How to Determine Activation Energy

All chemical reactions require a specific level of energy in order to begin. This quantity called the reaction's activation energy. In order to calculate it we must use a particular form of the Arrhenius equation that has been rearranged into the formula of a straight line (y = mx + b). This formula can be expressed as: ln(k) = -(Ea/R) x (1/T) + ln(A), where k is the reactions rate constant, A is its pre-exponential factor, R is the universal gas constant, T is the temperature at which the reaction is to take place, and Ea is the activation energy itself.

Difficulty: Moderate

Instructions

1. Using the Arrhenius plot, determine the y-intercept of the line and record this value. This value is the pre-exponential factor (A).

2. Determine the coordinates of two points on the line from the Arrhenius plot.

3. Determine the line's slope by using the algebraic equation: slope = (y2 - y1)/(x2 - x1).

4. Refer to the Arrhenius equation presented in the introduction and observe that our line's slope should be equal to (- Ea/R).

5. Divide the calculated slope by the universal gas constant to isolate the value (- Ea) from (- Ea/R)

6. Multiply (- Ea) by -1 to get Ea, the activation energy of our reaction.

Tips & Warnings

• The reaction rate (k) for most reactions can be found by referencing chemistry textbooks or online databases. Always double check your calculations for accuracy and correct units. The line's equation can be written by inserting the y-intercept from step 1 and the slope from step 3 into the linear Arrhenius equation from the introduction.
• Make sure all temperature values are in Kelvins, not Celsius Be careful not to mix up your y2 and y1, or x2 and x1 values in step 3. This will make your calculated slope incorrect.

Resources

• Tutorial on finding a line's slope.

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