Chemical Kinetics - Result Question 33
####33. Consider the chemical reaction,
$$ N _2(g)+3 H _2(g) \longrightarrow 2 NH _3(g) $$
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 $=-\frac{d\left[N _2\right]}{d t}=-\frac{1}{3} \frac{d\left[H _2\right]}{d t}=\frac{1}{2} \frac{d\left[NH _3\right]}{d t}$
(b) Rate $=-\frac{d\left[N _2\right]}{d t}=-3 \frac{d\left[H _2\right]}{d t}=2 \frac{d\left[NH _3\right]}{d t}$
(2002, 3M)
(c) Rate $=\frac{d\left[N _2\right]}{d t}=\frac{1}{3} \frac{d\left[H _2\right]}{d t}=\frac{1}{2} \frac{d\left[NH _3\right]}{d t}$
(d) Rate $=-\frac{d\left[N _2\right]}{d t}=-\frac{d\left[H _2\right]}{d t}=\frac{d\left[NH _3\right]}{d t}$
Show Answer
Answer:
Correct Answer: 33. (a)
Solution:
- For any general reaction,
$$ \begin{aligned} & a A+b B \longrightarrow c C+d D \ & \text { Rate }=-\frac{1}{a} \frac{d[A]}{d t}=-\frac{1}{b} \frac{d[B]}{d t} \ &=\frac{1}{c} \frac{d[C]}{d t}=\frac{1}{d} \frac{d[D]}{d t} \ & \Rightarrow \quad \text { For } \quad N _2+3 H _2 \longrightarrow 2 NH _3 \ & \text { Rate }=-\frac{d\left[N _2\right]}{d t}=-\frac{1}{3} \frac{d\left[H _2\right]}{d t}=\frac{1}{2} \frac{d\left[NH _3\right]}{d t} \end{aligned} $$
