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

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

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

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

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]

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

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?(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

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