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Arrhenius Equation Calculator

Chemistry

Calculate the rate constant k using the Arrhenius equation from activation energy, pre-exponential factor A, and temperature. Essential for reaction kinetics and chemical engineering.

75 kJ/mol
kJ/mol
10,000,000,000,000
298 K
K

Rate Constant (k)

0.713
ln(k)
-0.338
−Ea/RT
-30.272

This calculator computes your Rate Constant (k), ln(k), −Ea/RT from the values you enter.

Inputs
Activation Energy (Ea)Pre-exponential Factor (A)Temperature
Outputs
Rate Constant (k)ln(k)−Ea/RT

What is a Arrhenius Equation?

The Arrhenius Equation Calculator computes the rate constant k for a chemical reaction at a given temperature, using the Arrhenius equation: k = A × e^(−Ea/RT). It requires three inputs — the activation energy Ea (in kJ/mol), the pre-exponential factor A, and the absolute temperature T (in Kelvin) — and returns k alongside the natural log of k and the exponent value for step-by-step verification.

The Arrhenius equation is the central formula of chemical kinetics. It reveals that the rate constant is not fixed — it changes with temperature in a predictable, exponential way. A reaction with a high activation energy is extremely sensitive to temperature: a 10°C rise may increase the rate by a factor of 10 or more. A reaction with a low activation energy barely changes rate with temperature. Understanding this relationship is critical for designing reactors, predicting shelf lives of pharmaceutical products, and interpreting why living organisms must maintain tight temperature control.

To determine Ea and A from experimental data, use the Activation Energy Calculator with rate constants measured at two temperatures. Once Ea is known, this calculator predicts k at any third temperature — making the two calculators complementary tools for the full Arrhenius kinetics workflow.

How to use this Arrhenius Equation calculator

  1. Obtain the activation energy (Ea) for your reaction from a literature source, a previous experiment, or by computing it with the Activation Energy Calculator. Enter it in the Activation Energy (Ea) field in kJ/mol.
  2. Enter the pre-exponential factor A in the Pre-exponential Factor (A) field. A is specific to the reaction and its units match the rate constant units. For gas-phase bimolecular reactions, typical values are 10⁹–10¹¹ L/(mol·s).
  3. Enter the temperature in Kelvin in the Temperature field. Convert °C to K: add 273.15.
  4. Read the Rate Constant (k) — verify the order of magnitude is physically reasonable (not negative, not absurdly large).
  5. Check the −Ea/RT (exponent) value — it should be negative. Positive exponent would indicate a sign error in inputs.
  6. Use k to predict concentration vs. time profiles using integrated rate laws via the Rate Constant Calculator.

Formula & Methodology

Arrhenius equation:

k = A × e^(−Ea/RT)

Linear (logarithmic) form:

ln(k) = ln(A) − Ea/(R × T)

Derived outputs:

exponent = −Ea(J/mol) / (R × T)  [where Ea(J/mol) = Ea(kJ/mol) × 1000] ln(k) = ln(A) + exponent k = e^(ln k)

Worked example — rate constant for N₂O₅ decomposition:

Literature values: Ea = 103.4 kJ/mol, A = 4.94 × 10¹³ s⁻¹

At T = 338 K (65°C):

Step 1 — Convert Ea: 103.4 × 1000 = 103,400 J/mol  Step 2 — Exponent: −Ea/RT = −103,400 / (8.314 × 338) = −103,400 / 2,810 = −36.80  Step 3 — Rate constant: k = 4.94 × 10¹³ × e^(−36.80)   = 4.94 × 10¹³ × 8.59 × 10⁻¹⁷   = 4.24 × 10⁻³ s⁻¹

At 25°C (298 K) the same calculation gives k ≈ 3.4 × 10⁻⁵ s⁻¹. The 40°C temperature rise increases the rate constant by a factor of ~125 — consistent with the high activation energy of this reaction.

Frequently Asked Questions

The Arrhenius equation is k = A × e^(−Ea/RT), where k is the rate constant for a reaction, A is the pre-exponential (frequency) factor with the same units as k, Ea is the activation energy in J/mol, R is the gas constant (8.314 J/mol·K), and T is the absolute temperature in Kelvin. The equation quantifies how the rate constant increases exponentially with temperature and decreases exponentially with activation energy. It was proposed by Swedish chemist Svante Arrhenius in 1889 and remains the foundation of chemical kinetics.
The pre-exponential factor A (also called the frequency factor or collision frequency factor) represents the rate at which collisions occur between reactant molecules regardless of whether they have sufficient energy to react. It carries the same units as the rate constant k (s⁻¹ for first-order, L/mol·s for second-order) and depends on the frequency of molecular collisions and the geometric orientation requirements for reaction. A is typically determined experimentally by measuring k at multiple temperatures and performing an Arrhenius plot (ln k vs 1/T).
A and Ea address different aspects of reaction rate. The pre-exponential factor A governs the maximum possible rate at infinite temperature (when the exponential factor approaches 1) — it reflects collision frequency and orientation constraints. Ea governs how steeply the rate varies with temperature — a high Ea means a sharp temperature dependence, a low Ea means the reaction rate is relatively insensitive to temperature. Both must be known to calculate k at any given temperature.
Enter Ea in kJ/mol, the pre-exponential factor A, and the temperature T in Kelvin. The calculator converts Ea to J/mol (by multiplying by 1,000), computes the exponent −Ea/(RT) using R = 8.314 J/(mol·K), and returns k = A × e^(−Ea/RT). To find A and Ea from experimental data, use the two-temperature method in the [Activation Energy Calculator](/activation-energy-calculator/) — you need at least two (k, T) measurements.
For gas-phase bimolecular reactions, A is typically 10⁹–10¹¹ L/(mol·s), approaching the collision frequency. For unimolecular reactions (first-order), A is typically 10¹²–10¹⁵ s⁻¹, close to molecular vibrational frequencies. For enzyme-catalysed reactions, A can be much lower (10⁵–10⁹ L/mol·s) because the enzyme-substrate binding requirement reduces the effective collision frequency. If you do not know A, the [Activation Energy Calculator](/activation-energy-calculator/) can determine both Ea and A simultaneously from rate constant data at two temperatures.
k increases exponentially with temperature according to the Arrhenius equation. The exponential factor e^(−Ea/RT) grows rapidly as T increases, because the fraction of molecules with energy ≥ Ea rises sharply with temperature. As a rule of thumb (van't Hoff rule), many reactions approximately double in rate for every 10°C rise in temperature — this corresponds to an activation energy of about 50 kJ/mol near room temperature. For reactions with higher Ea, the rate increase per 10°C is larger.
Enter the activation energy Ea in kJ/mol (the calculator converts to J/mol internally). Enter the pre-exponential factor A in the same units as the rate constant you want (s⁻¹ for first-order, L/mol·s for second-order). Enter the temperature T in Kelvin. The calculator returns k = A × e^(−Ea/RT), along with ln(k) and the exponent −Ea/RT for verification.
Taking the natural log of both sides gives: ln(k) = ln(A) − Ea/(R × T). This is a linear equation in 1/T: a plot of ln(k) vs 1/T gives a straight line with slope = −Ea/R and y-intercept = ln(A). This Arrhenius plot is the standard experimental method for determining Ea and A from rate constant measurements at multiple temperatures. The negative slope confirms that higher temperature (lower 1/T) gives higher k.
Extensively — India is one of the world's largest producers of bulk drugs (APIs), dyes, agrochemicals, and fertilisers, all involving temperature-controlled reaction kinetics. The Arrhenius equation determines optimal reactor temperatures for maximum rate while controlling selectivity, and it underpins accelerated stability testing protocols required by CDSCO and followed at companies like Dr. Reddy's, Sun Pharma, and Cipla. It is also used in food processing (pasteurisation design), polymer curing, and cement chemistry.
The Eyring equation from transition state theory is k = (k_B × T / h) × e^(−ΔG‡/RT), where k_B is Boltzmann's constant, h is Planck's constant, and ΔG‡ is the Gibbs free energy of activation. Unlike the Arrhenius equation (which treats A and Ea as temperature-independent), the Eyring equation explicitly accounts for temperature dependence in the pre-exponential term (through the k_B × T / h factor) and separates ΔG‡ into entropic (ΔS‡) and enthalpic (ΔH‡) components. For most practical purposes within a limited temperature range, both equations give equivalent results and Ea ≈ ΔH‡ + RT.