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 $=-\frac{d\left[N _2\right]}{d t}=-\frac{d\left[H _2\right]}{d t}=\frac{d\left[NH _3\right]}{d t}$

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Answer:

Correct Answer: 33. (a)

Solution:

  1. For any general reaction,

$$ \begin{aligned} & a A+b B \longrightarrow c C+d D \ & \text { Rate }=-\frac{1}{a} \frac{d[A]}{d t}=-\frac{1}{b} \frac{d[B]}{d t} \ &=\frac{1}{c} \frac{d[C]}{d t}=\frac{1}{d} \frac{d[D]}{d t} \ & \Rightarrow \quad \text { For } \quad N _2+3 H _2 \longrightarrow 2 NH _3 \ & \text { Rate }=-\frac{d\left[N _2\right]}{d t}=-\frac{1}{3} \frac{d\left[H _2\right]}{d t}=\frac{1}{2} \frac{d\left[NH _3\right]}{d t} \end{aligned} $$



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