23.1    Orders of  Reaction and Rate  Equations

Rate Equation

• The rate of reaction is dependent on the concentration of the reactants. Doubling the concentration may double or triple the rate of reaction, just to name a few

 

• A rate equation shows this relationship mathematically

 

• A rate equation can only be obtained experimentally, it cannot be deduced from the stoichiometric equation and it may not include all reactants written in the equation

 

• For a general reaction:
  A + B → C + D
  The rate equation is:
• k is known as the rate constant, it is only a constant for a given reaction at a particular temperature. The unit of k depends on the rate equation and orders of reaction

 

• Note that the unit of rate is mol dm⁻³ s⁻¹ while the units of  [A] and [B] are mol dm⁻³.

 

Order of reaction

• The values m and n are known as the orders of reaction. Common values are 0, 1 and 2

 

• The order of reaction with respect to a reactant is the power to which the concentration of that reactant is raised in the experimentally determined rate equation.

 

• Like rate equations, orders of reaction must be determined experimentally

• If a reaction is zero-order with respect to a reactant  A:
  1. m = 1 and the rate equation becomes rate = k[A]⁰[B]ⁿ = k[B]ⁿ

1. The rate of reaction is independent of the concentration of A because [A]⁰ = 1 and it disappears from the equation. Changing the concentration of A will not alter the rate of reaction
2. – The rate-concentration graph is a horizontal line showing the rate of reaction does not change
   – The concentration-time graph is a straight line with constant gradient showing that rate is constant.

• If a reaction is ftrst-order with respect to a reactant  A:
  1. m = 1 and the rate equation becomes rate = k[A][B]ⁿ.
  2. The rate of reaction is proportional to the concentration of A. If [A] increases five times, the rate of reaction will increase five times as well
  3. – The rate-concentration graph will show a straight line through origin.
     – The concentration-time graph will show a curve with constant half-life.
  4. Half-life, t½ is the time taken for the initial concentration of reactant to decrease to half of its original value
  5. Only a first-order concentration-time graph will show a curve with constant half-life. That is, t1 = t2 = t3 = t½.
  6. The relationship between half-life and rate constant is given by:

• If a reaction if second-order with respect to a reactant A:
  1. m = 2 and the rate equation becomes rate = k[A]²[B]ⁿ.
  2. The rate of reaction is proportional to the square of concentration of A. If [A] increases five times, the rate of reaction will increase 5² = 25 times
  3. – The rate-concentration graph is a quadratic curve.
     – The concentration-time graph is a curve with non-constant half-life.

 

 

Deducing orders of  reaction

• Order of reaction must be determined experimentally, it can be deduced by either graphically or using initial rate experiments

• Deducing graphically involves plotting either a rate-concentration graph or concentration-time graph, and the order of a reaction may be deduced by looking at the pattern.

 

• Using initial rate experiments, the rate of reaction is measured at the very beginning of the experiment. This is done by calculating the gradient of a concentration-time graph at the beginning
• A guide to find the order of reaction from the processed data: Example 1: