Equal weights of methane and hydrogen are mixed in an empty container at 25°C. The fraction of the total pressure exerted by hydrogen is

Question

Equal weights of methane and hydrogen are mixed in an empty container at 25°C. The fraction of the total pressure exerted by hydrogen is

(a) 1/2 (b) 8/9 (c) 1/9 (d) 16/17

Answer 1

Correct optlon (b) \(8 / 9\)
Explanation:
Let the weight be w g.
Thus. moles of \(\mathrm{H}_{2}=w / 2\) and motes of \(\mathrm{CH}_{4}=w / 16\)
Total number of moles \(=w / 2-w / 16=9 w / 16\)
Partial pressure of \(\mathrm{H}_{2}=\) total pressure \(\mathrm{x}\) mole fraction of \(\mathrm{H}_{2}\)
$$
\begin{aligned}
&=p \times \frac{w / 2}{9 w / 16}=p \times \frac{w}{2} \times \frac{16}{9 w} \\
&=p \times \frac{8}{9}
\end{aligned}
$$
Hence, the fraction of the total pressure exerted by \(\mathrm{H}_{2}=8 / 9\).