Question

For 10 minute each, at 0 ${}^o$C, from two identical holes nitrogen and an unknown gas are leaked into a common vessel of 4 litre capacity. The resulting pressure is 2.8 atm and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknown gas?

• A. $448gmo{l}^{-1}$
• B. $224gmo{l}^{-1}$
• C. $226gmo{l}^{-1}$
• D. None of these

Answer 1

Answer: (A)

$448gmo{l}^{-1}$

$\frac{{}^n{N}_2}{n_x}=\sqrt{\frac{m_x}{M_{N_2}}}.............\left(i\right)$
$P_T{V}_T=n_{T}RT........\left(ii\right)$
$n_T=\frac{2.8\times 4}{0.0821\times 273}=0.5$
$n_x+{{}^{n}N}_2=0.5$

Given, ${{}^{n}N}_2=0.4$. So, $n_x=0.1$

Putting in eq (i), we get
$\frac{0.4}{0.1}=\sqrt{\frac{M_x}{28}};M_x=448.$ $gmo{l}^{-}$