Question

At room temperature, $N{H}_3$ gas at 1atm and HCl gas at P atm are allowed to effuse through identical pin holes from opposite ends of a glass tube of 1 metre length and of uniform cross-section. $N{H}_{4}Cl$ is first formed at a distance of 60 cm from the end through which HCl gas is sent in. What is the value of P? (in atm as nearest integer)

Answer 1

Let HCl and $N{H}_3$ are diffused at pressure P and 1 atm respectively

$\therefore \frac{r_{N{H}_3}}{r_{HCl}}=\sqrt{\frac{M_{HCl}}{M_{N{H}_3}}}\times \frac{P_{N{H}_3}}{P_{HCl}}$

Given $r_{N{H}_3}=\frac{d_{N{H}_3}}{t_{N{H}_3}}=\frac{40}{t}(\because d=40cm,t=tsec)$

$r_{HCl}=\frac{d_{HCl}}{t_{HCl}}=\frac{60}{t}(\because d=60cm,t=tsec)$
$\therefore \frac{40}{t}\times \frac{t}{60}=\sqrt{\frac{36.5}{17}}\times \frac{1}{P}$

$P=2.198atm$

so the value of integer part is 2.