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Question: A and B react to form C as \(A+B\to C\). The kinetics of reaction is studied and the following data ...

A and B react to form C as A+B→CA+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]
0.10.50.50.0975
0.12.00.50.0900
0.051.02.00.0450

The value of the rate constant is:
a.) K = 5x10−2M−2hr−1or mol−2L2hr−15 x {{10}^{-2}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}
b.) K = 4x10−3M−2hr−1or mol−2L2hr−14 x {{10}^{-3}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}
c.) K = 3x10−3M−2hr−1or mol−2L2hr−13 x {{10}^{-3}}{{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}
d.) None of these

Explanation

Solution

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→CA+B\to C

Initial conc. (M)(A)(B)Duration of exp. (hr)Final conc. (A)[A]Rate of the reaction
0.10.50.50.09750.1−0.09750.5=5X10−3\dfrac{0.1-0.0975}{0.5}=5X{{10}^{-3}}
0.12.00.50.09000.1−0.09000.5=2X10−3\dfrac{0.1-0.0900}{0.5}=2X{{10}^{-3}}
0.051.02.00.04500.1−0.0452=2.5X10−3\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 α[B]2\alpha {{[B]}^{2}}
And from the first and second experiment we can say that the rate is first order with respect to A
Rate α[A]\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 α[A][B]2\alpha [A]{{[B]}^{2}}
Rate = K[A][B]2K[A]{{[B]}^{2}}
5X10−3=K[0.13][1.0]25X{{10}^{-3}}=K[0.13]{{[1.0]}^{2}}
Value of K = K = 5x10−2M−2hr−1or mol−2L2hr−15 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−2hr−1or mol−2L2hr−1{{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.