Question

Consider the chemical reaction,
$N_2(g)+3H_2(g)\rightarrow 2NH_3(g)$ .
The rate of this reaction can be expressed in terms of time derivatives of concentration of $N_2(g), H_2(g)$ or $NH_3(g)$. Identify the correct relationship amongst the rate expressions

• A. Rate $=-\frac{d[N_2]}{dt}=-\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}$
• B. Rate $=-\frac{d[N_2]}{dt}=-3\frac{d[H_2]}{dt}=2\frac{d[NH_3]}{dt}$
• C. Rate $=-\frac{d[N_2]}{dt}=\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}$
• D. Rate $=-\frac{d[N_2]}{dt}=-\frac{d[H_2]}{dt}=\frac{d[NH_3]}{dt}$

Answer 1

Answer: (A)

For any general reaction,
$aA+bB\rightarrow cC+dD$
Rate $=-\frac{1}{a}\frac{d[A]}{dt}=\frac{1}{b}\frac{d[B]}{dt}$
$\frac{1}{c}\frac{d[C]}{dt}=\frac{1}{d}\frac{d[D]}{dt}$
$\Rightarrow$ For $ N_2+3H_2 \rightarrow 2NH_3$
Rate $=-\frac{d[N_2]}{dt}=-\frac{1}{3}\frac{d[H_2]}{dt}=\frac{1}{2}\frac{d[NH_3]}{dt}$
$\Rightarrow$ Rate $=k[N_2O_5]$
$\Rightarrow [N_2O_5]=\frac{\text{Rate}}{k}=\frac{2.40\times10^{-5}}{3\times10^{-5}}=0.80 \,M$