eyring equation calculator

What Is the Eyring Equation?

The Eyring equation is one of the central formulas in chemical kinetics and transition state theory. It links temperature and activation thermodynamics to a reaction rate constant. Instead of describing rates only through an empirical Arrhenius prefactor, the Eyring approach ties the rate to physically meaningful quantities: activation free energy, activation enthalpy, and activation entropy.

In practice, this gives you a deeper interpretation of why a reaction is fast or slow. A high activation free energy means the transition state is hard to reach, so the reaction is slow. A favorable activation entropy can increase the rate by making transition state formation statistically more likely.

Core Equations Used in This Calculator

Form 1: Using activation free energy

k = (k_BT/h) exp[-ΔG^‡/(RT)]

• k = rate constant
• k_B = Boltzmann constant
• h = Planck constant
• T = absolute temperature in K
• R = gas constant
• ΔG^‡ = Gibbs free energy of activation

Form 2: Using activation enthalpy and entropy

k = (k_BT/h) exp(ΔS^‡/R) exp[-ΔH^‡/(RT)]

This is useful when experimental analysis gives ΔH^‡ and ΔS^‡ directly from temperature-dependent measurements.

How to Use the Calculator

1. Choose a calculation mode.
2. Enter temperature and select unit (K, °C, or °F).
3. Enter thermodynamic input values with consistent units.
4. Click Calculate to get k or ΔG^‡.

The tool automatically converts units internally to SI, then displays results in common chemistry units such as kJ/mol and kcal/mol.

Worked Example

Suppose you enter:

• T = 298.15 K
• ΔG^‡ = 80 kJ/mol

The prefactor (k_BT/h) is around 6.2 × 10¹² s^-1. Multiplying by the exponential barrier term gives a much smaller value, resulting in a modest reaction rate constant. This demonstrates how strongly the exponential term controls kinetics.

Interpreting Results Correctly

1) Small changes in barrier, large changes in rate

Because of the exponential dependence, changing ΔG^‡ by only a few kJ/mol can shift k by orders of magnitude.

2) Temperature matters twice

Temperature appears in the prefactor and in the exponential denominator. As temperature increases, rate constants often rise significantly.

3) Entropy can speed up or slow down reaction

A positive ΔS^‡ generally increases k, while a strongly negative ΔS^‡ can reduce k by making the transition state less accessible.

Common Mistakes to Avoid

• Using Celsius directly in the equation (always convert to Kelvin).
• Mixing kJ/mol with J/mol without conversion.
• Entering non-positive k when solving for ΔG^‡.
• Ignoring unit definitions for entropy (J/mol·K vs cal/mol·K).

Final Notes

This calculator assumes the transmission coefficient is 1, which is a common default in transition state theory. Real systems can deviate, but this model is a powerful first-pass tool for reaction kinetics, catalysis, enzymology, and physical organic chemistry.