To understand the relationship between the equilibrium constant and the rate constant with temperature for a single-step chemical reaction, we need to consider the following concepts:
Rate Constant
(k) :
The rate constant of a reaction is influenced by temperature according to the Arrhenius equation:
k=Ae−‌where
A is the pre-exponential factor,
Ea is the activation energy,
R is the gas constant, and
T is the temperature in Kelvin. From this equation, it's clear that the rate constant
k generally increases with an increase in temperature.
Equilibrium Constant
(Keq) :
The equilibrium constant is related to the Gibbs free energy change
(∆G∘) of the reaction:
∆G∘=−RT‌ln‌K‌eq ‌If the reaction's
∆H is positive (endothermic), an increase in temperature results in an increase in
K‌eq ‌. Conversely, for an exothermic reaction (
∆H is negative), an increase in temperature results in a decrease in
K‌eq ‌. This is described by the van 't Hoff equation:
(‌)=‌ Thus, the behavior of the equilibrium constant with temperature depends on the nature of the reaction (whether it is endothermic or exothermic).
Given the above explanation, the correct answer is:
Option A: Equilibrium constant may increase or decrease but the rate constant always increases with temperature.