An structural isomer of bromobutane (C4H9Br) can be hydrolysed using aqueous sodium hydroxide to produce butanol. This can be represented by the following equation:


C4H9Br(l) + OH-(aq)  C4H9OH(l) + Br-(aq)
This reaction was investigated experimentally and the following results
were obtained:
Experiment
Initial [bromobutane], mol dm-3 Initial [OH-], mol dm-3 Initial rate, mol dm-3s-1
A 0.01 0.01 4.3 x 10-4
B 0.01 0.02 8.6 x 10-4
C 0.02 0.02 1.7 x 10-3

(b) (i) Deduce the overall order of the reaction and write the rate equation for this reaction (ii) What is meant by the rate-limiting step of a reaction mechanism?
(iii) What can you say about the rate-limiting step for the above reaction?
(iv) Suggest which isomer of bromobutane is likely to react via this rate-limiting step. Explain your answer fully.

To determine the overall order of the reaction and write the rate equation, we need to analyze the results obtained from the experiments.

(i) The overall order of a reaction can be obtained by adding up the individual orders of the reactants in the rate equation. Looking at the given data, we can see that the initial [bromobutane] is kept constant in all experiments, while the initial [OH-] is varied.

Let's compare Experiment A and B:
- Experiment A has [OH-] doubled compared to Experiment A, and the initial rate also doubled.
- This indicates that the rate is directly proportional to the concentration of OH-.

This suggests that the reaction rate is only dependent on the concentration of OH-. Therefore, the overall order of the reaction is 1 with respect to OH-, and 0 with respect to bromobutane.

The rate equation for this reaction can be written as:
Rate = k [OH-]

(ii) The rate-limiting step of a reaction mechanism refers to the slowest step in the overall reaction. It determines the rate at which the reaction occurs.

(iii) Based on the information provided, we cannot definitively determine the rate-limiting step for the given reaction. However, the experiment results indicate that the rate is directly proportional to [OH-], suggesting that the step involving OH- might be the rate-determining step.

(iv) To suggest which isomer of bromobutane is likely to react via this rate-limiting step, we need to consider the chemical structure of the isomers.

Bromobutane can exist in two isomeric forms: 1-bromobutane and 2-bromobutane. The difference between these isomers lies in the position of the bromine atom on the carbon chain.

In this case, we can assume that the reaction proceeds via an SN2 mechanism, where the nucleophile (OH-) attacks the carbon attached to the bromine. In an SN2 reaction, the rate is influenced by steric hindrance. The greater the steric hindrance, the slower the reaction.

Since the rate of the reaction is proportional to [OH-], we can infer that a higher concentration of OH- leads to a faster reaction. This indicates that the isomer with the least steric hindrance (minimal substitution near the reacting carbon) will react via the rate-limiting step.

In this context, 1-bromobutane is likely to be the isomer that reacts via the rate-limiting step. It has less steric hindrance compared to 2-bromobutane, as the nucleophile can attack the primary carbon (less substituted) more easily.

Please note that this answer is based on assumptions regarding the SN2 mechanism and steric hindrance. Experimental evidence or further information about the reaction mechanism would be needed for a more definitive answer.

(i) To determine the overall order of the reaction, we need to examine how the initial concentrations of the reactants (bromobutane and hydroxide ions) affect the initial rate of the reaction.

In Experiment A, when the initial concentration of bromobutane and hydroxide ions was both 0.01 mol dm-3, the initial rate was 4.3 x 10-4 mol dm-3s-1.

In Experiment B, when the initial concentration of bromobutane was still 0.01 mol dm-3 but the initial concentration of hydroxide ions was doubled to 0.02 mol dm-3, the initial rate also doubled to 8.6 x 10-4 mol dm-3s-1.

In Experiment C, when the initial concentration of bromobutane was doubled to 0.02 mol dm-3 while the initial concentration of hydroxide ions remained at 0.02 mol dm-3, the initial rate again doubled to 1.7 x 10-3 mol dm-3s-1.

Based on these results, we can conclude that the rate of the reaction is directly proportional to the concentration of bromobutane and hydroxide ions. Therefore, the overall order of the reaction is 1 + 1 = 2 (first order with respect to bromobutane and first order with respect to hydroxide ions).

The rate equation for this reaction can be written as: rate = k [C4H9Br] [OH-]

(ii) The rate-limiting step of a reaction mechanism is the slowest step in the overall reaction. It determines the overall rate of the reaction because the rate cannot exceed the rate at which this step occurs.

(iii) In this case, we do not have information about the reaction mechanism. However, if we assume that the rate-limiting step involves the breaking of the carbon-bromine bond in bromobutane, then the rate of the reaction will be dependent on the concentration of bromobutane. We can suggest that the rate-limiting step involves the bromobutane molecule.

(iv) Based on the assumption in the previous part, the isomer of bromobutane that is likely to react via the rate-limiting step is tertiary butyl bromide (also known as 2-bromo-2-methylpropane). This is because the t-butoxide ion, generated from the sodium hydroxide, can easily attack the tertiary carbon atom in t-butyl bromide. The carbon-bromine bond in t-butyl bromide is weaker than in other isomers due to the presence of more electron-withdrawing alkyl groups adjacent to the carbon-bromine bond. Therefore, the breaking of the carbon-bromine bond in t-butyl bromide is likely to be the slowest step and therefore the rate-limiting step.