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# Eyring equation

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:
$k = left\left(frac\left\{k_BT\right\}\left\{h\right\}right\right) expleft\left(frac\left\{Delta S^ddagger\right\}\left\{R\right\}right\right) expleft\left(-frac\left\{Delta H^ddagger\right\}\left\{RT\right\}right\right)$
The linear form of the Eyring equation is:
$ln frac\left\{k\right\}\left\{T\right\} = frac\left\{-Delta H^ddagger\right\}\left\{R\right\} cdot frac\left\{1\right\}\left\{T\right\} + ln frac\left\{k_b\right\}\left\{h\right\} + frac\left\{Delta S^ddagger\right\}\left\{R\right\}$
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 $ln\left(k/T\right)$ 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 $ln\left(k_b/h\right) + Delta S^ddagger / R$ from which the entropy of activation is derived