orders, rate equations and rate constants

• rate = quantity reacted or produced / time
• rate = change in concentration / change in time
• [A] is shorthand for 'concentration of A'

  [A] has the usual units of concentration mol dm -3 , if time has been measured in seconds, rate has the units of mol dm-3 s-1
• reaction rates measured by observing changes in quantities reactants/ products over time
• for each reactant, the power is the order of reaction for that reactant

  zero order (0)

  first order (1)

  second order (2)
• zero order

  when the concentration of a reactant has no effect on the rate, the reaction is zero order with respect to the reactant

  rate is proportional to [A]^0

  any number raised to the power zero is 1

  concentration does not influence the rate
• first order

  a reaction is first order with respect to a reactant when the rate depends on its concentration raised to the power of one

  rate is proportional to [A]^1

  if conc of A is doubled, the reaction rate increases by a factor of 2^1 = 2

  if conc of A is tripled, reaction rate increases by a factor of 3^1 = 3
• second order

  a reaction is second order with respect to a reactant when the rate depends on its concentration raised to the power of 2

  rate is proportional to [A]^2

  if conc of A is doubled, the reaction rate increases by a factor of 2^2 = 4

  if conc of A is tripled, the reaction rate increases by a factor of 3^2 = 9
• rate equation: mathematical relationship between the concentration of the reactants and the reaction rate

  rate constant k: proportionality constant. it is the number that mathematically converts between the rate of reaction and concentration and orders

  
• overall order: gives the overall effect of the concentrations of all reactants on the rate of reaction

  overall order = sum of orders with respect to each reactant

  rate = k[A]^m [B]^n overall order = m + n
• worked example: the rate equation and overall order for a reaction

  for a reaction A + B = C -> products, the orders are A: 0, B: 1 and C: 2

  step 1: write the overall order

  1 + 2 = 3

  step 2: write the rate equation

  rate = k[A]^0[B]^1[C]^2

  as [A]^0 = 1, zero order reactants are usually omitted

  as [B]^1 = [B], 1st order powers are usually omitted

  the rate equation is simplified to

  rate =k[B][C]^2
• the units of the rate constant depend upon the number of concentration terms in the rate equation. the units of k can be determined by:

  1. rearranging the equation to make k the subject
  2. substitute units into the expression for k
  3. cancel common units and show the final units on a single line

  
• worked example: units of the rate constant k

  what are the units of the rate constant k in the rate equation below?

  rate = k[A]^2[B]

  step 1: rearrange the rate equation to make the k the subject

  k = rate / [A]^2 [B]

  step 2: substitute units and cancel the common units
• worked example: rate constant from experimental results

  step 1: determine the orders, overall order and rate equation

  comparing experiment 1 and 2

  [NO2 (g)] doubles and [O3 (g)] stays the same

  the rate also doubles

  the reaction is 1st order with respect to NO2 (g)

  comparing experiment 2 and 3:

  [O3 (g)] doubles and [NO2 (g)] stays the same

  the rate also doubles

  the reaction is 1st order with respect to O3 (g)

  overall order = sum of individual orders = 1 + 1 = 2

  
• worked example: rate constant from experimental results

  step 2: write the rate equation

  rate = k [NO2 (g)] [O3 (g)]

  step 3: calculate the rate constant, including units

  rearrange the rate equation: k = rate / [NO2 (g)][O3 (g)]

  substitute values from experiment 1

  k = 1.28 x 10-2

  substitute units into k expression and cancel common units

  k = 1.28 x 10 -2 dm3 mol -1 s-1