# 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 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]n [Y]m

where k, m, and n are numbers that are determined experimentally!!

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 HgCl2 and C2O42- is found to have the rate law

Rate = k [HgCl2]2 [C2O42-]1

So the reaction is

2nd order wth respect to HgCl2
1st order with respect to C2O42-
3rd order over all (2 + 1 = 3)

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)p

or units for k = (M/s) / Mp = M1-p s-1

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

Overall Reaction Order Units for k
0 M s-1
1 s-1
2 M-1 s-1
3 M-2 s-1

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