The specific rate constant of a first order reaction depends on the

The correct answer is Option (4) → Temperature

The rate constant k is the rate of reaction when every reactant is at unit concentration. For a given reaction it is independent of concentration and time, but it changes with temperature according to the Arrhenius equation:

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

As T rises, the fraction of molecules with energy equal to or greater than E_a increases, so k increases; for many reactions it nearly doubles for a 10° rise. So the specific rate constant depends on temperature.

Why the other options are incorrect

• Option (1) Concentration of the reactant — Incorrect. The rate (= k[A]) depends on [A], but k itself does not; for a first order reaction k = (2.303/t) log([A]₀/[A]) gives the same value whatever [A]₀ is.

• Option (2) Concentration of the product — Incorrect. Products do not appear in the rate law of a simple first order reaction and do not change k.

• Option (3) Time — Incorrect. k stays constant throughout the reaction at a fixed temperature; it is the concentration that falls with time.

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). It was first proposed by Dutch chemist, J.H. van’t Hoff but Swedish chemist, Arrhenius provided its physical justification and interpretation. k = A e^−Ea/RT (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. R is gas constant and Ea is activation energy measured in joules/mole (J mol⁻¹).”