View source for Rate equation

The '''rate equation''' (or '''rate law''') is an [[equation]] used to calculate the speed of a [[chemical reaction]] (or '''rate of reaction'''). For a general reaction {{nowrap|''a''A + ''b''B → C}}, the rate equation is: 
:<math>v\; =\; k[\mathrm{A}]^x[\mathrm{B}]^y</math>
Here, [A] and [B] are the [[concentration]]s of A and B. ''x'' and ''y'' depend on which step is [[rate-determining step|rate-determining]]. If the [[reaction mechanism]] is a very simple one, where A and B hit each other and then go to products through one [[transition state]], then ''x''=''a'' and ''y''=''b''. ''k'' is the rate constant of the reaction. This changes with [[temperature]], [[pressure]] and other conditions.<ref name=":0">https://courses.lumenlearning.com/introchem/chapter/transition-state-theory/</ref><ref name=":0">https://courses.lumenlearning.com/introchem/chapter/transition-state-theory/</ref> 

The rate equation is a [[differential equation]]. If it is [[integral|integrated]], then an equation which tells how the concentration of reagents and products changes with time is found.

In special cases, it is very easy to solve the equation and find ''k''. For example, in a first-order reaction the equation is:
:<math> v  = -\frac{d[A]}{dt} = k[A]</math>

Integrating gives:

:<math>\ \ln{[A]} = -kt + \ln{[A]_0}</math>

So, a plot of  <math>\ln{[A]}</math> against time ''t'' gives a straight line with a slope of <math>-k</math>.

Sometimes, experiments can be made so that the reaction looks like a first-order one. If the concentration of one reagent is kept at the same high value then it can be thought of as a constant. The equation becomes <math> v=k[A][B]=k'[A]</math> where k' is the pseudo-first order rate constant. Then the method above can be used to calculate k'. 

== Reference ==
{{reflist}}

{{Reaction mechanisms}}

[[Category:Chemical kinetics]]