SATHEE: Chemical Kinetics - Result Question 12

Chemical Kinetics - Result Question 12

####13. For an elementary chemical reaction, $A_{2} \underset{k_{- 1}}{\overset{k_{1}}{⇌}} 2 A$ , the expression for $\frac{d [A]}{d t}$ is

(a) $2 k_{1} [A_{2}] - k_{- 1} [A]^{2}$

(b) $k_{1} [A_{2}] - k_{- 1} [A]^{2}$

(d) $k_{1} [A_{2}] + k_{- 1} [A]^{2}$

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Answer:

Correct Answer: 13. (c)

Solution:

The elementary reaction, $A_{2} \underset{k_{- 1}}{\overset{k_{1}}{⇌}} 2 A$

follows opposing or reversible kinetics,

(i) Rate of the reaction,

$\begin{aligned} r & = r_{forward} - r_{backward} & = k_{1} [A_{2}] - k_{- 1} [A]^{2} \end{aligned}$

(ii) Again, rate of the reaction can be expressed as,

$r = - \frac{d [A_{2}]}{d t} = + \frac{1}{2} \frac{d [A]}{d t}$

So, the rate of appearance of $A$ , i.e.

$\frac{d [A]}{d t} = 2 r = 2 k_{1} [A_{2}] - 2 k_{- 1} [A]^{2}$ [from Eq. (i)]

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Chemical Kinetics - Result Question 12

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