Rates: catalysts and the Arrhenius equation template

Reaction rates for A-level and NCERT Class 12: Maxwell–Boltzmann distributions at two temperatures with Eₐ and the catalysed Eₐ marked, an energy profile for a catalysed route through an intermediate (Fe²⁺ catalysis of S₂O₈²⁻ + I⁻), and the Arrhenius equation k = A e^(−Eₐ/RT) with its ln k against 1/T plot and a worked example.

What the template shows

• Only collisions with at least the activation energy react: temperature raises that fraction, a catalyst lowers the barrier
• Maxwell–Boltzmann distribution
• Catalysed route through an intermediate
• number of molecules with energy E
• Hatched: molecules at T₂ with E ≥ Eₐ. Moving Eₐ to the left (catalyst) also puts more of the area beyond it.
• The curve starts at the origin, never meets the energy axis, and the area under it is the same at every temperature.
• uncatalysed: two negative ions repel, so Eₐ is high
• step 2: Fe²⁺ regenerated
• The Arrhenius equation
• k rate constant · A pre-exponential (frequency) factor · Eₐ activation energy / J mol⁻¹ · R = 8.314 J K⁻¹ mol⁻¹ · T / K
• y = c + m x: plot ln k against 1/T
• Worked example
• Eₐ = 50 kJ mol⁻¹, T from 298 K to 308 K: k₂/k₁ = exp[(Eₐ/R)(1/T₁ − 1/T₂)] = 1.93, so the rate roughly doubles for a 10 K rise.
• Fraction of collisions with E ≥ Eₐ at 298 K: e^(−Eₐ/RT) ≈ 1.7 × 10⁻⁹
• At a higher temperature the Maxwell–Boltzmann curve flattens and shifts right (same area: same number of molecules), so many more molecules have E ≥ Eₐ; this, not the extra collisions, is why rate rises steeply.
• A catalyst gives an alternative route with a lower activation energy; it does not change ΔH or the position of equilibrium and is regenerated at the end.
• Heterogeneous catalysts (Fe in the Haber process, V₂O₅ in the Contact process) adsorb reactants on their surface; homogeneous catalysts (Fe²⁺ here) are in the same phase and form an intermediate.
• Arrhenius: ln k = ln A − Eₐ/(RT). A plot of ln k against 1/T is a straight line of gradient −Eₐ/R; NCERT form: log(k₂/k₁) = Eₐ/(2.303R) × (T₂ − T₁)/(T₁T₂).
• Every part of this figure is editable · sources on the template card

Drawn with 553 shapes – every one editable in MolDraw.

Sources

• Atkins, de Paula & Keeler, Atkins' Physical Chemistry, 11th ed., OUP 2018, ch. 17 Textbook
• Atkins, de Paula & Keeler, Atkins' Physical Chemistry, 11th ed., OUP 2018, ch. 1 Textbook
• NCERT, Chemistry Part I, Class XII, ch. 3 Chemical Kinetics Textbook