Reaction Orders (HL) (HL IB Chemistry)

How to determine reaction orders from graphs

• Reaction orders can be determined by using graphical representations of experimental data
• Two different types of graphs can be used:
  • Concentration-time graphs 
  • Rate-concentration graphs
• Rate-concentration graphs show the distinction between zero, first and second order more clearly than concentration-time graphs, as shown below

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

A concentration-time graph of a zero-order reaction shows that concentration is inversely proportional to time

• 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

A concentration-time graph of a first-order reaction curves downwards 

• 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

A concentration-time graph of a second-order reaction shows a downward curve with a steeper gradient than the curve for a first-order reaction

Reaction order using rate-concentration graphs

• In a zero-order reaction, the rate does not 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

A rate-concentration graph of a zero-order reaction shows a horizontal line

• 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

A rate-concentration graph of a first-order reaction shows a directly proportional relationship

• 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 graph of a second-order reaction

A rate-concentration graph of a second-order reaction shows an upward curve