Activation energy, abbreviated Ea, can best be described as the minimum energy required before a chemical reaction can proceed. It is like a barrier that has to be overcome in order for your chemical reaction to take place. Activation energy can be calculated in two ways: by using the rates of reaction at two different temperatures or by using the Arrhenius equation.

- Skill level:
- Moderate

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### Things you need

- Paper
- Pencil
- Graphing calculator

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## Instructions

- 1
Write down the equation for finding activation energy.

Activation energy, Ea = ((T1 x T2 x R) / (T2 - T1)) x In(k2 / k1)

"T1" is the first temperature and "T2" is the second temperature. R is the universal gas constant, which equals 8.314 J (K mol). "k1" is the rate of reaction at "T1" and "k2" is the rate of reaction at "T2."

- 2
Plug in the values for the temperatures, reaction rates and universal gas constant. As an instance, take a reaction that has a reaction rate of 0.0139 at 285K and a rate of reaction of 0.0493 at 350K. The resulting equation is:

Ea = (((285K x 350K x 8.314 J/(K mol)) / (350K - 285K))) x In(0.0493 / 0.00139).

- 3
Use your calculator to solve the equation and obtain the activation energy. In this case:

Ea = (829321 / 65) * In(35.47) = 45532.11 J/mol = 45.53 kJ/mol.

## By reaction rate at two different temperatures method

- 1
Take the natural logarithm of both sides of the Arrhenius equation. The Arrhenius equation is:

k = A e ^ -Ea/RT.

"k" is the rate of reaction constant, A is the pre-exponential factor which is assumed to be independent of temperature change, Ea is the activation energy itself, R is the universal gas constant and T the temperature in Kelvin (K).

This gives ln k = ln A - Ea/(RT).

- 2
Rearrange the equation into the formula of a straight line in the form y = mx + c. This yields:

ln k = -Ea/(RT) + constant or ln k = -(Ea/R)(1/T) + constant.

- 3
Use the second option to plot a graph of In k vs. 1/T with a graphing calculator to get (- Ea/R) as your slope as the second option is already in the form y = mx + c.

- 4
Divide the calculated slope by the universal gas constant to isolate the value (- Ea) from (- Ea/R).

- 5
Multiply (- Ea) by -1 to get Ea, the activation energy of your reaction. This forms the basis of the experimental determination of activation energy.

## By experimental method using the Arrhenius equation

#### Tips and warnings

- Always cross-reference your answer/final result with published values in laboratory data log books, chemistry textbooks or on online databases for accuracy and correct units.