JEE Advance - Chemistry (1982 - No. 16)

If t is the time taken for the formation of ammonium chloride by the combination of NH₃ and HCl, then

$${r_{HCl}} = {{60} \over t}$$ ; $${r_{N{H_3}}} = {{40} \over t}$$

The rate of diffusion, r is proportional to the root mean square velocity (u) which is equal to $$\sqrt {{{3P} \over d}} $$.

$$r \propto u \propto {{{3P} \over d}} $$

$$\therefore$$ $${{{r_{HCl}}} \over {{r_{N{H_3}}}}} = {{60/t} \over {40/t}} = {{\sqrt {{{3{P_{HCl}}} \over {{d_{HCl}}}}} } \over {\sqrt {{{3{P_{N{H_3}}}} \over {{d_{N{H_3}}}}}} }}$$

or $${{60} \over {40}} = {{\sqrt {{{3{P_{HCl}}} \over {18.25}}} } \over {\sqrt {{{3 \times 1\,atm} \over {8.5}}} }}$$

or $${\left( {{{60} \over {40}}} \right)^2} = {{3{P_{HCl}}} \over {18.25}} \times {{8.5} \over {3\,atm}}$$

or $${P_{HCl}} = {{60 \times 60} \over {40 \times 40}} \times {{18.25} \over {8.5}}$$ atm = 4.83 atm