Question

Natural gas is almost entirely methane. A container with a volume of 2.65L holds 0.120mol of methane. What will the volume be if an additional 0.182mol of methane is added to the container under constant temperature and pressure? Give your answer in three significant figures.

Answer 1

The final volume of the methane gas in the container is 6.67 L.

The given parameters;

• initial volume of gas in the container, V₁ = 2.65 L
• initial number of moles of gas, n₁ = 0.12 mol
• additional concentration, n = 0.182 mol

The total number of moles of gas in the container is calculated as follows;

$n_t = 0.12 + 0.182 = 0.302 \ mol$

The final volume of gas in the container is calculated as follows;

$PV = nRT\\\\\frac{V}{n} = \frac{RT}{P} \\\\\frac{V_1}{n_1} = \frac{V_2}{n_2} \\\\V_2 = \frac{V_1 n_2}{n_1} \\\\V_2 = \frac{2.65 \times 0.302}{0.12} \\\\V_2 = 6.67 \ L$

Thus, the final volume of the methane gas in the container is 6.67 L.

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