Question

Given a mixture with $0.5\mathrm{mole}$ of gas $\mathrm{A}$ and $\mathrm{Xmoles}$ of gas $\mathrm{B}$.Total pressure is $200\mathrm{pa}$at $1000\mathrm{k}$ temperature in a vessel of volume $10{\mathrm{cm}}^3.$Then, find $\mathrm{x},(\mathrm{R}\mathrm{is}\mathrm{universal}\mathrm{gas}\mathrm{constant}).$

• A. $\left(4-\mathrm{R}\right)/2R$
• B. $\left(4+\mathrm{R}\right)/2R$
• C. $\left(2-\mathrm{R}\right)/2R$
• D. $2/2$

Answer 1

The correct option is A

$\left(4-\mathrm{R}\right)/2R$

Answer:(A)

From ideal gas equation,

$\mathrm{PV}=\mathrm{nRT}$

$$\begin{gathered} \mathrm{P}=\mathrm{Total}\mathrm{pressure} \\ \mathrm{V}=\mathrm{Volume} \\ \mathrm{n}=\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{moles} \\ \mathrm{R}=\mathrm{Universal}\mathrm{gas}\mathrm{constant} \end{gathered}$$

Given that,

$$\begin{gathered} \mathrm{n}=;\mathrm{A}\to 0.5,\mathrm{B}\to \mathrm{x} \\ =(0.5+\mathrm{x});\mathrm{T}=1000\mathrm{k};\mathrm{V}=10{\mathrm{cm}}^3;\mathrm{P}=2000\mathrm{pa} \end{gathered}$$

$$\begin{gathered} 200\mathrm{Pa}\times 10{\mathrm{cm}}^3=\left(0.5+\mathrm{x}\right)\mathrm{R}\times 1000\mathrm{K} \\ \frac{2}{\mathrm{R}}=\frac{1}{2}+\mathrm{x}=\frac{2}{\mathrm{R}}-\frac{1}{2}=\mathrm{x} \\ =\frac{4-\mathrm{R}}{2\mathrm{R}}=\mathrm{x} \end{gathered}$$

Hence (A) is the correct option.