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# 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 :

Last updated date: 18th Jun 2024
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Answer
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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 -
${t_{\dfrac{1}{2}}}$ = $\dfrac{{0.693}}{k}$
- 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.