Question

Two vessels having equal volumes contain $H_2$ and $He$ at $1$ and $2atm$ respectively at same temperature. Then which one is/are correct:
$\left(i\right)$ $U_{rms}{H}_2=U_{rms}He$
$\left(ii\right)$ $r_{H_2}=\frac{r_{He}}{\sqrt{2}}$
$\left(iii\right)$ $U_{rms}{H}_2=\sqrt{2}{U}_{rms}He$
$\left(iv\right)$ $r_{H_2}=\sqrt{8}\times r_{He}$

• A. $i,ii,iii$
• B. $ii,iii$
• C. $i,iv$
• D. $iii,iv$

Answer 1

The correct option is B $ii,iii$

As we know,
$RMS$ speed is:
$U=\sqrt{\frac{3RT}{M}}$
$\frac{U_{H_2}}{U_{He}}=\sqrt{\frac{M_{He}}{M_{H_2}}}=\sqrt{\frac{4}{2}}=\sqrt{2}$

$U_{rms}{H}_2=\sqrt{2}{U}_{rms}He$

And diffusion rate is:

$\frac{r_{H_2}}{r_{He}}=\sqrt{\frac{M_{He}}{M_{H_2}}}\times \frac{P_{H_2}}{P_{He}}=\sqrt{\frac{4}{2}}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$

$r_{H_2}=\frac{r_{He}}{\sqrt{2}}$