The Arrhenius Equation
- The effect of temperature on reaction rate can be explained in terms of kinetic theory
- Increasing temperature greatly increases the fraction of molecules with very high velocity and high kinetic energies
- These molecules are more likely to react on collision and produce enough energy equal to or greater than the activation energy
- Hence, the higher the temperature, the larger the fraction of molecules that can provide the activation energy required for reaction
- Based on the collision model, the rate constant for an elementary reaction was given as
k = p × Z × f (equation 1)
- Where:
- Z, the collision frequency
- f, the fraction of collisions p, the steric factor
- The steric factor, p, is presumably temperature-independent
- The collision frequency, Z, is relatively insensitive to temperature
- For example, when the temperature increases from 500 to 600 K, Z increases by less than 10%
- On the other hand, the relationship between the fraction of collisions with energy greater than the activation energy and temperature has been shown as:
f = e-Ea/RT (equation 2)
- Where:
- e is a mathematical constant (can be found on your calculator - it has the approximate value of 2.718
- Ea is activation energy measured in J/mol
- R is the gas constant (8.314 Jmol-1K-1)
- T is the absolute temperature in K
- A combination of equations 1 and 2 gives the Arrhenius equation, which shows how the rate constant is dependent on temperature
k = Ae-Ea/RT
- Where A is a constant and called the frequency factor
- This factor is related to the frequency of collisions, Z and the steric factor, p
- In general, as the value of Ea increases, k decreases
- This is because the fraction of molecules that possess the required energy is smaller
- On taking the natural log of both sides of the Arrhenius equation, the equation becomes:
ln k = ln A - Ea/RT
- A plot of ln k against 1/T gives a straight line with a negative slope:
Arrhenius’s Plot
Graph showing the relationship between absolute temperature and the rate constant of a reaction
Exam Tip
- Although calculations involving Arrhenius’s equation will not be assessed this year (2024), it is important to take note of the relationship between rate constant, activation energy and temperature of a reaction