Rate Constant of Reaction by Eyring Equation Calculator

Eyring Equation:

\[ k = \frac{k_B \cdot T \cdot e^{\left(\frac{\Delta S^\ddagger}{R}\right)} \cdot e^{\left(-\frac{\Delta H^\ddagger}{R \cdot T}\right)}}{h} \]

Rate Constant (1/s):

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1. What is the Eyring Equation Calculator?

Definition: This calculator determines the rate constant of a chemical reaction using the Eyring equation from transition state theory.

Purpose: It helps chemists and chemical engineers predict reaction rates based on thermodynamic activation parameters.

2. How Does the Calculator Work?

The calculator uses the Eyring equation:

\[ k = \frac{k_B \cdot T \cdot e^{\left(\frac{\Delta S^\ddagger}{R}\right)} \cdot e^{\left(-\frac{\Delta H^\ddagger}{R \cdot T}\right)}}{h} \]

Where:

\( k \) — Reaction rate constant (1/s)
\( k_B \) — Boltzmann constant (1.38064852×10⁻²³ J/K)
\( T \) — Absolute temperature (K)
\( \Delta S^\ddagger \) — Entropy of activation (J/(K·mol))
\( \Delta H^\ddagger \) — Enthalpy of activation (J/mol)
\( R \) — Gas constant (8.3145 J/(mol·K))
\( h \) — Planck constant (6.626070040×10⁻³⁴ J·s)

Explanation: The equation relates the reaction rate to the temperature and the activation parameters of the transition state.

3. Importance of Rate Constant Calculation

Details: Accurate rate constants are essential for reaction engineering, kinetic modeling, and process design in chemical industries.

4. Using the Calculator

Tips: Enter the temperature in Kelvin, activation entropy in J/(K·mol), and activation enthalpy in J/mol. Temperature must be > 0K.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for activation parameters?
A: ΔS‡ ranges from -200 to +200 J/(K·mol), ΔH‡ typically 50-200 kJ/mol (convert to J/mol for calculation).

Q2: How does temperature affect the rate constant?
A: Rate generally increases with temperature, following the exponential terms in the Eyring equation.

Q3: What's the difference between Arrhenius and Eyring equations?
A: Eyring provides a physical interpretation via transition state theory, while Arrhenius is purely empirical.

Q4: Can I use this for enzyme-catalyzed reactions?
A: Yes, but biological systems may require additional considerations like pH effects.

Q5: Why are the constants so small?
A: The fundamental constants (kB, h) are very small, but the exponential terms often compensate.