CHM-17

Eyring equation

k = (kB T/h) exp(−ΔG‡ / RT). Transition-state rate.

Reading speed

KineticsEyring 1935

Governing equation

k=\dfrac{k_B T}{h}\exp(-\Delta G^\ddagger/RT)

where

T: Temperature (K)
\Delta G^\ddagger: Activation Gibbs energy (kJ/mol)
k: Rate constant (1/s)

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-17 — Eyring equation) is the form associated with Eyring 1935. Working symbols: $T$ , $\Delta G^\ddagger$ $\rightarrow$ $k$ . From statistical TST. The prefactor kB T/h is a universal frequency (~6×10¹² s⁻¹ at 300 K).

Purpose

Purpose: compute

k

from

T

\Delta G^\ddagger

in Physical chemistry via

k=\dfrac{k_B T}{h}\exp(-\Delta G^\ddagger/RT)

k = (kB T/h) exp(−ΔG‡ / RT). Transition-state rate. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T = 298.000\,\mathrm{K}

\Delta G^\ddagger = 80.000\,\mathrm{kJ/mol}

, the governing relation

k=\dfrac{k_B T}{h}\exp(-\Delta G^\ddagger/RT)

yields

k = 0.058965\,\mathrm{1/s}

. Unimolecular, transmission coefficient κ = 1. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Temperature T298 KActivation Gibbs energy \Delta G^\ddagger80 kJ/mol

Outputs

Rate constant k0.058965 1/s

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Unimolecular, transmission coefficient κ = 1.

From statistical TST. The prefactor kB T/h is a universal frequency (~6×10¹² s⁻¹ at 300 K).

Reading speed

Watch on YouTube