16.1.3 Graphical Representations

Reaction Order Using Concentration-Time Graphs

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

Concentration-time graph of a zero-order reaction

• The gradient of the line is the rate of reaction
  • Calculating the gradient at different points on the graph, will give a constant value for the rate of reaction

• When the order with respect to a reactant is 0, a change in the concentration of the reactant has no effect on the rate of the reaction
• Therefore:

Rate = k

• This equation means that the gradient of the graph is the rate of reaction as well as the rate constant, k

• 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 graph 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 a first-order reaction
  • The graph is a steeper curve going downwards:

Concentration-time graph 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

Reaction order using rate-concentration graphs

• 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-concentration 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 increases as the concentration of the reactant increases
  • This means that 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-concentration 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 increases more as the concentration of the reactant increases
  • This means that 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-concentration graphs of a second-order reaction