HOW TO FIND A RATE LAW

1
HOW TO FIND A RATE LAW
2

• I. To find a Rate Law, use a series of
  experimental results. Hold the concentration of
  one reagent constant, vary the concentration of
  the other and note what happens to the rate. For
  example, for the reaction
• 2 NO (g) Cl2 (g) ? 2 NOCl (g)
• Experiment NO0 Cl20 Rate, initial, M/sec
• 1. 0.10 0.10 3.0 x 10-5
• 2. 0.10 0.20 6.0 x 10-5
• 3. 0.20 0.10 1.2 x 10-4
• The rate is expressed in general terms as
• Rate k NOx Cl2y
• and you need to determine x and y

3

• A. To determine the value of the exponents,
  compare the concentrations of one reagent in
  two experiments. The concentration of any other
  reagent must be kept constant.
• (A2 /A1) y (Rate2/Rate1)
• where y is the exponent in the rate !

4

• B. Using Experiments 1 and 2 (where NO0 is
  constant)
• (Cl22 /Cl21) y (0.202/0.101)
• (6.0 x 10-5 M/sec/3.0 x 10-5 M/sec )
• so ... 2y 2 and y 1 the exponent
  for Cl2
• C. Using Experiments 1 and 3 (where Cl20 is
  constant)
• (NO3 /NO1) x (0.203/0.101)
• (1.2 x 10-4 M/sec/3.0 x 10-5 M/sec )
• so ... 2x 4 and x 2 the exponent
  for NO

5

• D. The rate constant, k, can now be calculated.
• Use data from any one experiment
• k Rate/NO2 Cl2
• For experiment 1
• k 3.0 x 10-5 M/sec/(0.10 M)2(0.10 M)
• k 3.0 x 10-2 M-2/sec
• For experiment 2
• k 6.0 x 10-5 M/sec/(0.10 M)2(0.20 M)
• k 3.0 x 10-2 M-2/sec

6

• II. Examples
• A. NO2(g) CO(g) ? CO2 (g) NO (g)
• Experiment NO20 CO0 Rate, initial,
  M/sec
• 1. 0.10 0.10 1.0
• 2. 0.10 0.020 1.0
• 3. 0.10 0.010 1.0
• 4. 0.020 0.10 0.040
• 5. 0.010 0.10 0.010

7

• Using Experiments 1 and 2,
• as CO doubles,
• Rate remains constant !
• So far, rate k CO0 !
• From Experiments 5 and 4,
• NO2 doubles,
• Rate quadruples !
• So now, Rate k NO22 CO0
• or Rate k NO22 !
• This Rate Law is second order in NO2
• and zero order in CO !

8

• B. Practice on this one
• 3 A B 2 C ? 3D
  E
• Rate
• Experiment initial
• A0 B0 C0 M/sec
• 1. 0.10 0.10 0.20 2.0
• 2. 0.30 0.10 0.20 18.0
• 3. 0.30 0.20 0.20 18.0
• 4. 0.10 0.10 0.40 16.0
• Determine the rate law ?
• Calculate the rate constant ?