Enter the temperature, ΔH‡, and ΔS‡ into the calculator to determine the rate constant using the Eyring (Eyring–Polanyi) equation (basic mode assumes κ = 1).
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Eyring Equation Formula
The Eyring (Eyring–Polanyi) equation from transition state theory relates the rate constant (k) at temperature (T) to the activation enthalpy and entropy (ΔH‡ and ΔS‡). A common form is:
k = \kappa \frac{k_B T}{h}\,e^{\Delta S^\ddagger/R}\,e^{-\Delta H^\ddagger/(R T)}Variables:
- k is the rate constant (commonly s-1 for unimolecular/first-order reactions)
- ΔS‡ is the entropy of activation (J/mol·K)
- ΔH‡ is the enthalpy of activation (J/mol)
- κ is the transmission coefficient (dimensionless; often approximated as 1)
- kB is the Boltzmann constant (1.380649×10-23 J/K)
- h is Planck’s constant (6.62607015×10-34 J·s)
- R is the universal gas constant (8.314462618 J/(mol·K))
- T is the temperature (K)
To calculate a rate constant using the Eyring equation, you need the temperature and the activation parameters (ΔH‡ and ΔS‡) for the transition state. These quantities describe the energetic and entropic barrier to forming the activated complex and determine how strongly the rate depends on temperature.
What is the Eyring Equation?
The Eyring equation, also known as the Eyring-Polanyi equation, is a theoretical model that describes the rate at which chemical reactions occur. It is based on transition state theory and provides a relationship between the rate constant of a reaction and the temperature, as well as the enthalpy and entropy of activation (ΔH‡ and ΔS‡). The equation is particularly useful in the field of chemical kinetics and is widely used to analyze reaction rates and understand reaction mechanisms.
How to Calculate Rate Constant Using the Eyring Equation?
The following steps outline how to calculate the rate constant using the Eyring equation.
- First, determine the temperature (T) at which the reaction occurs in Kelvin (K).
- Next, determine the enthalpy of activation (ΔH‡) in joules per mole (J/mol).
- Then, determine the entropy of activation (ΔS‡) in joules per mole per Kelvin (J/mol·K).
- Use the Eyring equation: k = κ (kBT/h) · e(ΔS‡/R) · e(-ΔH‡/(RT)) to calculate the rate constant (k).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Temperature (T) = 298 K
Enthalpy of activation (ΔH‡) = 40,000 J/mol
Entropy of activation (ΔS‡) = 100 J/mol·K
