5.5.8 Rates & Reaction Mechanisms

• Chemical kinetics can only suggest a reaction mechanism, they cannot prove it
  • However, they can be used to disprove a proposed mechanism

• Elementary steps are the steps involved in a reaction mechanism
  • For example, in the following general reaction:

A + B → C + D

• • The elementary steps could involve the formation of an intermediate:

Elementary step 1: A → R + D

Elementary step 2: R + B → C

• It is important that the elementary steps for a proposed mechanism agree with the overall stoichiometric equation
  • For example, combining the 2 elementary steps above gives the overall stoichiometric equation

A + R + B → R + C + D

A + B → C + D

Answers

Answer 1:

• • A one step reaction mechanism is simply the overall stoichiometric equation
  • Therefore, the correct answer is 2SO₂ + O₂ → 2SO₃

Answer 2:

• • One of the two elementary steps for this two step mechanism can be taken from the question:

Elementary step 1: 2NO + O₂ → 2NO₂

• • The second elementary step must involve the reaction of the nitrogen dioxide formed with sulfur dioxide:

Elementary step 2: NO₂ + SO₂ → NO + SO₃ (or 2NO₂ + 2SO₂ → 2NO + 2SO₃)

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)
  • This means that in terms of [popover id="GCXR2mfBwg279t3O" label=molecularity], the rate determining step is bimolecular

• 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

• Nucleophilic substitution reactions can occur in two different ways (known as S_N2 and S_N1 reactions) depending on the structure of the halogenoalkane involved

S_N1 reactions

• In tertiary halogenoalkanes, the carbon that is attached to the halogen is also bonded to three alkyl groups
• These halogenoalkanes undergo nucleophilic substitution by an S_N1 mechanism
  • ‘S’ stands for ‘substitution’
  • ‘N’ stands for ‘nucleophilic’
  • ‘1’ means that the rate of the reaction (which is determined by the slowest step of the reaction) depends on the concentration of only one reagent, the halogenoalkane

• The S_N1 mechanism is a two-step reaction
• In the first step, the C-X bond breaks heterolytically and the halogen leaves the halogenoalkane as an X^- ion (this is the slow and rate-determining step)
  • As the rate-determining step only depends on the concentration of the halogenoalkane, the rate equation for an S_N1 reaction is rate = k[halogenoalkane]
  • An S_N1 reaction is described as unimolecular because there is only molecule involved in the rate-determining step
  • This forms a tertiary carbocation (which is a tertiary carbon atom with a positive charge)
  • In the second step, the tertiary carbocation is attacked by the nucleophile

• For example, the nucleophilic substitution of 2-bromo-2-methylpropane by hydroxide ions to form 2-methyl-2-propanol

The mechanism of nucleophilic substitution in 2-bromo-2-methylpropane which is a tertiary halogenoalkane

S_N2 reactions

• In primary halogenoalkanes, the carbon that is attached to the halogen is bonded to one alkyl group
• These halogenoalkanes undergo nucleophilic substitution by an S_N2 mechanism
  • ‘S’ stands for ‘substitution’
  • ‘N’ stands for ‘nucleophilic’
  • ‘2’ means that the rate of the reaction (which is determined by the slowest step of the reaction) depends on the concentration of both the halogenoalkane and the nucleophile ions

• The S_N2 mechanism is a one-step reaction
  • The nucleophile donates a pair of electrons to the δ+ carbon atom of the halogenoalkane to form a new bond
    • As this is a one-step reaction, the rate-determining step depends on the concentrations of the halogenoalkane and nucleophile, the rate equation for an S_N2 reaction is rate = k[halogenoalkane][nucleophile]
    • An S_N2 reaction is bimolecular as there are two molecules involved in the rate-determining step

  • At the same time, the C-X bond is breaking and the halogen (X) takes both electrons in the bond
  • The halogen leaves the halogenoalkane as an X^- ion

• For example, the nucleophilic substitution of bromoethane by hydroxide ions to form ethanol

The S_N2 mechanism of bromoethane with hydroxide causing an inversion of configuration