Question

Two reactions, $A \to$products and $B \to$products, have rate constant ${K_a}$ and ${K_b}$ at temperature T and activation energies ${E_a}$and ${E_b}$ respectively. If ${K_a} > {K_b}$and ${E_a} > {E_b}$ and assuming that A for both the reactions is same then:
A.At higher temperature ${K_a}$ will be greater than ${K_b}$
B.At lower temperature ${K_a}$ and ${K_b}$will differ more and ${K_a} > {K_b}$
C.As temperature rises ${K_a}$ and ${K_b}$will be close to each other in magnitude
D.All of the above

Answer 1

To solve this question you must recall the Arrhenius equation. It gives the relation between the activation energy of the reaction and the rate at which the reaction proceeds.
Formula used:
${k_a} = A{e^{\dfrac{{ - \left( {{E_a}} \right)}}{{RT}}}}$and ${k_b} = A{e^{\dfrac{{ - \left( {{E_a}} \right)}}{{RT}}}}$
Where, ${{\text{k}}_{\text{a}}}$ is the rate constant of the reaction $A \to$products
${{\text{k}}_{\text{b}}}$ is the rate constant of the reaction $B \to$products
${{\text{E}}_{\text{a}}}$ is the activation energy of the reaction $A \to$products
${{\text{E}}_{\text{b}}}$ is the activation energy of the reaction $B \to$products
$T$ is the temperature
And $R$ is the gas constant.

Complete step by step answer:
It is given to us that ${K_a} > {K_b}$ and ${E_a} > {E_b}$.
So, from the Arrhenius equation, we can see that, at higher temperatures, ${K_a}$ will be greater than ${K_b}$.
As the temperature increases the rate increases, but the activation energy decreases the rate.
As a result, at greater temperatures, the difference in the values of ${K_a}$ and ${K_b}$ will be less.
As the temperature decreases, the change in the value of ${K_b}$ is more than that that in the value of ${K_a}$ and the values of ${K_a}$ and ${K_b}$ will differ more and ${K_a}$ will be greater than ${K_b}$.
Thus, we can see that all the given statements are true.

Thus, the correct option is D.

Note:
Activation energy is the energy that we need to provide to compounds in order for a chemical reaction to take place. The activation energy $\left( {{E_a}} \right)$ is commonly measured in joules per mole $\left( {{\text{J/mol}}} \right)$.
Activation energy can be considered as the magnitude of the energy barrier separating the initial and final thermodynamic states, namely the reactants and products. For a chemical reaction to occur at a good rate, the temperature of the system should be high enough so that there are an appreciable number of molecules with energy greater than or equal to the activation energy.