(C) The Arrhenius equation is given by $k = A e^{-\frac{E_a}{RT}}$.Taking the natural logarithm on both sides,we get $\ln k = \ln A - \frac{E_a}{RT}$.

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The graph of $\ln k$ vs $\frac{1}{T}$ is a straight line with a slope of $-\frac{E_a}{R}$.

(C) The Arrhenius equation is given by $k = A e^{-\frac{E_a}{RT}}$.Taking the natural logarithm on both sides,we get $\ln k = \ln A - \frac{E_a}{RT}$.Comparing this with the equation of a straight line $y = mx + c$,where $y = \ln k$ and $x = \frac{1}{T}$,the slope $m = -\frac{E_a}{R}$.Option $C$ is correct because the slope of the plot of $\ln k$ versus $\frac{1}{T}$ is $-\frac{E_a}{R}$.Note: If the plot is $\log_{10} k$ versus $\frac{1}{T}$,the slope is $-\frac{E_a}{2.303R}$.

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

Medium

Which of the following statements is correct regarding the Arrhenius equation and reaction kinetics?

A
Larger the activation energy,higher will be the value of temperature coefficient of reaction.
B
With an increase in temperature,in the high-temperature range,the rate constant increases more as compared to the low-temperature range.
C
The graph of $\ln k$ vs $\frac{1}{T}$ is a straight line with a slope of $-\frac{E_a}{R}$.
D
Chemical reactions with low activation energy always occur at a faster rate compared to reactions with higher activation energy.

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Class 12 Questions

Class 12

Chemistry Questions

Chapter

Chemical Kinetics

Subtopic

Collision theory, Energy of activation and Arrhenius equation

Assertion : If the activation energy of a reaction is zero,temperature will have no effect on the rate constant.
Reason : Lower the activation energy,faster is the reaction.

MediumAIIMS 2015

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At $300 \ K$,the activation energy and rate constant for the given reaction are $10 \ kJ \ mol^{-1}$ and $2.4 \times 10^{-5} \ s^{-1}$ respectively. At what temperature (in $K$) will the value of $t_{1/2}$ be $2 \ hr$?
$2N_2O_5 \to 4NO_2 + O_2$

Medium

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In which of the following cases is the percentage increase in rate constant maximum?
$Case$ $E_a \ (kcal/mol)$ $Temp. \ Change \ (K)$
$I$ $40$ $200 - 210$
$II$ $80$ $200 - 210$
$III$ $40$ $300 - 310$
$IV$ $80$ $300 - 310$

Medium

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If the rate constants of a reaction at $500 \ K$ and $700 \ K$ are $0.002 \ s^{-1}$ and $0.06 \ s^{-1}$,respectively,the value of activation energy is $(R=8.314 \ J \ mol^{-1} \ K^{-1}, \log 3=0.477)$.

MediumTS EAMCET 2018

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The rate constants for the decomposition of acetaldehyde have been measured over the temperature range $700-1000 \ K$. The data has been analysed by plotting a $\ln \ k \ vs \ \frac{10^{3}}{T}$ graph,which gives a slope of $-18.5$. The value of activation energy for the reaction is $...... \ kJ \ mol^{-1}$. (Nearest integer) (Given: $R = 8.31 \ J \ K^{-1} \ mol^{-1}$)

MediumJEE MAIN 2022

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$Case$	$E_a \ (kcal/mol)$	$Temp. \ Change \ (K)$
$I$	$40$	$200 - 210$
$II$	$80$	$200 - 210$
$III$	$40$	$300 - 310$
$IV$	$80$	$300 - 310$

Which of the following statements is correct regarding the Arrhenius equation and reaction kinetics?

Similar Questions

Assertion : If the activation energy of a reaction is zero,temperature will have no effect on the rate constant.Reason : Lower the activation energy,faster is the reaction.

At $300 \ K$,the activation energy and rate constant for the given reaction are $10 \ kJ \ mol^{-1}$ and $2.4 \times 10^{-5} \ s^{-1}$ respectively. At what temperature (in $K$) will the value of $t_{1/2}$ be $2 \ hr$?$2N_2O_5 \to 4NO_2 + O_2$

In which of the following cases is the percentage increase in rate constant maximum?$Case$$E_a \ (kcal/mol)$$Temp. \ Change \ (K)$$I$$40$$200 - 210$$II$$80$$200 - 210$$III$$40$$300 - 310$$IV$$80$$300 - 310$

If the rate constants of a reaction at $500 \ K$ and $700 \ K$ are $0.002 \ s^{-1}$ and $0.06 \ s^{-1}$,respectively,the value of activation energy is $(R=8.314 \ J \ mol^{-1} \ K^{-1}, \log 3=0.477)$.

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Assertion : If the activation energy of a reaction is zero,temperature will have no effect on the rate constant.
Reason : Lower the activation energy,faster is the reaction.

At $300 \ K$,the activation energy and rate constant for the given reaction are $10 \ kJ \ mol^{-1}$ and $2.4 \times 10^{-5} \ s^{-1}$ respectively. At what temperature (in $K$) will the value of $t_{1/2}$ be $2 \ hr$?
$2N_2O_5 \to 4NO_2 + O_2$

In which of the following cases is the percentage increase in rate constant maximum?
$Case$ $E_a \ (kcal/mol)$ $Temp. \ Change \ (K)$
$I$ $40$ $200 - 210$
$II$ $80$ $200 - 210$
$III$ $40$ $300 - 310$
$IV$ $80$ $300 - 310$