How To Find Activation Energy Instructions 6 Examples

Swedish scientist Svante Arrhenius pioneered the concept of activation energy and, in 1889, came up with an equation to calculate it. This is now known as the “Arrhenius equation:" k = Ae^(-E_a/RT)

The pre-exponential factor is a temperature-dependent representation of the frequency of molecular collisions.

k = Ae^(-E_a/RT) ln(k) = -E_a/R * 1/T + ln(A) E_a = -R * T * ln(k/A)

E_a = -R * T * ln(k/A) E_a = -8. 3145 * 234 * ln(21/31)

E_a = -1945. 6 * ln(0. 38946) E_a = -1945. 6 * -0. 38946 E_a = 757. 7 J/mol (0. 7577 kJ/mol)

As a refresher, the original Arrhenius equation is k = Ae^(-E_a/RT).

E_a = R * ln(k_1/k_2) / (1/T_2 - 1/T_1)

E_a = R * ln(k_1/k_2) / (1/T_2 - 1/T_1) E_a = 8. 3145 * ln(33/45) / (1/675 - 1/298)

E_a = 8. 3145 * ln(33/45) / (1/675 - 1/298) E_a = 8. 3145 * ln(0. 73333) / (0. 0014814 - 0. 0033557) E_a = 8. 3145 * -0. 31016 / -0. 0018743 E_a = 1375. 9 J/mol

k = Ae^(-E_a/RT) ln(k) = -E_a/R * 1/T + ln(A) E_a = -R * T * ln(k/A) E_a = -8. 3145 * 333 * ln(45/78) E_a = -2768. 7 * ln(0. 57692) E_a = -2768. 7 * -0. 55005 E_a = 1522. 92 J/mol

k = Ae^(-E_a/RT) ln(k) = -E_a/R * 1/T + ln(A) E_a = -R * T * ln(k/A) E_a = -8. 3145 * 517 * ln(32/95) E_a = -4298. 6 * ln(0. 33684) E_a = -4298. 6 * -1. 0881 E_a = 4677. 3 J/mol

k = Ae^(-E_a/RT) ln(k_1/k_2) = -E_a/R * (1/T_2 - 1/T_1) E_a = R * ln(k_1/k_2) / (1/T_2 - 1/T_1) E_a = 8. 3145 * ln(19/78) / (1/451 - 1/222) E_a = 8. 3145 * ln(. 24359) / (0. 0022173 - 0. 0045045) E_a = 8. 3145 * -1. 4122 / -0. 0022872 E_a = 5133. 7 J/mol

Calculate the slope (m) using the slope equation m = (y_2 - y_1) / (x_2 - x_1). To do this calculation, find the y and x coordinates at two separate points along the line. Plug the slope into E_a = -R * m, with R representing the ideal gas constant (8. 3145). So, in a simple example, let’s say m = -2/3: E_a = -8. 3145 * -2/3 → E_a = 5. 543 J/mol