Multi-Step Reactions (Cambridge International A-Level Chemistry)

Kinetics of Multi-Step Reactions

• The reaction mechanism of a reaction describes how many steps are involved in the making and breaking of bonds during a chemical reaction

• It is the slowest step in a reaction and includes the reactants that have an impact on the reaction rate when their concentrations are changed

  • Therefore, all reactants that appear in the rate equation will also appear in the rate-determining step
  • This means that zero-order reactants and intermediates will not be present in the rate-determining step

Predicting the reaction mechanism

• The overall reaction equation and rate equation can be used to predict a possible reaction mechanism of a reaction
• For example, nitrogen dioxide (NO₂) and carbon monoxide (CO) react to form nitrogen monoxide (NO) and carbon dioxide (CO₂)
• The overall reaction equation is:

NO₂(g) + CO (g) → NO (g) + CO₂(g)

• The rate equation is:

Rate = k [NO₂]²

• From the rate equation, it can be concluded that the reaction is zero order with respect to CO (g) and second order with respect to NO₂ (g)

• This means that there are two molecules of NO₂ (g) involved in the rate-determining step

• A possible reaction mechanism could therefore be:

  • Step 1:

    • 2NO₂(g) → NO (g) + NO₃(g) slow(rate-determining step)

  • Step 2:

    • NO₃(g) + CO (g) → NO₂(g) + CO₂(g) fast

  • Overall:

    • 2NO ₂ (g) + NO₃(g) + CO (g) → NO (g) + NO₃(g) + NO₂(g) + CO₂ (g)**
    • Which simplifies to** NO ₂ (g) + CO (g) → NO (g) + CO ₂ (g)

Predicting the reaction order & deducing the rate equation

• The order of a reactant and thus the rate equation can be deduced from a reaction mechanism given that the rate-determining step is known
• For example, the reaction of nitrogen oxide (NO) with hydrogen (H₂) to form nitrogen (N₂) and water

2NO (g) + 2H₂(g) → N₂(g) + 2H₂O (l)

• The reaction mechanism for this reaction is:

  • Step 1:

    • NO (g) + NO (g) → N₂O₂ (g) fast

  • Step 2:

    • N₂O₂(g) + H₂(g) → H₂O (l) + N₂O (g) slow(rate-determining step)

  • Step 3:

    • N₂O (g) + H₂(g) → N₂(g) + H₂O (l) fast

  • The second step in this reaction mechanism is the rate-determining step

  • The rate-determining step consists of:

    • N₂O₂ which is formed from the reaction of two NO molecules
    • One H₂molecule

• The reaction is, therefore, second order with respect to NO and first order with respect to H₂

  • So, the rate equation becomes:

Rate = k [NO]²[H₂]

• The reaction is, therefore, third-order overall

Identifying the rate-determining step

• The rate-determining step can be identified from a rate equation given that the reaction mechanism is known
• For example, propane (CH₃CH₂CH₃) undergoes bromination under alkaline solutions
• The overall reaction is:

CH₃CH₂CH₃+ Br₂+ OH^-→ CH₃CH₂CH₂Br + H₂O + Br^-

• The reaction mechanism is:

Reaction mechanism of the bromination of propane under alkaline conditions

• The rate equation is:

Rate = k [CH₃CH₂CH₃] [OH^-]

• From the rate equation, it can be deduced that only CH₃COCH₃ and OH^- are involved in the rate-determining step and not bromine (Br₂)

• CH₃COCH₃ and OH^- are only involved in step 1

  • Therefore, the rate-determining step is step 1 of the reaction mechanism

Identifying intermediates & catalyst

• When a rate equation includes a species that is not part of the chemical reaction equation then this species is a catalyst
• For example, the halogenation of butanone under acidic conditions
• The reaction mechanism is:

CH₃CH₂COCH₃+ I₂ $\overset{H^{+}}{\rightarrow}$CH₃CH₂COCH₂I + HI

• The reaction mechanism is:

Reaction mechanism of the halogenation of butanone under acidic conditions

The rate equation is:

Rate = k [CH₃CH₂COCH₃] [H⁺]

• The H⁺ is not present in the chemical reaction equation but does appear in the rate equation

  • H⁺ must therefore be a catalyst

• Furthermore, the rate equation suggests that CH₃CH₂COCH₃ and H⁺ must be involved in the rate-determining (slowest) step

• The CH₃CH₂COCH₃ and H⁺ appear in the rate-determining step in the form of an intermediate(which is a combination of the two species)

The intermediate formed in the reaction of CH₃CH₂COCH₃ and H⁺

This intermediate is formed in the rate-determining step