Kinetics :  Sample Rate Calculations

 

         Rate Laws
 

For each of the following, determine the rate law of the reaction and find the value of the rate constant (k) with proper units.


               1) 2 O3 O2

Experiment # 
Initial [O3] (M) 
Initial Rate (M/sec) 
2.00 
0.500 
4.00 
1.000 
6.00 
1.500 

 
  First, set up a generic rate law:


rate = k[A]X

Next, create a ratio with the rate laws for 2 experiments:


Simplify and solve for x:


The reaction is first order with respect to [O3] because the exponent was calculated to be 1.

Now we can write the rate law and solve for k by plugging in values for the rate and the [O3] from a single experiment:



            2) N2O42 NO2

Experiment. # 
Initial [N2O4 ] (M) 
Initial Rate (M/sec) 
0.50 
0.050 
1.00 
0.200 
1.50 
0.450 


            3)  Xe + 3 F2XeF6
Experiment. #
Initial [Xe] (M)
Initial [F2] (M)
Initial Rate (M/sec)
1
0.50
0.25
0.00156
2
1.50
1.00
0.05625
3
0.75
0.25
0.0032
4
1.50
0.25
0.01406
5
0.50
1.00
0.00625

 

  The rate law includes the concentrations of all the reactants:


rate = k[Xe]X[F2]Y

Therefore, we must solve for both X and Y separately.
First choose two experiments in which the initial [F2] are the same and set up a ratio with these experiments:


The [F2] cancel each other out ,and the equation simplifies to find that X = 2. The reaction is second order with respect to [Xe].

Next, we do the same to solve for Y.  Choose two experiments in which the initial [Xe] are the same and set up a ratio.


The [Xe] cancel each other out, and the equation simplifies to find that Y = 1.  The reaction is first order with respect to [F2].

Now we can write the rate law:


* The reaction is first order with respect to F2 and second order with respect to Xe.

Now we have to solve for k:


Next:  "Collision Molecular Theory"