5.6.1 Basics of Kinetics

• The rate of reaction refers to the change in the amount or concentration of a reactant or product per unit time and can be found by:
• Measuring the decrease in the concentration of a reactant OR
• Measuring the increase in the concentration of a product over time
  • The units of rate of reaction are mol dm^-3 s^-1

Rate equation

• The thermal decomposition of calcium carbonate (CaCO₃) will be used as an example to study the rate of reaction

CaCO₃ (s) → CaO (s) + CO₂ (g)

• The rate of reaction at different concentrations of CaCO₃ is measured and tabulated

Rate of reactions table

• A directly proportional relationship between the rate of the reaction and concentration of CaCO₃ is observed when a graph is plotted

Rate of thermal decomposition of CaCO₃ over the concentration of CaCO₃

• The rate of reaction for the thermal decomposition of CaCO₃ can also be written as:

Rate of reaction = k x [CaCO₃]

• The proportionality constant k is the gradient of the graph and is also called the rate constant
• The rate equation is the overall expression for a particular reaction without the ‘x’ sign

Rate of reaction = k [CaCO₃]

• Rate equations can only be determined experimentally and cannot be found from the stoichiometric equation

Rate of reaction = k [A]^m [B]ⁿ

[A] and [B] = concentrations of reactants

m and n = orders of the reaction

• For example, the rate equation for the formation of nitrogen gas (N₂) from nitrogen oxide (NO) and hydrogen (H₂) is rate = k [NO]² [H₂]

2NO (g) + 2H₂ (g) → N₂ (g) + 2H₂O (g)

rate = k [NO]² [H₂]

• As mentioned before, the rate equation of the reaction above cannot be deduced from the stoichiometric equation but can only experimentally be determined by:
  • Changing the concentration of NO and determining how it affects the rate while keeping [H₂] constant
  • This shows that the rate is proportional to the square of [NO]

Rate = k₁ [NO]²

• Then, changing the [H₂] and determining how it affects the rate while keeping [NO] constant
• This shows that the rate is proportional to [H₂]

Rate = k₂ [H₂]

• Combining the two equations gives the overall rate equation (where k = k₁ + k₂)

Rate = k [NO]² [H₂]

Order of reaction

• The order of reaction shows how the concentration of a reactant affects the rate of reaction
  • It is the power to which the concentration of that reactant is raised in the rate equation
  • The order of reaction can be 0, 1,2 or 3
  • When the order of reaction of a reactant is 0, its concentration is ignored

• The overall order of reaction is the sum of the powers of the reactants in a rate equation
• For example, in the following rate equation, the reaction is:

Rate = k [NO₂]²[H₂]

• • Second-order with respect to NO
  • First-order with respect to H₂
  • Third-order overall (2 + 1)

Half-life

• The half-life (t_1/2) is the time taken for the concentration of a limiting reactant to become half of its initial value

Rate-determining step & intermediates

• The rate-determining step is the slowest step in a 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

• This reaction is, therefore, a bimolecular reaction
  • Unimolecular: one species involved in the rate-determining step
  • Bimolecular: two species involved in the rate-determining step

• The intermediate is derived from substances that react together to form it in the rate-determining step
  • For example, for the reaction above the intermediate would consist of CH₃Br and OH^-

The intermediate is formed from the species that are involved in the rate-determining step (and thus appear in the rate equation)