Most chemical reactions are accelerated by an increase in temperature. The temperature dependence of the rate of a chemical reaction is explained by the Arrhenius equation
\[k = A\,e^{-E_a/RT}\]
where \(A\) is the Arrhenius factor (also called the frequency factor or pre-exponential factor) and \(E_a\) is the activation energy, expressed in J mol−1. A plot of ln \(k\) against \(1/T\) is a straight line with slope \(-E_a/R\). The rate constants \(k_1\) and \(k_2\) of a reaction at temperatures \(T_1\) and \(T_2\) are related as
\[\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left[\frac{T_2 - T_1}{T_1T_2}\right]\]
For a chemical reaction, a rise in temperature by 10 K nearly doubles the rate constant, because the fraction of molecules having energy equal to or greater than the activation energy increases.
Consider the following statements about the temperature dependence of the rate of a reaction.
(A) In the decomposition of N2O5, the time taken for half of the original amount of material to decompose is 5 h at 25°C.
(B) The Arrhenius equation was first proposed by Arrhenius, and van’t Hoff provided its physical justification and interpretation.
(C) The Arrhenius factor, A, is a constant specific to a particular reaction.
(D) Ludwig Boltzmann and James Clark Maxwell used statistics to predict the behaviour of a large number of molecules.
Which of the statements given above are correct? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
Most reactions become faster when the temperature is raised. The Arrhenius equation, \( k = A\,e^{-E_a/RT} \), describes this temperature dependence of the rate constant.
(A) In the decomposition of N2O5, the time taken for half of the original amount of material to decompose is 5 h at 25°C. — True. The time is 12 min at 50°C, 5 h at 25°C and 10 days at 0°C; it becomes shorter as the temperature rises.
(B) The Arrhenius equation was first proposed by Arrhenius, and van’t Hoff provided its physical justification and interpretation. — False. The names are the other way round: the equation was first proposed by the Dutch chemist van’t Hoff, and the Swedish chemist Arrhenius gave its physical justification and interpretation.
(C) The Arrhenius factor, A, is a constant specific to a particular reaction. — True. A, also called the frequency factor or pre-exponential factor, has its own value for each reaction.
(D) Ludwig Boltzmann and James Clark Maxwell used statistics to predict the behaviour of a large number of molecules. — True. All the molecules do not have the same kinetic energy, and the behaviour of one molecule cannot be predicted with precision, so Boltzmann and Maxwell used statistics to describe the distribution of kinetic energy.
NCERT (2026-27 edition):
3.4 Temperature Dependence of the Rate of a Reaction – “Most of the chemical reactions are accelerated by increase in temperature. For example, in decomposition of N2O5, the time taken for half of the original amount of material to decompose is 12 min at 50oC, 5 h at 25oC and 10 days at 0oC.”
“…It was first proposed by Dutch chemist, J.H. van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation.”
\( \displaystyle k = A\,e^{-E_a/RT} \qquad (3.18) \)
“where A is the Arrhenius factor or the frequency factor. It is also called pre-exponential factor. It is a constant specific to a particular reaction.”
“All the molecules in the reacting species do not have the same kinetic energy. Since it is difficult to predict the behaviour of any one molecule with precision, Ludwig Boltzmann and James Clark Maxwell used statistics to predict the behaviour of large number of molecules.”