# 16.2.3 Activation Energy from Rate Constants

### Activation Energy from Rate Constants at Different Temperatures

#### Arrhenius Plots

• Arrhenius plots for two reactions with different activation energies can be drawn on the same graph

Arrhenius plots for two reactions with different activation energies

• The reaction with a steeper gradient has the higher activation energy, Ea
• This indicates that the rate constant, and therefore rate, will change quicker with temperature changes

#### Calculating the Activation Energy

• The activation energy, Ea, can be calculated using rate constant values, k1 and k2, for two given temperatures, T1 and T2
• This requires the use of the following equation that is given in the data booklet:

Double Arrhenius Calculation equation (remove once inserted)

#### Worked Example

Hydrogen iodide decomposes in the gas phase to form hydrogen and iodine

2HI (g) → H2 (g) + I2 (g)

At 283 oC, the rate constant is 3.52 x 10-7 mol dm-3 s-1

At 508 oC, the rate constant is 3.95 x 10-2 mol dm-3 s-1

Calculate the activation energy, Ea, for the reaction

1. Convert the temperatures from oC to K:
• T1: 283 + 273 = 556 K
• T2: 508 + 273 = 781 K
2. Write the appropriate Arrhenius equation from the data booklet
3. Substitute the values
4. Evaluate the equation to get the activation energy, Ea

Double Arrhenius WE1 answer (remove once inserted)

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