The Eyring Equation Calculator helps scientists and engineers calculate the rate constant of a chemical reaction based on transition state theory. This tool is especially useful in physical chemistry, biochemistry, and chemical kinetics. It simplifies complex thermodynamic relationships and provides insights into how temperature, entropy, and enthalpy influence the speed of a reaction.
By inputting temperature and activation parameters, users can determine how fast a reaction will proceed. This supports the design of chemical processes, drug development, enzyme kinetics studies, and other areas where reaction rates are critical.
Formula of Eyring Equation Calculator
Eyring Equation:
k = (k_B × T / h) × e^(−ΔG‡ / (R × T))
Where:
k = rate constant (1/s for unimolecular reactions)
k_B = Boltzmann constant = 1.380649 × 10⁻²³ J/K
T = absolute temperature (K)
h = Planck’s constant = 6.62607015 × 10⁻³⁴ J·s
ΔG‡ = Gibbs free energy of activation (J/mol)
R = universal gas constant = 8.314462618 J/mol·K
e = Euler’s number ≈ 2.71828
Alternate form using enthalpy and entropy of activation:
k = (k_B × T / h) × e^(ΔS‡ / R) × e^(−ΔH‡ / (R × T))
Where:
ΔH‡ = activation enthalpy (J/mol)
ΔS‡ = activation entropy (J/mol·K)
This calculator takes these variables and returns the reaction rate constant, helping users understand the energy dynamics of a transition state.
Reference Table for Common Constants and Parameters
| Constant or Variable | Meaning | Value or Unit |
|---|---|---|
| k_B | Boltzmann constant | 1.380649 × 10⁻²³ J/K |
| h | Planck’s constant | 6.62607015 × 10⁻³⁴ J·s |
| R | Universal gas constant | 8.314462618 J/mol·K |
| T | Temperature | Input by user (K) |
| ΔG‡ | Gibbs free energy of activation | Input by user (J/mol) |
| ΔH‡ | Enthalpy of activation | Input by user (J/mol) |
| ΔS‡ | Entropy of activation | Input by user (J/mol·K) |
| k | Rate constant | Output (1/s or relevant unit) |
Use this table to better understand each variable and ensure the correct unit system is applied during calculations.
Example of Eyring Equation Calculator
Suppose a reaction is studied at 298 K with the following data:
ΔG‡ = 75000 J/mol
Using the Eyring equation:
k = (1.380649 × 10⁻²³ × 298 / 6.62607015 × 10⁻³⁴) × e^(−75000 / (8.314462618 × 298))
k ≈ (6.209 × 10¹²) × e^(−30.23)
k ≈ (6.209 × 10¹²) × 7.09 × 10⁻¹⁴ ≈ 0.44 s⁻¹
This means the reaction occurs approximately 0.44 times per second under the given conditions.
Most Common FAQs
This tool falls under the scientific and chemistry calculator category, often used in chemical kinetics and thermodynamics.
Yes, especially for enzyme-catalyzed reactions or any molecular processes where activation energy is relevant. It’s widely used in biochemistry.
The Eyring equation is derived from transition state theory and includes entropy and enthalpy effects, making it more detailed than the Arrhenius equation which mainly considers activation energy and temperature.