(C) According to the Arrhenius equation,$K = A \, e^{-Ea/RT}$.Assuming the pre-exponential factor $A$ is the same for both reactions:$K_1 = A \, e^{-E

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(C) According to the Arrhenius equation,$K = A \, e^{-Ea/RT}$.Assuming the pre-exponential factor $A$ is the same for both reactions:$K_1 = A \, e^{-Ea_1/RT}$$K_2 = A \, e^{-Ea_2/RT}$Given $Ea_1 = \frac{Ea_2}{3}$,we have $Ea_2 = 3Ea_1$.Substituting $Ea_2$ into the expression for $K_2$:$K_2 = A \, e^{-3Ea_1/RT}$Now,divide $K_1$ by $K_2$:$\frac{K_1}{K_2} = \frac{A \, e^{-Ea_1/RT}}{A \, e^{-3Ea_1/RT}} = e^{(-Ea_1 + 3Ea_1)/RT} = e^{2Ea_1/RT}$Therefore,$K_1 = K_2 \, e^{2Ea_1/RT}$.

Class 12 Chemistry Chemical Kinetics Collision theory, Energy of activation and Arrhenius equation

Medium

Reactant $A$ shows two reactions:
$A \xrightarrow{K_1} B$,activation energy $= Ea_1$
$A \xrightarrow{K_2} C$,activation energy $= Ea_2$
If $Ea_1 = \frac{Ea_2}{3}$,then the relation between $K_1$ and $K_2$ is:

A
$K_2 = K_1 \, e^{Ea_1/RT}$
B
$K_2 = K_1 \, e^{2Ea_1/RT}$
C
$K_1 = K_2 \, e^{2Ea_1/RT}$
D
$K_1 = 2K_2 \, e^{Ea_1/RT}$

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Class 12

Chemistry Questions

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Chemical Kinetics

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Collision theory, Energy of activation and Arrhenius equation

The decomposition of $N_2O$ into $N_2$ and $O_2$ in the presence of argon follows first-order kinetics. If the rate constant is given by $K = 5.0 \times 10^{11} \, e^{-2000/T}$,what is the activation energy of the reaction?

Medium

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Which of the following statements is true about the equilibrium constant and rate constant of a single-step chemical reaction?

MediumWBJEE 2024

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How fast is the reaction at $25\, ^\circ C$ as compared to $0\, ^\circ C$,if the activation energy is $65\, kJ/mol$?

Medium

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The reaction $X \to Y$ is an exothermic reaction. The activation energy of the forward reaction $X \to Y$ is $150\,kJ\,mol^{-1}$. The enthalpy of the reaction is $-135\,kJ\,mol^{-1}$. The activation energy for the reverse reaction,$Y \to X$,will be $.......\,kJ\,mol^{-1}$.

DifficultJEE MAIN 2013

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Find True $(T)$ and False $(F)$ statements in the following:
$1.$ Effective collision depends on rate.
$2.$ When the reactant converts into product,the bonds in the reactant break and new bonds form.
$3.$ The breaking of old bonds and the formation of new bonds take place simultaneously.

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Reactant $A$ shows two reactions:$A \xrightarrow{K_1} B$,activation energy $= Ea_1$$A \xrightarrow{K_2} C$,activation energy $= Ea_2$If $Ea_1 = \frac{Ea_2}{3}$,then the relation between $K_1$ and $K_2$ is:

Similar Questions

The decomposition of $N_2O$ into $N_2$ and $O_2$ in the presence of argon follows first-order kinetics. If the rate constant is given by $K = 5.0 \times 10^{11} \, e^{-2000/T}$,what is the activation energy of the reaction?

Which of the following statements is true about the equilibrium constant and rate constant of a single-step chemical reaction?

How fast is the reaction at $25\, ^\circ C$ as compared to $0\, ^\circ C$,if the activation energy is $65\, kJ/mol$?

The reaction $X \to Y$ is an exothermic reaction. The activation energy of the forward reaction $X \to Y$ is $150\,kJ\,mol^{-1}$. The enthalpy of the reaction is $-135\,kJ\,mol^{-1}$. The activation energy for the reverse reaction,$Y \to X$,will be $.......\,kJ\,mol^{-1}$.

Find True $(T)$ and False $(F)$ statements in the following:$1.$ Effective collision depends on rate.$2.$ When the reactant converts into product,the bonds in the reactant break and new bonds form.$3.$ The breaking of old bonds and the formation of new bonds take place simultaneously.

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Reactant $A$ shows two reactions:
$A \xrightarrow{K_1} B$,activation energy $= Ea_1$
$A \xrightarrow{K_2} C$,activation energy $= Ea_2$
If $Ea_1 = \frac{Ea_2}{3}$,then the relation between $K_1$ and $K_2$ is:

Find True $(T)$ and False $(F)$ statements in the following:
$1.$ Effective collision depends on rate.
$2.$ When the reactant converts into product,the bonds in the reactant break and new bonds form.
$3.$ The breaking of old bonds and the formation of new bonds take place simultaneously.