Orders and rate equations

• Rate equations link the reaction rate to the reactant concentrations

• They show how the rate of reaction is affected by the concentration of reactants

• For the general equation: A + B → C + D

• The rate equation would be: Rate = K[A]^m[B]ⁿ

• m is the order of reaction with respect to reactant A and shows how the concentration of A affects the rate of reaction

• n is the order of reaction with respect to reactant B and shows how the concentration of B affects the rate of reaction

• K is the rate constant

• A bigger rate constant, means the reaction is faster

• The rate constant is always the same for a reaction at a particular temperature

• The units of K vary and can be worked out

• K increases with increasing temperature

Orders

• If [A] changes and the rate stays the same, the order of reaction with respect to A is 0

  • If [A] doubled, the rate will remain unchanged

• If the rate is proportional to the [A] (rate ∝ [A]), the order of reaction with respect to A is 1

  • If [A] doubles, the rate doubles

• If the rate is proportional to the [A]² (rate ∝ [A]²), the order of reaction with respect to A is 2

  • If [A] double, the rate quadruples

• A reaction can have an overall order. This is just the sum of the orders of all the different reactants

Finding orders

• Orders of reaction can only be found from experimental data

• Methods of finding orders:

  • Use initial rates to construct a rate-concentration graph and examine its shape

  • Directly compare the initial rates for different concentrations of reactant

  • Use the continuous monitoring method to construct a concentration time graph and compare successive half lives

• The concentration of all other reactants not being investigated must be present in excess so that their concentrations don’t significantly affect the rate and any change in rate is due to a change in the concentration of the reactant being investigated

Obtaining orders from graphs

• Concentration-time graphs

  • A straight line indicates 0 order

  • A curved indicates first or second order

• Rate-concentration graphs

  • A straight horizontal graph indicates 0 order

  • A straight line going through the origin indicates first order

  • A curved line indicates second order