Question

Consider the reaction, $2A+B\to Products$. When concentration of B alone was doubled, the half-life of B did not change. When the concentration of A alone was doubled, the rate increased by two times. The unit rate constant for this reaction is :

Answer 1

Hint: The rate constant quantifies the rate and direction of chemical reaction. The general equation for finding rate constant of a reaction is $mo{l}^{1-n}{L}^{n-1}{s}^{-1}$
Where n = order of reaction
The order can be found from the reaction.

Complete Solution :
We have reaction -
$2A+B\to Products$
- Further, we have been given that when A is doubled, the rate doubles. This means that rate is directly proportional to A.
Thus, the order of reaction with respect to A is 1.
When B is doubled, the half-life does not change.
- We know that in a first order reaction, half-life is independent of concentration.

The half-life can be given as -
$t_{{\displaystyle \frac{1}{2}}}$ = ${\displaystyle \frac{0.693}{k}}$
- So, this means the reactant B follows first order rate.
Thus, the order of reaction with respect to B = 1
So, rate = [A] [B]
Thus, order of reaction = 2
So, the reaction is a Second order reaction.
The units of second order reaction are - $Lmo{l}^{-1}{s}^{-1}$

Note: The overall order of a reaction can be found from the sum of partial orders of the reactants. For example - In the above chemical reaction, the partial order of reactants A and B are 1. But the total order of reaction is 2. The order of reaction can be zero but it can not be negative.