Question

A and B react to form C as $A+B\to C$. The kinetics of reaction is studied and the following data is collected in three separate experiments.

Initial conc. (M)(A)	(B)	Duration of exp. (hr)	Final conc. (A)[A]
0.1	0.5	0.5	0.0975
0.1	2.0	0.5	0.0900
0.05	1.0	2.0	0.0450

The value of the rate constant is:
a.) K = $5 x {{10}^{-2}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$
b.) K = $4 x {{10}^{-3}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$
c.) K = $3 x {{10}^{-3}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$
d.) None of these

Answer 1

Hint: Rate is defined as the speed at which a chemical reaction occurs. Rate is generally expressed in the terms of concentration of reactant which is consumed during the reaction in a unit of time or the concentration of product which is produced during the reaction in a unit of time.

Complete step by step answer:
Rate is defined as the change in concentration of reactant or product with respect to time.
Given reaction: $A+B\to C$

Initial conc. (M)(A)	(B)	Duration of exp. (hr)	Final conc. (A)[A]	Rate of the reaction
0.1	0.5	0.5	0.0975	$\dfrac{0.1-0.0975}{0.5}=5X{{10}^{-3}}$
0.1	2.0	0.5	0.0900	$\dfrac{0.1-0.0900}{0.5}=2X{{10}^{-3}}$
0.05	1.0	2.0	0.0450	$\dfrac{0.1-0.045}{2}=2.5X{{10}^{-3}}$

From the first and second experiment we can say that the rate is second order with respect to B
Rate $\alpha {{[B]}^{2}}$
And from the first and second experiment we can say that the rate is first order with respect to A
Rate $\alpha [A]$
The overall order of the reaction will be = 3
Now calculate the value of rate constant i.e. K from experiment 1:
Rate $\alpha [A]{{[B]}^{2}}$
Rate = $K[A]{{[B]}^{2}}$
$5X{{10}^{-3}}=K[0.13]{{[1.0]}^{2}}$
Value of K = K = $5 x {{10}^{-2}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$
So, the correct answer is “Option A”.

Note: The reaction is a third order reaction, the unit for third order reaction is ${{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$. The negative and positive sign in the expression of the rate or reaction only means the change in concentration. A negative charge indicates that the concentration of the reactant is decreasing, similarly a positive charge means that the concentration of product is increasing.