Question

$0.5$ moles of gas $A$ and $x$ moles of gas $B$ exert a pressure of $200\, Pa$ in a a container of volume $10\, m^3$ at $1000\, K$. given $R$ is the gas constant in $JK^{-1} \; mol^{-1} m, x$ is :

• A. $\frac{2 R}{4 + 12}$
• B. $\frac{2 R}{4 - R}$
• C. $\frac{4 - R}{2 R}$
• D. $\frac{4 + R }{2 R}$

Answer 1

Answer: (C)

$n_T = (0.5 + x)$
$PV = n \times R \times T$
$200 \times 10 = (0.5 + x) \times R \times 1000$
$2 = (0.5 + x) R$
$\frac{2}{R} = \frac{1}{2} + x $
$ \frac{4}{R} - 1 = 2x$
$ \frac{4-R}{2R} =x $