Question

Match the rate expressions in LIST-I for the decomposition of $X$ with the corresponding profiles provided in LIST-II. $X_s$ and $k$ constants having appropriate units.

LIST I		LIST II
I	$\text{ rate }=\frac{k[X]}{X_s+[X]}$ under all possible initial concentration of $X$	i
II	$\text{ rate }=\frac{k[X]}{X_s+[X]}$ where initial concentration of $X$ are much less than $X_s$	ii
III	$\text{ rate }=\frac{k[X]}{X_s+[X]}$ where initial concentration of $X$ are much higher than $X_s$	iii
IV	$\text{ rate }=\frac{k[X{]}^2}{X_s+[X]}$ ,br/>where initial concentration of $X$ is much higher than $X_s$	iv
		v

• A. I $\to$ P; II $\to$ Q; III $\to$ S; IV $\to$ T
• B. $I\to R$; II $\to$ S; III $\to$ S; IV $\to$ T
• C. I $\to$ P; II $\to$ Q; III $\to$ Q; IV $\to$ R
• D. $I\to R$; II $\to S$; III $\to$ Q; IV $\to R$

Answer 1

Answer: (A)

(I)$\text{ rate }=\frac{k[x]}{x_s+[x]}=\frac{k}{\frac{x_s}{[x]}+1}$
$\text{ If }[x]\to \infty \Rightarrow \text{ rate }\to k\Rightarrow \text{ order }=0$
$\Rightarrow (I)-(R),(P)$
(II)$[x]<<x_s\Rightarrow \text{ rate }=\frac{k[x]}{x_s}\Rightarrow \text{ order }=1$
$\Rightarrow \text{ (II) }-(Q),\text{ (T) }$
(III) $[x]>>x_s\Rightarrow$ rate $=k\Rightarrow$ order $=0$
$\Rightarrow (III)-(P),(S)$
(IV)$\text{ rate }=\frac{k[x{]}^2}{x_s+[x]}$
$[x]>>x_s\Rightarrow \text{ rate }=k[x]$
$\Rightarrow (IV)-(Q),(T)$