How do I convert activation energy from kJ/mol to J/mol?

Multiply the value in kJ/mol by 1,000 to get J/mol. For example, an activation energy of 75 kJ/mol equals 75,000 J/mol. This is necessary because the gas constant R = 8.314 J/(mol·K) uses joules, not kilojoules. This calculator accepts both units: select kJ/mol from the dropdown and the conversion is applied automatically.

What does the pre-exponential factor A represent?

The pre-exponential factor A (also called the frequency factor or collision frequency) represents the maximum possible rate constant if every collision between reactant molecules led to a reaction, regardless of orientation or energy. Its units match those of k: for a first-order reaction, A is in s⁻¹; for a second-order reaction, A is in L/(mol·s). A accounts for the frequency of collisions and the fraction of molecules that have the correct orientation to react. Typical values range from about 10^10 to 10^13 s⁻¹ for gas-phase reactions.

Rate Constant (Arrhenius) Calculator

This calculator works out the reaction rate constant k using the Arrhenius equation, the standard way chemists predict how much faster or slower a reaction runs as temperature changes. In single-temperature mode, you enter the pre-exponential factor A, the activation energy Ea in kJ/mol or J/mol, and the temperature in Kelvin or Celsius. It returns the rate constant k, its natural log ln(k), and a step-by-step breakdown showing the Ea/(RT) ratio and the Boltzmann factor that produced it. Switch to two-temperature mode when you already know a rate constant k1 at one temperature T1 and want to find k2 at a different temperature T2 for the same activation energy; this mode returns k1, k2, and the k2/k1 ratio, showing how many times faster or slower the reaction runs at the new temperature. Both panels include a worked example matching the default inputs, so you can check your own figures follow the same steps. This is useful for planning laboratory experiments, checking coursework, or understanding why reaction rates climb so sharply with heat, since even a modest activation energy makes k extremely sensitive to temperature. The equation assumes A and Ea stay constant with temperature, which holds well for most simple reactions but can break down at very high or very low temperatures, so treat the output as a theoretical estimate rather than a substitute for measured laboratory data.

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Method verified 2025 Arrhenius equation as stated in IUPAC recommendations. R = 8.314 J/(mol·K).

1. Reaction Parameters

Pre-exponential factor (A) same units as k

s⁻¹ (or appropriate)

Activation energy (Ea)

kJ/mol

Activation energy units

2. Temperature

Temperature

Temperature unit

k = A · exp(−Ea ÷ (R · T))

Arrhenius Result

Temperature (K)

298.00 K

Absolute temperature

Rate Constant k
0.7132
Arrhenius result

ln(k)

-0.3380

Natural log of k

Calculation Steps

A (pre-exponential factor)1 × 10^13

Ea (activation energy)7.500e+4 J/mol

T (temperature)298.00 K

R (gas constant)8.314 J/(mol·K)

Ea / (R · T)30.2716

e^−Ea/(RT)7.132 × 10^-14

k = A · e^−Ea/(RT)0.7132

Worked Example

A1 × 10¹³ s⁻¹

Ea75 kJ/mol (75,000 J/mol)

T298 K (25 °C)

Ea/(RT)75000 / (8.314 × 298) = 30.27

e^−30.277.13 × 10⁻¹⁴

k0.713 s⁻¹

Result: Enter values above to calculate the rate constant.

1. Known State (k1 at T1)

Rate constant k1

Temperature T1

2. Target State

Activation energy (Ea)

kJ/mol

Activation energy units

Temperature T2

ln(k2/k1) = (Ea/R) · (1/T1 − 1/T2)

Two-Temperature Result

k1 (at T1)

Known rate constant

k2 (at T2)
-
Calculated rate constant

k2 / k1 ratio

Speed-up factor

Calculation Steps

Ea in J/mol-

T1 (K)-

T2 (K)-

1/T1 − 1/T2-

(Ea/R) · (1/T1 − 1/T2)-

k2/k1 = e^above-

k2 = k1 × (k2/k1)-

Worked Example

k10.713 s⁻¹ at 298 K

Ea75 kJ/mol (75,000 J/mol)

T2323 K (50 °C)

1/298 − 1/3232.597 × 10⁻⁴ K⁻¹

(Ea/R) · Δ(1/T)2.343

k2/k1 = e^2.34310.41

k27.42 s⁻¹

Result: Enter values above to calculate k2.

What Is the Arrhenius Equation?

The Arrhenius equation describes the temperature dependence of chemical reaction rate constants. Published by Svante Arrhenius in 1889, it remains the standard way to predict how much faster a reaction proceeds when temperature increases. The equation is:

k = A · e^{−Ea / (R · T)}

Where:

k is the rate constant (units depend on reaction order)
A is the pre-exponential factor (same units as k), representing the maximum collision frequency
Ea is the activation energy in joules per mole (J/mol)
R is the universal gas constant: 8.314 J/(mol·K)
T is the absolute temperature in Kelvin (K = °C + 273.15)

How to Use This Calculator

Single temperature mode: enter A, Ea, and T to find k directly. This is the most common use case for laboratory calculations.

Two-temperature mode: if you already know k at one temperature and want to find k at another temperature, use this mode. It applies the linearised Arrhenius equation:

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

This avoids needing to know A separately.

Worked Example

A first-order reaction has A = 1 × 10¹³ s⁻¹ and Ea = 75 kJ/mol. What is k at 25 °C (298 K)?

Convert Ea to J/mol: 75 kJ/mol × 1,000 = 75,000 J/mol
Compute Ea/(RT) = 75,000 / (8.314 × 298) = 30.27
Compute e^−30.27 = 7.13 × 10⁻¹⁴
Multiply: k = 1 × 10¹³ × 7.13 × 10⁻¹⁴ = 0.713 s⁻¹

This matches the calculator output for the default inputs.

Units of k and A

Reaction Order	Units of k	Units of A
Zero order	mol L⁻¹ s⁻¹	mol L⁻¹ s⁻¹
First order	s⁻¹	s⁻¹
Second order	L mol⁻¹ s⁻¹	L mol⁻¹ s⁻¹

The units of A must always match those of k. The Boltzmann factor e^−Ea/(RT) is dimensionless, so it does not affect the units.

The 10-Degree Rule

A common approximation in chemistry is that reaction rates roughly double for every 10°C rise in temperature. This is a useful rule of thumb, but the Arrhenius equation gives a more accurate answer because the actual ratio depends on the activation energy. A reaction with Ea = 75 kJ/mol and T1 = 298 K has k2/k1 = 10.4 when T rises by 25 K to 323 K, as shown in the worked example above.

Related Calculators

Sources and method: Arrhenius, S. (1889). "Uber die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Sauren." Zeitschrift fur Physikalische Chemie. IUPAC compendium of chemical terminology (Gold Book): rate of reaction and rate constant. Atkins, P.; de Paula, J. (2014). Physical Chemistry (10th ed.), Oxford University Press.

This calculator provides results based on the standard Arrhenius equation for educational and laboratory-planning purposes. It assumes ideal conditions where A and Ea are temperature-independent. For some reactions, particularly at very high or very low temperatures, deviations from Arrhenius behaviour may occur. The pre-exponential factor A is typically determined from experimental data.