Question

According to the Arrhenius equation, $k = Ae^{-E_a/RT}$ . If ${E_a} = $$RT$ ,then
A. The rate of reaction does not depend upon initial concentration
B. The rate constant becomes about $37\% $ of the Arrhenius constant $A$
C. The rate constant becomes equal to $73\% $ of the Arrhenius constant $A$
D. The rate of the reaction becomes zero or infinite

Answer 1

Hint: Temperature plays a very important role in determining the rate of the reaction. . It has been experimentally found that for a chemical reaction with a rise in temperature by $$10^\circ $$, the rate constant is nearly doubled. The Arrhenius equation is used to determine the relationship between temperature and rate constant.

Formula used:
We use the formula, $k = Ae^{-E_a/RT}$
$A = $ Arrhenius constant or frequency factor.
${E_a} = $ Activation Energy
$R = $ Universal gas constant
$k = $ Rate constant
$T = $ Absolute temperature $\left( K \right)$

Complete answer:
Chemical kinetics is the branch in chemistry that deals with the rate of reaction. The rate of a reaction is how fast a chemical reaction is occurring, that is the rate at which the reactants are forming products. Various factors affect the rate of a reaction such as the concentration of reactants, nature of the solvent, presence of a catalyst, etc.
One such factor is temperature. When the temperature is increased, the number of collisions of reactants per second increases. Therefore the rate of reaction increases. But it depends on the nature of the reaction also that is whether the reaction is an endo or exothermic reaction. Accordingly, the reaction moves forward or backward. It has been experimentally found that for a chemical reaction with a rise in temperature by $$10^\circ $$ , the rate constant is nearly doubled.
The Arrhenius equation describes the relationship between the rate of reaction and temperature. It is given by
$k = Ae^{-E_a/RT}$
$A = $ Arrhenius constant or frequency factor.
${E_a} = $ Activation Energy
Activation Energy is the minimum energy required by the reactant molecules to form products that is the reaction to begin.
$R = $ Universal gas constant
$k = $ Rate constant
Rate constant defines the direction of the reaction that is whether the reaction will move forward or backward.
$T = $ Absolute temperature $\left( K \right)$
According to the given equation, we have ${E_a} = RT$ ,
$k = Ae^{-E_a/RT}$
Putting ${E_a} = RT$ in Arrhenius equation
$ \Rightarrow k = A{e^{\dfrac{{^{ - RT}}}{{RT}}}}$
$ \Rightarrow k = A{e^{ - 1}}$
It can be written as
$ \Rightarrow k = \dfrac{A}{e}$……$\left( 1 \right)$
$e$ is an exponential factor and has a value approximately equal to $$2.718$$
$ \Rightarrow \dfrac{1}{e} \simeq 0.37$
Write it in percentage and put the value in $\left( 1 \right)$
$k \simeq 37\% A$

Therefore, the correct option is B

Note:
It is important to know that we have calculated the approximate value of K. Also, there are other factors that affect the rate of a reaction. For example, according to the collision theory, molecules of reactants collide with each other to form products. If the concentration of reactants is increased, the number of collisions also increases thus increasing the rate of the reaction. The presence of a catalyst lowers the activation energy of the reaction thus increasing the rate of the reaction. The phase and surface area of reactants also affects the rate of the reaction.