AQA A Level Chemistry

Revision Notes

5.2.2 Deriving Rate Equations

Deducing Orders

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 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

Reaction Kinetics - Zero Order Concentration, downloadable AS & A Level Chemistry revision notes

Concentration-time graphs of a zero-order reaction

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

Reaction Kinetics - First Order Concentration, downloadable AS & A Level Chemistry revision notes

Concentration-time graphs of a first-order reaction

  • 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

Reaction Kinetics - Second Order Concentration, downloadable AS & A Level Chemistry revision notes

Concentration-time graphs of a second-order reaction

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

Reaction Kinetics - Zero Order Rate, downloadable AS & A Level Chemistry revision notes

Rate-time graph of a zero-order reaction

  • 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]

Reaction Kinetics - First Order Rate, downloadable AS & A Level Chemistry revision notes

Rate-time graph of a first-order reaction

  • 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

Reaction Kinetics - Second Order Rate, downloadable AS & A Level Chemistry revision notes

Rate-time graphs of a second-order reaction

Order of reaction from half-life

  • The order of a reaction can also be deduced from its half-life (t1/2 )
  • 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

Reaction Kinetics - Half-Life, downloadable AS & A Level Chemistry revision notes

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

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) the reaction equation and rate are as follows:

CH3Br + OH → CH3Br + Br (aq)

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

Deriving Rate Equations

Deriving Rate Equations

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