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

Hint: 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:
 $k_a=A{e}^{{\displaystyle \frac{-\left(E_a\right)}{RT}}}$and $k_b=A{e}^{{\displaystyle \frac{-\left(E_a\right)}{RT}}}$
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.