View source for Reaction rate law

Reaction rates usually depend on concentrations.  The rate law is a mathematical equation which relates the reaction rate to the reactant concentrations.  Consider the general reaction 


:a X + b Y [[File:reactionarrow.gif]] Products


where ‘a’ and ‘b’ are the coefficients in the balanced chemical equation,  X and Y are the reactants.

The rate of a reaction is proportional to the products of the reactants each raised to some power.

:rate = k [X]<sup>n</sup> [Y]<sup>m</sup>

<span style="color:red;">where k, m, and n are numbers that are determined experimentally!!</span>

The reaction is determined to be:
:mth order with respect to X
:nth order with respect to Y
:The overall reaction order is m + n.

m and n are usually small whole numbers but may be fractional, negative or zero.  They are often not related to a and b.   m and n must be determined experimentally.


For example, the reaction between HgCl<sub>2</sub> and C<sub>2</sub>O<sub>4</sub><sup>2-</sup> is found to have the rate law

:Rate = k [HgCl<sub>2</sub>]<span style="color:red;">'''<sup>2</sup>'''</span> [C<sub>2</sub>O<sub>4</sub><sup>2-</sup>]<span style="color:blue;">'''<sup>1</sup>'''</span>

So the reaction is
:<span style="color:red;">'''2'''</span>nd order wth respect to HgCl<sub>2</sub>
:<span style="color:blue;">'''1'''</span>st order with respect to C<sub>2</sub>O<sub>4</sub><sup>2-</sup> 
:<span style="color:green;">'''3'''</span>rd order over all (<span style="color:red;">'''2'''</span> + <span style="color:blue;">'''1'''</span> = <span style="color:green;">'''3'''</span>)


k is the rate constant.
:The bigger the value of rate constant, k, the faster the reaction.
:k is temperature dependent.
:k is reaction dependent.
:k has units that depend on the order of the reaction.

If concentration is in the units of M and time in the units of s then the rate of reaction has units of M/s.  If the reaction has an overall order of p then considering the units in the rate law gives (units in brackets)


:Rate(M/s) = k (M)<sup>p</sup> 

or units for k = (M/s) / M<sup>p</sup> = M<sup>1-p</sup> s<sup>-1</sup>

  
The following table gives the units of k for some orders of reaction.

:{|cellpadding="10" cellspacing="0" border="1" 
|-
! Overall Reaction Order
! Units for k
|-
|align="center"|0
|align="center"|M s<sup>-1</sup>
|-
|align="center"|1
|align="center"|s<sup>-1</sup>
|-
|align="center"|2
|align="center"|M<sup>-1</sup> s<sup>-1</sup>
|-
|align="center"|3
|align="center"|M<sup>-2</sup> s<sup>-1</sup>
|}

Knowing the rate law, the effect on the rate of the reaction when the concentrations are changed can be predicted.