Question

Consider a tube that has a frilled disk sealed in its centre so that gases can effuse through it in both directions. If the left hand side contains $H_2$ at a pressure $P$ and temperature $T$ and the right hand side contains $He$ at a pressure $2P$ and temperature $T$, then initial ratio of rate of effusion is:

• A. $0.71$
• B. $1.00$
• C. $1.41$
• D. $0.50$

Answer 1

The correct option is A $0.71$

According to the ratio of rate of effusion,
$\frac{r_{H_2}}{r_{He}}=\frac{P_{H_2}}{P_{He}}\sqrt{\frac{M_{He}}{M_{H_2}}}$
Given, $P_{H_2}$ = P and $P_{He}$ = 2P
Molar mass of $H_2$ = 2 g/mol and $He$ = 4 g/mol
Put up the values in the formula
i.e $\frac{r_{H_2}}{r_{He}}=\frac{P}{2P}\sqrt{\frac{4}{2}}$
$\Rightarrow$ $\frac{r_{H_2}}{r_{He}}=0.707$

Theory:

Diffusion:

Net spontaneous flow of gaseous molecules from a region of higher concentration $\left(\frac{n}{V}\right)$ to a region of lower concentration. Similarly higher partial pressure to lower partial pressure

$P=\left(\frac{n}{V}\right)RT$

Effusion:

Gas escaping or passing through a small orifice (hole) is called effusion.

Graham’s Law of Diffusion / Effusion:

Rate of diffusion or effusion of different gases is inversely proportional to square root of the density of different gases. Under the same conditions of $T$ and $P$ (partial pressure).