Question

Consider the chemical reaction,
$N_2\left(g\right)+3H_2\left(g\right)\to 2N{H}_3\left(g\right)$
The rate of this reaction can be expressed in terms of time derivatives of concentration of $N_2\left(g\right),H_2\left(g\right)orN{H}_3\left(g\right)$. Identify the correct relationship amongst the rate expressions.

• A. $Rate=-\frac{d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
• B. $Rate=-\frac{d\left[N_2\right]}{dt}=-3\frac{d\left[H_2\right]}{dt}=2\frac{d\left[N{H}_3\right]}{dt}$
• C. $Rate=\frac{d\left[N_2\right]}{dt}=\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
• D. $Rate=-\frac{d\left[N_2\right]}{dt}=-\frac{d\left[H_2\right]}{dt}=\frac{d\left[N{H}_3\right]}{dt}$

Answer 1

The correct option is A

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

For any general reaction,
$aA+bB\to cC+dD$
$Rate=-\frac{1}{a}\frac{d\left[A\right]}{dt}=-\frac{1}{b}\frac{d\left[B\right]}{dt}$
$=\frac{1}{c}\frac{d\left[C\right]}{dt}=\frac{1}{d}\frac{d\left[D\right]}{dt}$
$\Rightarrow For{N}_2+3H_2\to 2N{H}_3$
$Rate=-\frac{d\left[N_2\right]}{dt}=-\frac{1}{3}\frac{d\left[H_2\right]}{dt}=\frac{1}{2}\frac{d\left[N{H}_3\right]}{dt}$
$Rate=k\left[N_2{O}_5\right]$
$\Rightarrow \left[N_2{O}_5\right]=\frac{Rate}{k}=\frac{2.40\times {10}^{-5}}{3\times {10}^{-5}}=0.80M$