ChemBench

Arrhenius Equation Calculator

How temperature controls reaction speed.

Pre-exponential factor A

Activation energy (J/mol)

Temperature (K)

Rate constant k

0.713

What you entered

Pre-exponential factor A: 10000000000000Activation energy (J/mol): 75000Temperature (K): 298

1
k = A × e^(−Ea ÷ RT)
10000000000000 × e^(−75000 ÷ (8.314 × 298))= 7.1322e-1

Result

Rate constant k: 0.713

At 298K, the rate constant k is 7.1322e-1.

Rate constant from activation energy and temperature

k equals A times e to the power of minus Ea over RT. The exponential makes the rate constant extraordinarily sensitive to activation energy.

Pre-exponential A	Activation energy	Temperature	Rate constant k
1 x 10^13	25 kJ/mol	298.15 K	4.1682 x 10^8
1 x 10^13	50 kJ/mol	298.15 K	1.7374 x 10^4
1 x 10^13	50 kJ/mol	310 K	3.7562 x 10^4
1 x 10^13	75 kJ/mol	298.15 K	7.2416 x 10^-1
1 x 10^13	100 kJ/mol	298.15 K	3.0184 x 10^-5
1 x 10^12	50 kJ/mol	350 K	3.4486 x 10^4

Rows two and three show the familiar rule of thumb: a 10 degree rise roughly doubles the rate. Rows one to five show the other half of the story, where doubling the activation energy from 50 to 100 kJ/mol slows the reaction by nine orders of magnitude.

Why heat speeds up reactions so dramatically

The Arrhenius equation shows the rate constant depends exponentially on temperature — this is why a modest temperature increase (say, 10°C) can roughly double a reaction's rate, far more than a linear relationship would predict.

Where activation energy comes in

A higher activation energy makes a reaction more sensitive to temperature changes — this is the same math behind why refrigeration dramatically slows food spoilage reactions.

Frequently asked questions

With A = 1 × 10¹⁰ s⁻¹, Ea = 50 kJ/mol, and T = 298 K, what is the rate constant?

k = A × exp(-Ea/RT) = 1×10¹⁰ × exp(-50000/(8.314×298)) = 1×10¹⁰ × exp(-20.2) = 1×10¹⁰ × 1.67×10⁻⁹ ≈ 16.7 s⁻¹.

How is the Arrhenius calculator different from the activation energy calculator?

This calculator computes the rate constant k from known Ea, A, and T. The activation energy calculator works backward — it finds Ea from two experimental rate constants measured at two different temperatures.

What does the pre-exponential factor A represent?

A reflects how often molecules collide with the correct orientation. It is typically determined experimentally and ranges from about 10⁸ to 10¹³ s⁻¹ for most reactions.

Why does a 10°C increase roughly double most reaction rates?

For typical activation energies around 50-75 kJ/mol near room temperature, the exponential term approximately doubles for each 10°C rise. Lower Ea reactions are less sensitive; higher Ea reactions are more sensitive.