Factors affecting Rate Constant (CIE A Level Chemistry)

• 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:

• • 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  gives a line with an equation of the form y = mx + c

• • Where:
    • y = ln k 
    • x = 
    • m =  (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 -E_a/R