Chemical Kinetics - Result Question 20
23. For the non-stoichiometric reaction, $2 A+B \rightarrow C+D$, the following kinetic data were obtained in three separate experiments, all at $298 K$.
(2014 Main)
| Initial concentration $[A]$ |
Initial concentration $[B]$ |
Initial rate of formation of $\boldsymbol{C}$ $\left(mol L^{-1} s^{-1}\right)$ |
|
|---|---|---|---|
| (i) | $0.1 M$ | $0.1 M$ | $1.2 \times 10^{-3}$ |
| (ii) | $0.1 M$ | $0.2 M$ | $1.2 \times 10^{-3}$ |
| (iii) | $0.2 M$ | $0.1 M$ | $2.4 \times 10^{-3}$ |
The rate law for the formation of $C$ is
(a) $\frac{d C}{d t}=k[A][B]$
(b) $\frac{d C}{d t}=k[A]^{2}[B]$
(c) $\frac{d C}{d t}=k[A][B]^{2}$
(d) $\frac{d C}{d t}=k[A]$
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Answer:
Correct Answer: 23. (d)
Solution:
- This problem can be solved by determining the order of reaction w.r.t. each reactant and then writing rate law equation of the given equation accordingly as
$ R=\frac{d C}{d t}=k[A]^{x}[B]^{y} $
where, $x=$ order of reaction w.r.t $A$
$ y=\text { order of reaction w.r.t } B $
$ \begin{gathered} 1.2 \times 10^{-3}=k(0.1)^x(0.1)^y \\ 1.2 \times 10^{-3}=k(0.1)^x(0.2)^y \\ 2.4 \times 10^{-3}=k(0.2)^x(0.1)^y \\ R=k[A]^1[B]^0 \end{gathered} $
As shown above, rate of reaction remains constant as the concentration of reactant $(B)$ changes from 0.1 M to 0.2 M and becomes double when concentration of $A$ change from 0.1 to 0.2 , (i.e. doubled).
BETA
