Advanced Topic 492 of 1102 Kinetics & Equilibrium
Eyring Equation
Relates rate constants to activation enthalpy and entropy via transition state theory.
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In-depth explanation of Eyring Equation
The Eyring equation from transition state theory gives the rate constant as k = (kB T/h) exp(-delta G double dagger/RT), where kB is the Boltzmann constant, h is Planck's constant and delta G double dagger is the standard Gibbs energy of activation. Since delta G double dagger equals delta H double dagger minus T delta S double dagger, the equation gives activation enthalpy and entropy from rate constants measured at several temperatures. A plot of ln(k/T) against 1/T gives the activation enthalpy from its slope and the activation entropy from its intercept. A negative activation entropy indicates a highly ordered transition state, while a positive value indicates a looser one.
Going deeper: Eyring Equation
Key ideas: Linear form: ln(k/T) = -delta H double dagger/(R T) + ln(kB/h) + delta S double dagger/R. Plot ln(k/T) against 1/T: slope = -delta H double dagger/R, intercept = ln(kB/h) + delta S double dagger/R. Constants: kB = 1.381 x 10^-23 J per K, h = 6.626 x 10^-34 J s, so kB T/h is about 6.2 x 10^12 per s at 298 K.
Common mistakes and connections: Students confuse delta G double dagger with Ea, or forget that delta H double dagger is smaller than Ea by RT for solution reactions. Another mistake is using ln k and not ln(k/T) for the slope. Units of delta S double dagger depend on the standard state chosen, so compare only values with the same reference. Connects to transition state theory, the Arrhenius equation and pre-exponential factor.
Visualization of Eyring Equation
An Eyring plot of ln(k/T) against 1/T has slope -delta H double dagger/R and gives delta S double dagger from its intercept; here 60 kJ/mol and -40 J/mol K. The interactive lesson shows this as a live animation or chart.
Worked example and use case
A large negative activation entropy indicates a highly ordered transition state, typical of bimolecular associations in which two molecules must align closely.
Frequently asked questions about Eyring Equation
What is Eyring Equation?
Relates rate constants to activation enthalpy and entropy via transition state theory.
Is Eyring Equation a beginner, intermediate or advanced topic?
Eyring Equation is a advanced topic in Kinetics & Equilibrium. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Eyring Equation?
Study these earlier topics in Kinetics & Equilibrium first: Principle of Microscopic Reversibility, Kinetic vs Thermodynamic Product, Hammond Postulate.
What comes after Eyring Equation?
The next topics in Kinetics & Equilibrium are Lindemann Mechanism and Diffusion-Controlled Reactions.
Can I practise Eyring Equation with quizzes?
Yes. The interactive lesson includes a self-check question on Eyring Equation, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Eyring Equation fits in Kinetics & Equilibrium
Eyring Equation is topic 73 of 91 in Kinetics & Equilibrium.