β‘ Arrhenius Equation Calculator
Rate constants, activation energy, and temperature effects.
How to Use This Calculator
Choose what to solve for, enter the known values, and calculate. Temperatures are entered in Celsius and converted to kelvin automatically.
The Arrhenius Equation
ln(k) = ln(A) - Ea / RT
R = 8.314 J/(mol K), T in kelvin
The exponential term is the fraction of molecules with energy above Ea. Because it is exponential, small temperature changes cause large rate changes. Plotting ln(k) against 1/T gives a straight line with slope -Ea/R, the classic Arrhenius plot.
Worked Example
A = 1e13 /s, Ea = 75 kJ/mol, T = 25 C (298.15 K): exponent = -75,000 / (8.314 x 298.15) = -30.26. k = 1e13 x e^-30.26 = 7.2e-1 /s roughly. Raise T to 35 C and k roughly doubles.
What Activation Energy Tells You
Activation energy is the hill reactants must climb before becoming products. Low Ea (under 40 kJ/mol) means a fast reaction at room temperature; high Ea (over 100 kJ/mol) means the reaction barely proceeds without heat. Catalysts work by providing a lower-energy path, not by changing the start or end points. Enzymes are spectacular at this: they can cut activation energies by 50 kJ/mol or more, speeding reactions by millions of times.
The Rule of Thumb
Reaction rates roughly double for every 10 C rise in temperature, which falls out of the Arrhenius equation for typical activation energies around 50 kJ/mol. Food spoils faster on the counter than in the fridge for exactly this reason. But the rule breaks down for very high or low activation energies, so use this calculator for real numbers instead of guessing.
Catalysts and the Equation
A catalyst lowers Ea without being consumed, which the Arrhenius equation shows as a dramatically larger k. Enzymes achieve this by stabilizing the transition state. The pre-exponential factor A can also change with catalysts since the reaction pathway and collision geometry differ from the uncatalyzed route.
Frequently Asked Questions
What is the Arrhenius equation?
k = A x e^(-Ea/RT) relates a reaction rate constant k to temperature T. A is the pre-exponential factor, Ea the activation energy, R the gas constant. It explains why reactions speed up dramatically with heat.
How do I find activation energy from two rate constants?
Use the two-point form: ln(k2/k1) = (Ea/R)(1/T1 - 1/T2). Measure k at two temperatures, plug in, and solve for Ea. This calculator does it directly.
What are typical activation energies?
Most organic reactions fall between 40 and 120 kJ/mol. Enzyme reactions are lower, 20 to 50 kJ/mol. Combustion and explosions can be under 20 kJ/mol, which is why they run away so fast.
Why do reactions go faster when heated?
Higher temperature means more molecules have enough energy to clear the activation barrier, and they collide more often. A 10 C rise roughly doubles most reaction rates near room temperature.
What units do I use for R?
Use 8.314 J/(mol K) with Ea in J/mol, or 0.008314 kJ/(mol K) with Ea in kJ/mol. Temperature must always be in kelvin. This calculator handles the conversions.