Problem: Consider the following general reaction and data:2A + 2B + C → D + 3E(a) What is the reaction order with respect to each reactant?(b) Calculate the rate constant.(c) Write the rate law for this reaction. 

FREE Expert Solution

We’re being asked to calculate the rate law and the value of the rate constant (k) based on the reaction and data given.


Recall that the rate law only focuses on the reactant concentrations and has a general form of:

rate law=kAxBy

k = rate constant
A & B = reactants
x & y = reactant orders


Step 1. Calculate the order of the reaction with respect to [A].


            [A]i (M)                   [B]I (M)                [C]I (M)                 Initial Rate (M-1 s-1)

1                     0.024                      0.085                    0.032                     6.0 x 10-6
2                     0.096                      0.085                    0.032                     9.6 x 10-5
3                     0.024                      0.034                    0.080                     1.5 x 10-5
4                     0.012                      0.170                    0.032                     1.5 x 10-6


Calculate order with respect to NO:

rate 2rate 1=Ax at rate 2Ax at rate 19.6 × 10-56.0 × 10-6=0.096x0.024x16 = [4]x

x = order

(Larger concentration should be on the numerator)

2 raised to the 2nd power = 4

x = 2 → 2nd order with respect to [A]


Step 2. Calculate the order of the reaction with respect to [B].


            [A]i (M)                   [B]I (M)                [C]I (M)                 Initial Rate (M-1 s-1)

1                     0.024                      0.085                    0.032                     6.0 x 10-6
2                     0.096                      0.085                    0.032                     9.6 x 10-5
3                     0.024                      0.034                    0.080                     1.5 x 10-5
4                     0.012                      0.170                    0.032                     1.5 x 10-6


Calculate order with respect to [B]:

rate 4rate 2=[A]xBy at rate 4[A]xBy at rate 21.5 × 10-69.6 × 10-5=0.01220.17y0.09620.085y0.0156 = [0.0156][0.2]y0.01560.0156=[0.2]y1=[0.2]y

y = order

(Larger concentration should be on the numerator)

0.2 raised to the 0th power = 1

y = 0 → 0th order with respect to [B]


Step 3. Calculate the order of the reaction with respect to [C].


            [A]i (M)                   [B]I (M)                [C]I (M)                 Initial Rate (M-1 s-1)

1                     0.024                      0.085                    0.032                     6.0 x 10-6
2                     0.096                      0.085                    0.032                     9.6 x 10-5
3                     0.024                      0.034                    0.080                     1.5 x 10-5
4                     0.012                      0.170                    0.032                     1.5 x 10-6


Calculate order with respect to [C]:

rate 3rate 2=[A]xByCz at rate 3[A]xBy[C]z  at rate 21.5 × 10-59.6 × 10-5=0.02420.0340[0.080]z0.09620.0850[0.032]z0.156 = [0.0625][2.5]z0.1560.0625=[2.5]z2.5=[2.5]z

z = order

(Larger concentration should be on the numerator)

2.5 raised to the 1st power = 2.5

y = 1 → 1st order with respect to [C]



Step 4. Determine the rate law of the reaction

rate law=k[A]x[B]y[C]z

Substitute NO and O2 and their orders:

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

or simply

rate law = k[A]2[C]


The rate law is rate law = k[A]2[C]


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Problem Details

Consider the following general reaction and data:

2A + 2B + C → D + 3E

(a) What is the reaction order with respect to each reactant?

(b) Calculate the rate constant.

(c) Write the rate law for this reaction.