Match the rate expressions in List-I for the decomposition of $X$ with the corresponding profiles pr

Question

Match the rate expressions in List-I for the decomposition of $X$ with the corresponding profiles provided in List-II, $X_{s}$ and $k$ are constants having appropriate units.

Professor PC Thomas Classes · Answer

(a) : $\mathrm{I} ightarrow \mathrm{P} ; \mathrm{II} ightarrow \mathrm{Q} ; \mathrm{III} ightarrow \mathrm{S} ; \mathrm{IV} ightarrow \mathrm{T}$\ I. Rate $=\frac{k[X]}{X_{s}+[X]}$; Rate $=\frac{k}{\frac{X_{s}}{[X]}+1}$\ [When $X ightarrow \infty \Rightarrow$ Rate $=k$ ]\ So, it is a zero order reaction.\ $\mathrm{I} ightarrow \mathrm{P}, \mathrm{R}$\ II. Rate $=\frac{k[X]}{X_{s}+[X]}$;\ $X_{s} \ggg X ; X_{s}+X \approx X_{s}$\ Rate $=\frac{k[X]}{X_{s}}$\ So, it is a $1^{	ext {st }}$ order reaction. For a $1^{	ext {st }}$ order reaction $t_{1 / 2}$ is independent of initial concentration.\ $\mathrm{II} ightarrow \mathrm{Q}, \mathrm{T}$\ III. Rate $=\frac{k[X]}{X_{s}+[X]} ; X \ggg>X_{s}$\ $\Rightarrow \quad X_{s}+[X] \approx X$\ Rate $=\frac{k[X]}{[X]}=k$\ So, it is zero order reaction.\ $\mathrm{III} ightarrow \mathrm{P}, \mathrm{S}$\ IV. Rate $=\frac{k[X]^{2}}{X_{s}+[X]}$;\ $X \ggg>X_{s} \Rightarrow X_{s}+X \approx X$\ Rate $=k \frac{[X]^{2}}{[X]}=k[X]$\ So, it is a $1^{	ext {st }}$ order reaction.\ $\mathrm{IV} ightarrow \mathrm{Q}, \mathrm{T}$\