• 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 CaCO_3?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)