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 having the units $J{K}^{-}1mo{l}^{-}1$. $X$ is :

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

Answer 1

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

The total number of moles '$n$' = $(0.5+X)$

$PV=nRT$

$n=\frac{PV}{RT}$

$(0.5+X)=\frac{200\times 10}{1000\times R}$

$(0.5+X)=\frac{2}{R}$

$X=\frac{2}{R}-\frac{1}{2}$

$X=\frac{4-R}{2R}$