Question

$0.5$ moles of gas $A$ and $x$ moles of gas $B$ exert a pressure of $200Pa$ in a container of volume $10m^3$ at $1000K$. Given $R$ is the gas constant in $J{K}^{-1}mo{l}^{-1}$, then $x$ is:

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

Answer 1

The correct option is C $\frac{4-R}{2R}$

Number of moles $n_1$ of gas $A=0.5$
Number of moles $n_2$ of gas $B=x$
Pressure $\left(P\right)=200$ $Pa$
Volume $\left(V\right)=$ $10m^3$
Temprature $\left(T\right)=1000K$
We know that
$PV=nRT$
Total number of moles $n=n_1+n_2=0.5+x$
$200\times 10=(0.5+x)R\times 1000$
$\Rightarrow (0.5+x)R=\frac{2000}{1000}=2$
$\Rightarrow 0.5+x=\frac{2}{R}$
$\Rightarrow x=\frac{2}{R}-\frac{1}{2}=\frac{4-R}{2R}$
$\therefore x=\frac{4-R}{2R}$