The '''Eyring equation''' also known as '''Eyring-Polyanyi equation''' in chemical kinetics relates the reaction rate to temperature It was developed by Henry Eyring This equation follows from his transition state theory and contrary to the empirical Arrhenius equation this model is theoretical

The general form of the

Eyring equation is:

$k\; =\; left(frac\{k\_BT\}\{h\}right)\; expleft(frac\{Delta\; S^ddagger\}\{R\}right)\; expleft(-frac\{Delta\; H^ddagger\}\{RT\}right)$The

linear form of the

Eyring equation is:

$ln\; frac\{k\}\{T\}\; =\; frac\{-Delta\; H^ddagger\}\{R\}\; cdot\; frac\{1\}\{T\}\; +\; ln\; frac\{k\_b\}\{h\}\; +\; frac\{Delta\; S^ddagger\}\{R\}$with:

- $k$ = reaction rate constant
- $T$ = absolute temperature
- $Delta\; H^ddagger$ =
**enthalpy of activation**
- $R$ = gas constant
- $k\_b$ = Boltzmann constant
- $h$ = Planck's constant
- $Delta\; S^ddagger$ =
**entropy of activation**

A certain

chemical reaction is performed at different temperatures and the

reaction rate is determined The plot of

$ln(k/T)$ versus

$1/T$ gives a straight line with

slope $-Delta\; H^ddagger\; /\; R$ from which the

enthalpy of activation can be derived and with intercept

$ln(k\_b/h)\; +\; Delta\; S^ddagger\; /\; R$ from which the

entropy of activation is derived

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