States of Matter 1 Question 9
9. $\quad 0.5$ moles of gas $A$ and $x$ moles of gas $B$ exert a pressure of 200 $\mathrm{Pa}$ in a container of volume $10 \mathrm{~m}^{3}$ at $1000 \mathrm{~K}$. Given $R$ is the gas constant in $\mathrm{JK}^{-1} \mathrm{~mol}^{-1}, x$ is
(2019 Main, 9 Jan I)
(a) $\frac{2 R}{4-R}$
(b) $\frac{4-R}{2 R}$
(c) $\frac{4+R}{2 R}$
(d) $\frac{2 R}{4+R}$
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Solution:
- From the ideal gas equation,
$$ p V=\Sigma n R T $$
Given: $p=200 \mathrm{~Pa}, V=10 \mathrm{~m}^{3}, T=1000 \mathrm{~K}$
$$ n_{A}=0.5 \text { moles, } n_{B}=x \text { moles } $$
On substituting the given values in equation (i), we get
$$ \begin{aligned} 200 \times 10 & =\left(n_{A}+n_{B}\right) \times R \times 1000 \
