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Temperature Dependence of the Rate of a Reaction

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Estimated time: 5 minutes
CBSE: Class 12

Definition: Arrhenius Equation

The Arrhenius equation is a mathematical expression to give a quantitative relationship between the rate constant and temperature.

CBSE: Class 12

Key Points: Temperature dependence of the rate of reaction (Arrhenius equation)

Temperature Coefficient:

The temperature coefficient μμ is the ratio of rate constants at two temperatures differing by 10°C:

\[\mu=\frac{k_{T+10}}{k_T}=2\mathrm{~to~3}\]

The two reference temperatures are typically 35°C (308 K) and 25°C (298 K).

If R1​ = reaction rate at T1​ and R2​ = reaction rate at T2​:

\[\frac{R_1}{R_2}=\frac{\mu T}{10}\]

Arrhenius Equation:

\[k=A\cdot e^{-E_a/RT}\]

where:

  • k = rate constant
  • A = pre-exponential factor (frequency factor)
  • EaEa​ = activation energy (J mol⁻¹)
  • R = gas constant (8.314 J mol⁻¹ K⁻¹)
  • T = temperature in Kelvin

The factor \[e^{-E_a/RT}\] is called the Boltzmann factor.

Logarithmic form:

\[\log k=\log A-\frac{E_a}{2.303RT}\]

A plot of log k vs 1/T is a straight line with:

\[\mathrm{Slope}=-\frac{E_a}{2.303R}\]

Intercept = log A

This is of the form y = mx + c.

Two-Temperature Form:

\[\log\frac{k_2}{k_1}=\frac{E_a}{2.303R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)=\frac{E_a}{2.303R}\left(\frac{T_2-T_1}{T_1T_2}\right)\]

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