Factors affecting Rate Constant (Cambridge International A-Level Chemistry)

Effect of Temperature on the Rate Constant

• At higher temperatures, a greater proportion of molecules have energy greater than the activation energy

• Since the rate constant and rate of reaction are directly proportional to the fraction of molecules with energy equal or greater than the activation energy, then at higher temperatures:

  • The rate constant increases
  • The rate of reaction increases

• The relationship between the rate constant and the temperature is given by the following equation:

$\mathrm{ln}k=\mathrm{ln}A-\frac{E_{a}}{RT}$

• Where:

  • **ln k = natural logarithm of the rate constant
  • A = constant related to the collision frequency and orientation of the molecules
  • E_a** = activation energy (joules, J)
  • R = gas constant (8.31 J K^-1 mol^-1)
  • T = temperature (kelvin, K)

• A varies only a little bit with temperature, it can be considered a constant

• E_a and R are also constants

• A graph of ln k against $\frac{1}{T}$ gives a line with an equation of the form y = mx + c

$\mathrm{ln}k=\frac{-E_{a}}{R}\frac{1}{T}+\mathrm{ln}A$

• Where:

  • y = ln k
  • x = $\frac{1}{T}$
  • m = $\frac{-E_{a}}{R}$ (the gradient)
  • c = ln A (the y-intercept)

• The equation shows that an increase in temperature (higher value of T) gives a greater value of ln k (and therefore a higher value of k)

• Since the rate of the reaction depends on the rate constant(k) an increase in k also means an increased rate of reaction

Example graph of ln k over 1/T

The graph of ln k over 1/T is a straight line with gradient -Ea/R

Exam Hint You are not required to learn this equation however it is helpful in understanding the effects of temperature on the rate constant.