From the statements given, choose the correct option based on the Arrhenius equation
\( k=Ae^{-Ea/RT} \)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → rate constant increases exponentially with decreasing activation energy and increasing temperature.
The Arrhenius equation links the rate constant to the activation energy Ea and the absolute temperature T:
\( \displaystyle k = A\,e^{-E_a/RT} \)
The term \( E_a/RT \) carries a minus sign in the exponent, so k becomes larger when this term becomes smaller:
a smaller activation energy makes \( E_a/RT \) smaller, so k increases;
a higher temperature also makes \( E_a/RT \) smaller, so k increases.
Because Ea and T appear in an exponent, the change in k is exponential. So the rate constant increases exponentially with decreasing activation energy and increasing temperature.
NCERT (2026-27 edition):
Temperature Dependence of the Rate of a Reaction – …
