Arrhenius Equation Calculator

Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

Arrhenius equation: A model that relates a reaction rate constant to temperature, activation energy, and a pre-exponential factor: k = A exp(-Ea/(RT)). [2]

Rate constant (k): A number in a rate law that describes reaction speed under stated conditions. Its unit depends on reaction order.

Pre-exponential factor (A): The scale factor in the Arrhenius equation. It has the same unit as k.

Activation energy (Ea): The energy term in the Arrhenius model, commonly stated in J/mol or kJ/mol.

Absolute temperature: Temperature measured in Kelvin (K). The Arrhenius equation uses Kelvin, not Celsius or Fahrenheit.

R: The molar gas constant, 8.31446261815324 J/(mol K), used after Ea is converted to J/mol. [1]

ln: The natural logarithm. It is defined only for positive numbers.

Mistake: Entering 25 as Kelvin when the source says 25 C.
Fix: Enter 25 and choose C. The calculator converts it to 298.15 K.

Mistake: Entering Ea in kJ/mol while "Activation-energy unit" is set to J/mol.
Fix: Match the selector to the unit beside Ea. For example, enter 50 with kJ/mol for 50 kJ/mol.

Mistake: Entering zero or a negative value for A or a known k.
Fix: Check the source value and any scientific notation. The supported equations require positive A and positive known rate constants.

Mistake: Using different units for k1 and k2 in a two-temperature calculation.
Fix: Convert one rate constant first so k1 and k2 have the same unit before entering them.

Mistake: Treating k as reaction time, percent yield, or product amount.
Fix: Report k as a rate constant with its reaction-order-dependent unit, such as s^-1 or L mol^-1 s^-1.

Mistake: Using the same temperature for T1 and T2 when finding activation energy from two temperatures.
Fix: Use two different temperatures, each paired with its measured rate constant.

• The calculation assumes Arrhenius behavior over the entered temperatures; a reaction can depart from this model if its mechanism or controlling conditions change.
• Predicting k at a second temperature assumes that A and Ea do not change between the two conditions.
• Every entered temperature must convert to more than 0 K.
• A and any known k used in a logarithm must be positive. Finding Ea from two temperatures also requires different T1 and T2 values.
• The calculator preserves a rate-constant unit you enter, but does not infer reaction order or convert between rate-constant unit systems for different reaction orders.
• Very large exponent magnitudes can exceed normal computer number range, so no numeric result is shown in that case.
• A negative fitted Ea can be calculated, but its physical interpretation depends on the experimental system and model.

Equation and unit conversion

The calculator uses the Arrhenius relationship between rate constant, pre-exponential factor, activation energy, and absolute temperature. [2] It converts entered temperatures to Kelvin and Ea to J/mol before using the gas constant.

k = A exp(-Ea / (R T))

T(K) = T(C) + 273.15

T(K) = (T(F) - 32) x 5/9 + 273.15

Ea(J/mol) = Ea(kJ/mol) x 1000

R is 8.31446261815324 J/(mol K), the CODATA molar gas constant. [1]

Other unknowns

For another selected unknown, the calculator uses the matching rearrangement. In two-temperature calculations, k1 and k2 must use the same unit.

Ea = -R T ln(k / A)

A = k exp(Ea / (R T))

T = -Ea / (R ln(k / A))

k2 = k1 exp((-Ea / R) x (1 / T2 - 1 / T1))

Ea = R ln(k2 / k1) / (1 / T1 - 1 / T2)

Worked mini-example

With A = 1000 s^-1, Ea = 2.494338785445972 kJ/mol, and T = 26.85 C, the calculator converts Ea to 2494.338785445972 J/mol and T to 300 K. The equation gives k = 367.879441171442 s^-1, which is about 368 s^-1 to three significant figures.

Rounding and checks

The significant-figures setting changes displayed rounding only; calculations use unrounded values. The calculator also checks that temperatures are above 0 K and that values used inside ln are positive.