Question

The time taken for a given volume of gas E to effuse through a hole is 75 sec. Under identical conditions the same volume of a mix of CO & $N_2$ (containing 40% of $N_2$ by volume) effused in 70 sec. Calculate
(i) the relative mol mass of E, and
(ii) the RMS velocity (in $ms$ units) of E at $0^{\circ }C$.

• A. $32.14g/mol,460.28m/s$
• B. $64.28g/mol,230.14m/s$
• C. $20g/mol,400m/s$
• D. $Noneofthese$

Answer 1

Answer: (A)

$32.14g/mol,460.28m/s$

A mixture. molecular mass of the mixture $=0.4\times 28+0.6\times 28=28$

(i) rate of diffusion $\propto$ $\frac{1}{t}\propto \frac{1}{\sqrt{M}}$

$t\propto \sqrt{M}$

$\frac{75}{70}=\sqrt{\frac{M}{28}}\Rightarrow M=32.1428gm/mole$
(ii) $v=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 8.314\times 273}{32.1428\times {10}^{-3}}}=460.28m/s$
Option A is correct.