1/3

) yields a total pressure of

375\text{ kPa}

Step-by-Step Solution

Calculate the amount of moles of each gas present in the mixture.

n_{\text{CH}_4} = \frac{4.0\text{ g}}{16\text{ g/mol}} = 0.25\text{ mol}

and

n_{\text{N}_2} = \frac{14.0\text{ g}}{28\text{ g/mol}} = 0.50\text{ mol}

Molar masses are determined from relative atomic masses:

\text{CH}_4 = 12 + 4(1) = 16\text{ g/mol}

and

\text{N}_2 = 2(14) = 28\text{ g/mol}

Calculate total moles and the mole fraction of methane.

n_{\text{total}} = 0.25 + 0.50 = 0.75\text{ mol}

;

X_{\text{CH}_4} = \frac{0.25\text{ mol}}{0.75\text{ mol}} = \frac{1}{3}

Mole fraction is the ratio of the number of moles of a specific gas component to the total number of moles in the gas mixture.

Apply Dalton's Law of Partial Pressures to find total pressure.

P_{\text{total}} = \frac{P_{\text{CH}_4}}{X_{\text{CH}_4}} = \frac{125\text{ kPa}}{1/3} = 375\text{ kPa}

According to Dalton's Law, the partial pressure of a gas is equal to its mole fraction multiplied by the total pressure (

P_i = X_i \times P_{\text{total}}

Key Concept

Dalton's Law of Partial Pressures and Mole Fraction

Estimated Time:1m 30s

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