Question

At room temp, $N{H}_3$ gas at one atm and $HCl$ gas at ${}^{\prime }{P}^{\prime }$ atm are allowed to effuse through identical pin holes to the opposite ends of a glass tube $1m$ long and uniform cross-section. A white deposit is observed at a distance of $60cm$ from the $HCl$ end. What is ${}^{\prime }{P}^{\prime }$?

Answer 1

According to Graham's law of effusum the rate gases at same temperature and pressure is mutually proportional to square root of density

$\frac{V_1}{V_2}=\sqrt{\frac{d_2}{d_1}}$

$\frac{d_2}{d_1}=\frac{M_2}{M_1}\Rightarrow \frac{V_1}{V_2}=\sqrt{\frac{M_2}{M_1}}$

If two gases are at different present

$\frac{V_1}{V_2}=\frac{P_1}{P_2}\sqrt{\frac{M_2}{M_1}}$

Tube is $100cm$ long $\left(1m\right)$

Let us suppose white solid is depend after $1$ second

$V_{HCl}=60cm$

$V_{N{H}_3}=40cm/s$

$P_{HCl}=P_{atm}$

$P_{N{H}_3}=1atm$

$M_{HCl}=36.5g$

$M_{N{H}_3}=17g$

$\frac{V_{HCl}}{N_{N{H}_3}}=\frac{P_{HCl}}{P_{N{H}_3}}\sqrt{\frac{M_{N{H}_3}}{M_{HCl}}}$

$\frac{60}{40}=\frac{P}{1}\sqrt{\frac{17}{36.5}}\Rightarrow P=2.19atm$