Arrhenius EquationJEE Advanced

Temperature and activation energy — interactive Chemistry simulation for IIT-JEE.

Concept

Reactions speed up with temperature because more molecules carry enough energy to clear the activation barrier $E_a$ . The Arrhenius equation captures this: a small rise in $T$ can multiply the rate constant several-fold.

Key formula

k = A\,e^{-E_a/RT} \quad\Rightarrow\quad \ln k = \ln A - \frac{E_a}{R}\cdot\frac1T

Derivation

The exponential $e^{-E_a/RT}$ is the Boltzmann fraction of molecules with energy at least $E_a$ ; $A$ counts how often they collide with the right orientation.

Taking logs gives a straight line of $\ln k$ against $1/T$ with slope $-E_a/R$ — the standard way to measure activation energy experimentally.

Scenarios to explore

Arrhenius Equation — Activation energy and the rate–temperature link.

Real-world applications

Predicting shelf-life and refrigeration benefits (Q₁₀ rule).
Measuring $E_a$ from rate-vs-temperature data.
Catalysis — catalysts lower $E_a$ , raising $k$ .

JEE exam tips

Two-temperature form: $\ln\dfrac{k_2}{k_1} = \dfrac{E_a}{R}\left(\dfrac1{T_1}-\dfrac1{T_2}\right)$ .
A catalyst provides a lower- $E_a$ path; it does not change $\Delta H$ or equilibrium.

Common mistakes

Using $E_a$ in kJ but $R$ in J — convert to consistent units.
Forgetting the slope of the Arrhenius plot is $-E_a/R$ (negative).
Thinking $A$ changes with temperature — it is nearly constant.

Exam traps to avoid

The Arrhenius plot uses $1/T$ on the x-axis, not $T$ .
Rate roughly doubles per 10 K only as a rule of thumb — the exact factor depends on $E_a$ .