Experiments were conducted to study the rate of the reaction represented by the

Question

Experiments were conducted to study the rate of the reaction represented by the equation above. Initial concentrations and rates of reaction are given in the table below Determine the order for each of the reactants, NO and H_2 and write the overall rate law tor the reaction. Show all work. Calculate the value of the rate constant, k, for the reaction. Include units. The following sequence of elementary steps is a proposed mechanism tor the reaction. Based on the data presented, which of the above is the rate-determining step? Show that the mechanism is consistent with the observed rate law for the reaction.

Explanation / Answer

Let the rate r= K [NO]a [H]b

a and b are orders of the reaction with respect to NO and H2

from experiment -1

1.8*10-4 = K[ 0.006]a [0.001]b    (1)

From experiment-2

3.6*10-4 = K[ 0.006]a [0.002]b    (2)

Eq.2/Eq.1 gives 2= 2b, b=1

From experiment -3

0.3*10-4 = K[ 0.0010]a [0.0060]b    (3)

From experiment -4

1.2*10-4 = K[ 0.0020]a [0.0060]b    (4)

Dividing Eq.4 and Eq.3 gives

4= 2a and a= 2

So the rate equation r= K[ NO]2 [H2]1

From experiment-1

1.8*10-4 = K[ 0.006]2 [0.001]1    (1)

K= 1.8*10-4/3.6*10-8

K= 5000/min.M2

so the rate becomes r= 5000 [NO]2 [H2]

The second one is rate determining step

For intermediate N2O2

Let K1, K-1, K2 and K3 be the rate constants.

d/dt [N2O2] = K1[NO]2- K-1 [ N2O2] - K2 [N2O2] [H2] =0    Since N2O2 is intermediate its net rate =0

[N2O2]   = K1[ NO]2 / ([K2[H2]+K-1)

d/dt[ N2O] = K2[N2O2] [H2] – K3[N2O] [H2] =0

[N2O] = K1[ N2O2]/ K3[ N2O]

Rate r = K2 [N2O2] [H2] = K2 K1 [NO]2 [H2/ ( K2[ H2]+K-1]

When K2[H2]<< K-1

Rate = K2K1/K2 [ NO]2 [H2]= K1[ NO]2 [H2]

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