CourseCourseQ BankQuestion BankDocsDocuments

2.2.12 (HL)—Arrhenius equation

Syllabus
First assessment 2025
Objective
2.2.12
Level
HL

The Arrhenius Equation

HL only

lnk=(−Ea/R)(1/T)+lnAln k = (−Ea/R)(1/T) + ln A

On a plot of ln k against 1/T, gradient = −Ea/R and intercept = ln A. Use kelvin, preserve the negative gradient and convert J mol−1 to kJ mol−1 when required.

A steeper negative ln k versus 1/T gradient means a larger activation energy. When two temperatures are given, subtracting the two linear equations removes ln A and lets Ea be found without knowing the frequency factor.

ln(k2/k1)=−(Ea/R)(1/T2−1/T1)withTinKandEainJmol−1whenR=8.31Jmol−1K−1ln(k₂/k₁) = −(Eₐ/R)(1/T₂ − 1/T₁) with T in K and Eₐ in J mol⁻¹ when R = 8.31 J mol⁻¹ K⁻¹

Worked Arrhenius-plot example: using line points (0.00302 K−1,−6.8)(0.00302\,\mathrm{K^{-1}},-6.8) and (0.00334 K−1,−10.8)(0.00334\,\mathrm{K^{-1}},-10.8), the gradient is [−6.8−(−10.8)]/(0.00302−0.00334)=−1.25×104 K[-6.8-(-10.8)]/(0.00302-0.00334)=-1.25\times10^4\,\mathrm{K}. Since gradient =−Ea/R=-E_a/R, Ea=−(−1.25×104)(8.31)=1.04×105 J mol−1=104 kJ mol−1E_a=-(-1.25\times10^4)(8.31)=1.04\times10^5\,\mathrm{J\,mol^{-1}}=104\,\mathrm{kJ\,mol^{-1}}. The negative plot gradient therefore produces a positive activation energy.

Finding Ea from an Arrhenius Plot

HL only

Assessment in practice

Representative question

Question 1

[Maximum number: 2]

Determine the activation energy of the reaction, EaE_{\mathrm{a}}, in kJmol−1\mathrm{kJ} \mathrm{mol}^{-1}, from the Arrhenius plot. Use sections 1 and 2 of the data booklet.

Rate and Mechanisms Summary

Retrieve the route: measure a tangent rate, explain effective collisions, map rate factors, read Ea and energy profiles, evaluate mechanisms, determine molecularity and orders, calculate k, then use Arrhenius gradient and intercept for Ea and A.

Check tangent versus average slope, energy versus orientation, barrier labels, intermediate versus transition state, one-variable trial comparisons, order-dependent units, kelvin temperature and the signs of gradient and Ea.