Pettythug

$\Delta G=-RT\ln K\,$

$\Delta G=\Delta H-T\Delta S\,$

$\Delta H-T\Delta S=-RT\ln K\,$

$K\ ={\frac {k}{\beta }}$

$k={\frac {t_{R}-t_{M}}{t_{M}}}$

$\Delta H-T\Delta S=-RT\ln {\frac {k}{\beta }}$

$ln{\frac {k}{\beta }}={\frac {-\Delta H}{RT}}+{\frac {\Delta S}{R}}$

$lnk-ln\beta ={\frac {-\Delta H}{RT}}+{\frac {\Delta S}{R}}$

$lnk={\frac {-\Delta H}{RT}}+{\frac {\Delta S}{R}}+ln\beta$

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