Arrhenius Equation Calculator

Two rate constants at two temperatures are enough, because the pre-exponential factor cancels between them.

Pre-exponential factor1.5125 × 10¹⁰in the same units as the rate constants

Activation energy143.7496 kJ/mol143,749.6 J/mol

Rate ratio between these temperatures11.25 ×

Fraction of molecules over the barrier at 300 °C7.9339 × 10⁻¹⁴

Effect of a further 10 degrees1.5499 ×from 350 to 360 °C

Effect of lowering the barrier by 10 kJ/mol8.15 ×what a catalyst does

This barrier is outside the 40 to 70 kJ/mol band where the "double per 10 degrees" rule works, so do not expect that shorthand to describe this reaction.

The formula

k = A exp(-Ea / RT) ; ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1)

The two-point form

Measuring a rate constant at two temperatures is enough to recover the activation energy, because the pre-exponential factor cancels between the two readings. That is why the two-point form is the one used in practice: A is awkward to measure directly and rarely needed.

Where the rule of thumb comes from

Chemists say a reaction roughly doubles in rate for every 10 degree rise near room temperature. Put a doubling between 298 and 308 K through the equation and it returns an activation energy of about 53 kJ/mol — which is simply a typical value for ordinary solution chemistry. The rule is a consequence of that coincidence, not a law, and it fails badly for reactions with very high or very low barriers.

The barrier dominates

The activation energy sits in an exponent, so modest changes in it produce enormous changes in rate. At room temperature, lowering the barrier by 6 kJ/mol multiplies the rate by more than ten. That is the whole business of catalysis: not making the reaction more favourable, but lowering the hill in front of it.

Balanced first, always

Every quantity on this page depends on a balanced equation. The coefficients set the molar ratio, the ratio sets the theoretical yield, and the yield is what the percentage is measured against. An unbalanced equation does not give a slightly wrong answer — it gives an answer to a different question.