Editing Reaction rate constant (section)

== Relationship to other parameters ==
For a first-order reaction (including a unimolecular one-step process), there is a direct relationship between the unimolecular rate constant and the half-life of the reaction: <math display="inline">t_{1/2} = \frac{\ln 2}{k}</math>. [[Transition state theory]] gives a relationship between the rate constant <math>k(T)</math> and the Gibbs free energy of activation {{nowrap|<math>{\Delta G^{\ddagger} = \Delta H^{\ddagger} - T\Delta S^{\ddagger}} </math>,}} a quantity that can be regarded as the free energy change needed to reach the transition state.  In particular, this energy barrier incorporates both enthalpic {{nowrap|(<math>\Delta H^{\ddagger}</math>)}} and entropic {{nowrap|(<math>\Delta S^{\ddagger}</math>)}} changes that need to be achieved for the reaction to take place:<ref>{{cite book |last1=Laidler |first1=Keith J. |author-link=Keith J. Laidler|title=Chemical Kinetics |date=1987 |publisher=Harper & Row |isbn=0-06-043862-2 |page=113 |edition=3rd}}</ref><ref>{{cite book |last1=Steinfeld |first1=Jeffrey I. |last2=Francisco |first2=Joseph S. |last3=Hase |first3=William L. |title=Chemical Kinetics and Dynamics |date=1999 |publisher=Prentice Hall |isbn=0-13-737123-3 |page=301 |edition=2nd}}</ref> The [[Eyring equation|result from transition state theory]] is {{nowrap|<math display="inline">k(T) = \frac{k_{\mathrm{B}}T}{h}e^{-\Delta G^{\ddagger}/RT}</math>,}} where ''h'' is the [[Planck constant]] and ''R'' the [[molar gas constant]].  As useful rules of thumb, a first-order reaction with a rate constant of 10<sup>−4</sup> s<sup>−1</sup> will have a half-life (''t''<sub>1/2</sub>) of approximately 2 hours.  For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (Δ''G''<sup>‡</sup>) is approximately 23 kcal/mol.