Chemical Kinetics Calculations (CIE A Level Chemistry)

Order of reaction

• The order of reaction shows how the concentration of a reactant affects the rate of reaction

Rate = k [A]^m [B]ⁿ

• When m or n is zero = the concentration of the reactants does not affect the rate
• When the order of reaction (m or n) 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 reaction below, the overall order of reaction is 2 (1 + 1)

Rate = k [NO₂] [Cl₂]

Order of reaction from concentration-time graphs

• In a zero-order reaction, the concentration of the reactant is inversely proportional to time
  • This means that the concentration of the reactant decreases with increasing time
  • The graph is a straight line going down

A zero-order concentration-time graph

A zero-order concentration-time graph is a straight line

• In a first-order reaction, the concentration of the reactant decreases with time
  • The graph is a curve going downwards and eventually plateaus

A first-order concentration-time graph

A first-order concentration-time graph is a smooth curve

• In a second-order reaction, the concentration of the reactant decreases more steeply with time
  • The concentration of reactant decreases more with increasing time compared to in a first-order reaction
  • The graph is a steeper curve going downwards

A second-order concentration-time graph

A second-order concentration-time graph is a smooth and steep curve

Order of reaction from initial rate

• The progress of the reaction can be followed by measuring the initial rates of the reaction using various initial concentrations of each reactant
• These rates can then be plotted against time in a rate-time graph
• In a zero-order reaction, the rate doesn’t depend on the concentration of the reactant
  • The rate of the reaction therefore remains constant throughout the reaction
  • The graph is a horizontal line
  • The rate equation is rate = k 

A zero-order rate-time graph

A zero-order rate-time graph is a flat line

• In a first-order reaction, the rate is directly proportional to the concentration of a reactant
  • The rate of the reaction decreases as the concentration of the reactant decreases when it gets used up during the reaction
  • The graph is a straight line
  • The rate equation is rate = k [A] 

A first-order rate-time graph

A first-order rate-time graph is a straight line with a fixed gradient, k

• In a second-order reaction, the rate is directly proportional to the square of concentration of a reactant
  • The rate of the reaction decreases more as the concentration of the reactant decreases when it gets used up during the reaction
  • The graph is a curved line
  • The rate equation is rate = k [A]² 

A second-order rate-time graph

A second-order rate-time graph is a smooth curve

Order of reaction from half-life

• The order of a reaction can also be deduced from its half-life (t_1/2 )
• For a zero-order reaction, the successive half-lives decrease with time
  • This means that it would take less time for the concentration of reactant to halve as the reaction progresses
• The half-life of a first-order reaction remains constant throughout the reaction
  • The amount of time required for the concentration of reactants to halve will be the same during the entire reaction
• For a second-order reaction, the half-life increases with time
  • This means that as the reaction is taking place, it takes more time for the concentration of reactants to halve

Half-lives of zero, first and second-order reactions

Zero-order reactions have a decreasing half-life, first-order reactions have a constant half-life and second-order reactions have an increasing half-life 

Calculating the initial rate

• The initial rate can be calculated by using the initial concentrations of the reactants in the rate equation
• For example, in the reaction of bromomethane (CH₃Br) with hydroxide (OH^-) ions to form methanol (CH₃OH):

CH₃Br + OH^- → CH₃OH + Br^- 

• The rate equation is:

Rate = k [CH₃Br] [OH^-]

• • Where k = 1.75 x 10^-2 dm^-2 mol^-1 s^-1
• If the initial concentrations of CH₃Br and OH^- are 0.0200 and 0.0100 mol dm^-3 respectively, the initial rate of reaction is:
  • Rate = k [CH₃Br] [OH^-]
  • Initial rate = 1.75 x 10^-2 x (0.0200) x (0.0100)
  • Initial rate = 3.50 x 10^-6 mol dm^-3 s^-1 

Calculating Units

• When you are asked to calculate the rate constant, k, for a reaction you must also be able to deduce the units
• This is done by replacing the values in the rearranged rate equation with the units of that value
• The units can then be combined or cancelled as required
• For example, to calculate the units for the above reaction: