Effect of Temperature on Rate Constant, k

Quick Notes

• Increasing temperature increases the rate of a reaction and rate constant, k.
• Higher temperature means more molecules with E ≥ E_a giving faster rate and larger k.
• The Arrhenius equation shows how rate constant (k) changes with temperature:

• where:
  • A = Arrhenius constant (pre-exponential factor)
  • E_a = Activation energy (J mol⁻¹)
  • R = Gas constant (8.31 J mol⁻¹ K⁻¹)
  • T = Temperature (K)
• The equation can be rearranged into a linear form:

• This allows us to find activation energy (Ea) and A by plotting a ln k vs. 1/T graph, with slope = -E_a / R.

Full Notes

See rates and rate equations for essential background theory to this page.

Reaction rate increases with temperature, giving a larger value of k, the rate constant.

This is because reactant particles have more kinetic energy and the frequency of collisions between particles with at least the activation energy (E_a) increases.

The link between temperature and k is explained mathematically using the Arrhenius equation.

The Arrhenius Equation and Arrhenius Plots

The Arrhenius Equation, how to rearrange it and using Arrhenius Plots has been covered in more detail in this video. What is on this page is just the essentials you need to know for OCR (A) A-level Chemistry :)

The Arrhenius equation shows how activation energy (E_a), temperature (T) and the proportion of collisions with correct orientation (A) can be linked together by the rate constant, k.

where:

• A = Arrhenius constant (collision frequency factor).
• E_a = Activation energy (J mol⁻¹).
• R = Gas constant (8.31 J mol⁻¹ K⁻¹).
• T = Temperature (K).

This also shows why k increases with temperature — the e^-E_a/RT part of the expression gets bigger as T increases.

The Arrhenius equation is an exponential equation because it contains ‘e’. To make it easier to work with, we can rearrange it to a straight line form (y = mx+c) by multiplying both sides by ln:

This can be rearranged to follow the y = mx + c function of a straight line, where y = ln k and x = 1/T:

This allows us to plot ln k vs. 1/T (called an Arrhenius plot).

The gradient of the line = -E_a / R, allowing activation energy to be calculated:

−E_a ÷ R = m → E_a = −m × R

Matt’s exam tip

When using the Arrhenius equation in calculations, don’t forget units of activation energy (E_a) are kJ mol⁻¹. The gas constant, R, has units of J K⁻¹ mol⁻¹, meaning you must convert any calculated E_a value to kJ by dividing by 1000.

Summary

• Increasing temperature increases the rate constant, k, due to more molecules having E ≥ E_a.
• The Arrhenius equation links k, A, E_a, R and T.
• Rearranging the equation allows a linear form to be plotted as ln k vs. 1/T.
• The slope of the plot is −E_a/R, which allows calculation of activation energy.