Identify the correct expression of Arrhenius equation:

The correct answer is Option (1) → \(k = Ae^{-E_a/RT}\)

The Arrhenius equation gives the temperature dependence of the rate constant:

    \( \displaystyle k = A\,e^{-E_a/RT} \)

Here A is the Arrhenius (frequency) factor, \( E_a \) the activation energy, R the gas constant and T the absolute temperature. The factor \( e^{-E_a/RT} \) is the fraction of molecules with energy equal to or greater than \( E_a \). A higher temperature or a lower activation energy makes the exponent less negative, so k increases. Taking logarithms gives the straight-line form used for graphs:

    \( \displaystyle \ln k = \ln A - \frac{E_a}{RT} \)

Why the other options are incorrect

• Option (2) \(k = Ae^{E_a/RT}\) — Incorrect. With a positive exponent, k would fall as the temperature rises and rise with the activation energy, the opposite of what is observed.

• Option (3) \(k = Ae^{E_a/T}\) — Incorrect. \( E_a/T \) has the unit J mol⁻¹ K⁻¹; an exponent must have no unit, which needs the gas constant in the denominator. The sign is also wrong.

• Option (4) \(k = Ae^{E_a/R}\) — Incorrect. Temperature is missing, so this form could not describe how k changes with temperature; \( E_a/R \) also has the unit K.

NCERT (2026-27 edition):
Temperature Dependence of the Rate of a Reaction – “… The temperature dependence of the rate of a chemical reaction can be accurately explained by Arrhenius equation (3.18).”

    \( k = A\,e^{-E_a/RT} \)

“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. R is gas constant and E_a is activation energy measured in joules/mole (J mol^–1).”