Question

In the synthesis of ammonia from nitrogen and hydrogen gases, if $6\times {10}^{-2}$ mol of hydrogen disappears in $10\text{min}$, the number of moles of ammonia formed in $0.3$ minutes is:

• A. $1.8\times {10}^{-2}\text{mol}$
• B. $1.2\times {10}^{-4}\text{mol}$
• C. $4\times {10}^{-4}\text{mol}$
• D. $3.6\times {10}^{-2}\text{mol}$

Answer 1

The correct option is B $1.2\times {10}^{-4}\text{mol}$

$N_2+3H_2\to 2N{H}_3$
$\text{Rate}=\frac{-d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=+\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$

Rate of disappearance of $H_2$,
$i.e.\frac{-d\left(H_2\right)}{dt}=\frac{6\times {10}^{-2}}{10}=6\times {10}^{-3}\text{mol/min}$

Rate of formation of $N{H}_3$:
$i.e.\frac{d\left(N{H}_3\right)}{dt}=\frac{2}{3}\left[\frac{-d\left(H_2\right)}{dt}\right]=\frac{2}{3}\times 6\times {10}^{-3}=4\times {10}^{-3}\text{mol/min}$

Now, if t = 0.3 min,
$N{H}_3\text{formed}=\frac{4\times {10}^{-3}}{10}\times 0.3=1.2\times {10}^{-4}\text{mol}$