# 5.2.4 The Arrhenius Equation

### The Arrhenius Equation

• At higher temperatures, a greater proportion of molecules have energy greater than than the activation energy
• Since the rate constant and rate of reaction is 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: ln k = natural logarithm of the rate constant

A = constant related to the collision frequency and orientation of the molecules

Ea = 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
• Ea and R are also constants
• 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

#### Exam Tip

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

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