(D) For a first-order reaction,the rate constant $k$ is given by the Arrhenius equation: $k = A e^{-E_a/RT}$.Substituting the given values: $k = 10^{2

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(D) For a first-order reaction,the rate constant $k$ is given by the Arrhenius equation: $k = A e^{-E_a/RT}$.Substituting the given values: $k = 10^{20} \times e^{-\frac{191.48 \times 10^3}{8.314 \times 1000}}$.$k = 10^{20} \times e^{-23.031} \approx 10^{20} \times e^{-\ln(10^{10})} = 10^{20} \times 10^{-10} = 10^{10} \ s^{-1}$.The half-life $t_{1/2}$ is given by: $t_{1/2} = \frac{0.693}{k}$.$t_{1/2} = \frac{0.693}{10^{10}} = 6.93 \times 10^{-11} \ s$.Converting to picoseconds $(1 \ ps = 10^{-12} \ s)$: $t_{1/2} = 69.3 \ ps$.The nearest integer is $69$.

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

Difficult

$A \rightarrow B$. The molecule $A$ changes into its isomeric form $B$ following first-order kinetics at a temperature of $1000 \ K$. If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \ kJ \ mol^{-1}$ and the frequency factor is $10^{20} \ s^{-1}$,the time required for $50 \%$ of molecules of $A$ to become $B$ is $..............$ picoseconds (nearest integer). $[R = 8.314 \ J \ K^{-1} \ mol^{-1}]$

JEE MAIN 2025 All JEE MAIN

A
$23$
B
$65$
C
$70$
D
$69$

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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

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For a reversible reaction $A \rightleftharpoons B$,which one of the following statements is wrong from the given energy profile diagram?

MediumTS EAMCET 2008

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For a certain reaction,a large fraction of molecules has energy more than the threshold energy,yet the rate of reaction is very slow. Why?

Easy

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For an exothermic reaction,where the enthalpy of reaction is $\Delta H$ in $kJ/mol$,the minimum value for the activation energy will be:

Easy

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Consider the given plot of enthalpy of the following reaction between $A$ and $B$: $A + B \to C + D$. Identify the incorrect statement.

DifficultJEE MAIN 2019

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$A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
The curves $M$ and $N$ represent the variation of energy with reaction coordinate for the reaction in absence and presence of catalyst.
Which value represents the activation energy $(E_a)$ for the backward reaction in the presence of catalyst?

Medium

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For a reversible reaction $A \rightleftharpoons B$,which one of the following statements is wrong from the given energy profile diagram?

For a certain reaction,a large fraction of molecules has energy more than the threshold energy,yet the rate of reaction is very slow. Why?

For an exothermic reaction,where the enthalpy of reaction is $\Delta H$ in $kJ/mol$,the minimum value for the activation energy will be:

Consider the given plot of enthalpy of the following reaction between $A$ and $B$: $A + B \to C + D$. Identify the incorrect statement.

$A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$The curves $M$ and $N$ represent the variation of energy with reaction coordinate for the reaction in absence and presence of catalyst.Which value represents the activation energy $(E_a)$ for the backward reaction in the presence of catalyst?

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