The final volume of the methane gas in the container is 6.67 L.
The given parameters;
- initial volume of gas in the container, Vā = 2.65 L
- initial number of moles of gas, nā = 0.12 mol
- additional concentration, n = 0.182 mol
The total number of moles of gas in the container is calculated as follows;
[tex]n_t = 0.12 + 0.182 = 0.302 \ mol[/tex]
The final volume of gas in the container is calculated as follows;
[tex]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[/tex]
Thus, the final volume of the methane gas in the container is 6.67 L.
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