5.5.7 Rate-Determining Steps

Rate-determining step & intermediates

• A chemical reaction can only go as fast as the slowest part of the reaction
  • So, the rate-determining step is the slowest step in the reaction

• If a reactant appears in the rate-determining step, then the concentration of that reactant will also appear in the rate equation
• For example, the rate equation for the reaction below is rate = k [CH₃Br] [OH^-]

CH₃Br + OH^- → CH₃OH + Br^-

• • This suggests that both CH₃Br and OH^- take part in the slow 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
  • This shows the individual reaction steps which are taking place

• 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 and zero molecules of CO (g)
• 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:

    2NO₂ (g) + NO₃ (g) + CO (g) → NO (g) + NO₃ (g) + NO₂ (g) + CO₂ (g)

   =     NO₂ (g) + CO (g) → NO (g) + CO₂ (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 if 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 H₂ molecule

• 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 for 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 CH₃CH₂CH₃ and OH^- are involved in the rate-determining step and not bromine (Br₂)
• CH₃CH₂CH₃ and OH^- are only involved in the first step of the reaction mechanism, therefore the rate-determining step is:
  • CH₃CH₂CH₃ + OH^- → CH₃CH₂CH₂^- + H₂O