With a tertiary alcohol (e.g. methylpropan-2-ol) the alcohol slowly loses a hydroxide ion in the rate-determining step. The carbo-cation so formed then reacts quickly with the bromide ion. As the rate-determining step only involves the alcohol, this is the sole species found in the rate equation and the reaction is first order. The rate is zero-order with respect to bromide because bromide is not involved in the rate-determining step.

With a primary alcohol (e.g. methanol) the hydroxide ion does not leave the molecule until the bromide ion attacks the molecule from the other side. There is a concerted reaction with the bromide pushing the hydroxide off the carbon atom. Because both alcohol and bromide are involved in this step the rate equation involves both species and is therefore second order. That’s the simple story. Zero-order is a bit of a lie, though, because if you reduce the bromide ion concentration to zero in either of the above reactions, it is obvious that bromination will not occur at all.

A more general rule is that 1/(overall rate) = 1/(rate of step 1) + 1/(rate of step 2) + 1/(rate of step 3) etc.

From this it can be seen that if one step is very slow, 1/(overall rate) = 1/(rate of slow step) i.e. the slow step determines the rate. If two or more steps are slow, then the more general equation can be used to calculate the rate.

This is based on 1/rate being proportional to the time spent in each step of the reaction. See ‘Transit times’ in Fersht, A (1985) Enzyme Structure And Mechanism (2nd ed) p118 WH Free man & Co.

An example is the protolysis of thiosulphate to give sulphur and sulphur dioxide. It is first-order with respect to thiosulphate. At high acid concentration, it is zero-order for acid, but at low concentrations it is first-order.

The presence of thiosulphate in two steps of the reaction does not imply that it is directly involved in the second step. The reactant in the second step may be a derivative of thiosulphate formed in a relatively rapid equilibrium. The concentration of this derivative is thus proportional to the thiosulphate concentration. This is a steady-state assumption see Fersht p98 etc.

An oddity that can be explained in this way are the third-order kinetics of NO oxidation which are slowed by increasing temperature. The rate- determining step probably does not involve three reactants, but the product of a rapid equilibrium and a second reactant.

• Explanation of order
• Order of reaction for iodine-catalysed decomposition of hydrogen peroxide
• Rate-determining step
• General help:
  • http://www.rjclarkson.demon.co.uk/hfhf/hfhf3.htm
  • http://learn.chem.vt.edu/tutorials/kinetics/index.html
  • http://www.wpi.edu/Academics/Depts/Chemistry/Courses/CH1010/Stream1/concep15.ht ml (very thorough)

Ewen McLaughlin