how fast

• Rate equation


  Relates mathematically the rate of reaction to the concentration of the reactants
• Rate of reaction


  The change in concentration of a substance in unit time

  
• Unit of rate


  mol dm-3s-1
• Generalised rate equation


  r = k[A]m[B]n
• r


  Symbol for rate
• k


  Rate constant
• m, n


  Reaction orders
• Orders are usually integers 0,1,2
• 0 means the reaction is zero order with respect to that reactant
• 1 means first order
• 2 means second order
• The orders have nothing to do with the stoichiometric coefficients in the balanced equation. They are worked out experimentally.
• Total order


  Worked out by adding all the individual orders together (m+n)
• Calculating orders from initial rate data

  1. For zero order: the concentration of A has no effect on the rate of reaction

  2. For first order: the rate of reaction is directly proportional to the concentration of A

  3. For second order: the rate of reaction is proportional to the concentration of A squared

  
• For a rate concentration graph to show the order of a particular reactant the concentration of that reactant must be varied whilst the concentrations of the other reactants should be kept constant.

  
• When a graph of concentration of reactant is plotted vs time, the gradient of the curve is the rate of reaction.

  
• The initial rate is the rate at the start of the reaction where it is fastest.
• Rate constant (k)


  • 1. The units of k depend on the overall order of reaction. It must be worked out from the rate equation
  • 2. The value of k is independent of concentration and time. It is constant at a fixed temperature.
  • 3. The value of k refers to a specific temperature and it increases if we increase temperature
• Unit of k for 1st order overall reaction

  1. 1
• Unit of k for 2nd order overall reaction

  mol-1dm3s-1
• Unit of k for 3rd order overall reaction

  mol-2dm6s-1
• Calculating units of k

  1. Rearrange rate equation to give k as subject

  2. Insert units and cancel
• If half-lives are constant then the order is 1st order
• If half-lives rapidly increase then the order is 2nd order
• Working out orders from experimental initial rate data

  1. Compare between experiments where only one reactant concentration is changed

  2. If conc is doubled and rate stays the same: order= 0

  3. If conc is doubled and rate doubles: order= 1

  4. If conc is doubled and rate quadruples : order= 2
• The overall rate equation is r = k [A] [B]2
• The reaction is 3rd order overall and the unit of the rate constant =mol-2dm6s-1
• Working out orders when two reactant concentrations are changed simultaneously

  1. If the [A] is x2 that rate would x2

  2. If the [B] is x3 that rate would x32= x9

  3. If these changes happened at the same time then the rate would x2x9= x 18
• The overall rate equation is r = k [X] [Y]2
• Calculating a value for k using initial rate data

  Use the rate equation rearranged to give k, and insert the values from one of the experiments
• Increasing temperature


  Increases the value of the rate constant k
• Arrhenius equation


  k = Ae-EA/RT where A is a constant, R is gas constant and EA is activation energy
• The Arrhenius equation can be rearranged to ln k = constant - EA/(RT)
• Y


  Must be second order
• Overall rate equation


  r = k [X] [Y]2
• Calculating a value for k using initial rate data


  1. r = k [X] [Y]2

  2. k = r / ([X] [Y]2)
• k is the same for all experiments done at the same temperature
• Increasing the temperature


  Increases the value of the rate constant k
• Calculating activation energy EA from graph

  1. ln (Rate) vs 1/T

  2. Gradient = - EA/R

  3. EA = - gradient x R
• The unit of EA using this equation will be J mol-1. Convert into kJ mol-1 by dividing 1000