Activation Energy Calculator

This activation energy calculator uses the two-point form of the Arrhenius equation to work out the activation energy of a reaction from measurements of its rate constant at two different temperatures. Enter the rate constant and absolute temperature for each measurement and the calculator returns the activation energy in kilojoules per mole, along with the same value in joules per mole and kilocalories per mole, and the ratio by which the rate constant grew between the two temperatures. This is the standard first-year chemistry and kinetics exercise: measure how much faster a reaction runs when you warm it, then back out the energy barrier that the reacting molecules must climb. The rate constants can be in any units you like, first order, second order, it does not matter, because only their ratio enters the maths, but the two temperatures must be in kelvin, so add 273.15 to Celsius values before you type them in. Students use this to check kinetics homework and lab write-ups, while formulators and food technologists use the same equation to judge how strongly a spoilage or degradation reaction responds to storage temperature. A larger activation energy always means a reaction whose speed is more sensitive to temperature change.

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K
K
105.32 kJ/mol
activation energy (Ea)
In joules105,317 J/mol
In kilocalories25.17 kcal/mol
Rate ratio k2/k114

Formula: Ea = R x ln(k2/k1) / (1/T1 - 1/T2), with R = 8.314 J/(mol K). Temperatures must be in kelvin (Celsius + 273.15); both rate constants must share the same units. Assumes the Arrhenius pre-exponential factor is constant over the range.

How it works

The Arrhenius equation, k = A x e^(-Ea/RT), links a rate constant to temperature through the activation energy Ea and the pre-exponential factor A. Writing the equation at two temperatures and dividing one by the other eliminates A, leaving the two-point form: ln(k2/k1) = (Ea/R) x (1/T1 - 1/T2). Rearranged for the activation energy, Ea = R x ln(k2/k1) / (1/T1 - 1/T2). The calculator takes the natural log of the rate constant ratio, computes the difference of the reciprocal temperatures, multiplies by the gas constant, and converts the result from joules to kilojoules and kilocalories per mole.

Worked example

A reaction has a rate constant of 0.0025 at 300 K, and warming it to 320 K raises the rate constant to 0.035, which is 14 times faster. The natural log of 14 is about 2.6391, and 1/300 - 1/320 = 0.00020833. So Ea = 8.314 x 2.6391 / 0.00020833, which is about 105,317 joules per mole, or 105.32 kJ/mol. Dividing by 4,184 gives the same energy as 25.17 kcal/mol. A 20 degree rise producing a 14-fold speed-up is the signature of a fairly high energy barrier.

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Frequently asked questions

How do you calculate activation energy from two rate constants?

Use the two-point Arrhenius equation: Ea = R x ln(k2/k1) / (1/T1 - 1/T2), where R is the gas constant 8.314 J/(mol K) and T1 and T2 are absolute temperatures in kelvin. If a rate constant rises from 0.0025 to 0.035 between 300 K and 320 K, Ea = 8.314 x ln(14) / (1/300 - 1/320), which is about 105.3 kJ/mol.

What is activation energy?

Activation energy is the minimum energy colliding molecules need before a reaction can occur. It sets how strongly a reaction speeds up with temperature: reactions with a large activation energy are very temperature sensitive, while those with a small one change speed only modestly as the temperature rises.

What units should the temperatures and rate constants be in?

Temperatures must be absolute, in kelvin: add 273.15 to a Celsius temperature. The two rate constants can be in any units as long as both use the same units, because only their ratio enters the equation. The result comes out in joules per mole and is usually quoted in kilojoules per mole.