# 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

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 HgCl_{2} and C_{2}O_{4}^{2-} is found to have the rate law

- Rate = k [HgCl
_{2}][C^{2}_{2}O_{4}^{2-}]^{1}

So the reaction is

**2**nd order wth respect to HgCl_{2}**1**st order with respect to C_{2}O_{4}^{2-}**3**rd 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) / M^{p} = M^{1-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.