CHM-17

Eyring equation

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

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KineticsEyring 1935

Governing equation

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

$T \in \left[200, 600\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$T \in \left[200, 600\right]$

$T = 200$ $k = 5.33\times 10^{-9}$

Along the curve

②

Domain of the variable — blue

T_{\min} = 200,\quad T_{\max} = 600

$T \in \left[200, 600\right]$

$T = 200$ $T = 200$

Along the curve

③

Response curve — green

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

$T \in \left[200, 600\right]$

$T = 200$ $k = 5.33\times 10^{-9}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}k}{\mathrm{d}T}

$T \in \left[200, 600\right]$

$T = 202.5$ $k^{\prime} = 2.48\times 10^{-9}$

Along the curve

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

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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