Question

For the chemical reaction ${\text{A}} \to {\text{products}}$ , it is found that the rate increases by a factor of $6.25$, when the concentration of A is increased by a factor of $2.5$. The order of this reaction with respect to A is:
A. $2.5$
B. 2
C. 1
D. $0.5$

Answer 1

Dependence of rate of reaction on concentration can be found only experimentally as according to rate law. The order of reactions helps to define the proportionate change in rate of reaction with changing concentration of species.

Complete step by step solution:
Rate of reaction is defined as the change in concentration of a reactant or product with respect to time. Rate of reaction depends upon the nature of reactant, intensity of light, catalyst, temperature and concentration. Rate law explains the dependence of rate of reaction on concentration of species in a reaction. This dependence is very complex as it changes with change in concentration of species. Dependence of concentration can be found only experimentally. Order of reaction describes the dependence of rate of reaction on concentration of species. It could be zero, positive or negative.

According to the given reaction in question; ${\text{A}} \to {\text{products}}$. The rate of reaction can be written as:
${\text{Rate}} = {\left[ {\text{A}} \right]^{\text{n}}}$ where n is the order of reaction with respect to A.
As on increasing the concentration of A by a factor of $2.5$, the rate of reaction increases by a factor of $6.25$. It can be written as:
$\left( {6.25 \times {\text{rate}}} \right) = {\left[ {2.5 \times {\text{A}}} \right]^{\text{n}}}$
So, $6.25 = {\left( {2.5} \right)^{\text{n}}}$
So, $6.25 = 2.5 \times 2.5 = {\left( {2.5} \right)^2} = {\left( {2.5} \right)^{\text{n}}}$
Thus, n is equal to 2. The order of reaction with respect to A is 2.

So, the Correct option is B.

Note: Molecularity is defined for the elementary step of the reaction. It describes the number of molecules/atoms of reactants that take part in elementary chemical reactions. Molecularity is always a natural number. It can neither be negative nor fraction. But on the other hand, the order of the reaction can be zero/negative/positive.