Question

$100{cm}^3$ of ${NH}_3$ diffuses through a pin hole in $32.5$ second. How much time(in seconds) will $60cc$ of $N_2$ take to diffuse under same condition?

Answer 1

${\gamma }_{{NH}_3}=\frac{V_{{NH}_3}}{t_{{NH}_3}}{\gamma }_{N_2}=\frac{V_{N_2}}{t_{N_2}}⟹\frac{{\gamma }_{{NH}_3}}{{\gamma }_{N_2}}=\frac{V_{{NH}_3}\cdot t_{N_2}}{t_{{NH}_3}\cdot V_{N_2}}⟹\frac{\sqrt{M_{N_2}}}{\sqrt{M_{{NH}_3}}}=\frac{V_{{NH}_3}\cdot t_{N_2}}{t_{{NH}_3}\cdot V_{N_2}}⟹\frac{\sqrt{28}}{\sqrt{17}}=\frac{100\cdot t_{N_2}}{32.5\times 600}⟹t_{N_2}=250.4sec$