1. Calculate the rate constant, k, and write the rate law expression for the cat

Question

1. Calculate the rate constant, k, and write the rate law expression for the catalyzed decomposition of hydrogen peroxide. Explain how you determined the order of the reaction in H2O2 and KI.
2. The following mechanism has been proposed for this reaction:
H2O2+ I– IO– H2O
H2O2 + IO– I– + H2O + O2
If this mechanism is correct, which step must be the rate-determining step? Explain.
3. Use the Arrhenius equation to determine the activation energy, Ea, for this reaction.

4mL 10% HO: +1 ml* 0.5 MKJ ALYSIS [HOd [F1 Rele onstant Inital tame Parr aftef mining after mixing I 3.93x-*105lp elp 7.94x10- II gleDX ig? | -709(0-09-1.73 x 10-1 III 340 X ID- 111 NV iL2.32xIO1,105pleID Ila] x 104,

Explanation / Answer

1) Consider the given table:

Part

Initial Rate (mol/L.s)

[H2O2] after mixing (M)

[I-] after mixing (M)

Rate constant k

I

3.93*10-5

0.7056

0.10

7.89*10-5

II

8.60*10-7

0.7056

0.05

1.73*10-7

III

7.40*10-6

0.3528

0.10

5.94*10-5

IV

6.32*10-5

0.7056

0.10

1.27*10-4

Since H2O2 is consumed in the reaction, the rate of the reaction can be written as

-d[H2O2]/dt = k[H2O2]m[I-]n

where m and n define the order of the reaction with respect to H2O2 and I-. Consider the 3rd and the 4th rows in the table above. [I-] remains unchanged while [H2O2] is doubled. Note that the reaction rate constant, k remains constant throughout both the trials. Therefore,

7.40*10-6 = k(0.3528)m(0.10)n ….(1)

6.32*10-5 = k(0.7056)m(0.10)n ….(2)

Divide (2) by (1) and obtain

(6.32*10-5)/(7.40*10-6) = (0.7056)m/(0.3528)m

===> 8.540 = (2)m

===> ln (8.540) = m*ln (2)

===> 2.1448 = m*(0.693)

===> m = 2.1448/0693 = 3.09 3.0 (we take the nearest whole number for simplicity purpose).

Therefore, the rate of the reaction with respect to H2O2 is 3 (ans).

Next consider the first two rows in the table above where [H2O2] is held constant and [I-] is halved. Again,

3.93*10-5 = k(0.7056)3(0.10)n …..(3)

8.60*10-7 = k(0.7056)3(0.05)n …..(4)

Divide (3) by (4) and write

(3.93*10-5)/(8.60*10-7) = (2)n

45.6976 = 2n

===> ln (45.6976) = n*ln (2)

===> 3.8220 = n*(0.693)

===> n = 3.8220/0.963 = 5.515 5 (nearest whole number)

Therefore, the order of the reaction with respect to I- is 5 (ans).

2) The mechanism is provided. Both the reactants must occur in the slowest rate-determining step of the reaction. Since the 1st step in the proposed mechanism contains both the reactants, the 1st step is the rate-determining step of the reaction (ans).

Part

Initial Rate (mol/L.s)

[H2O2] after mixing (M)

[I-] after mixing (M)

Rate constant k

I

3.93*10-5

0.7056

0.10

7.89*10-5

II

8.60*10-7

0.7056

0.05

1.73*10-7

III

7.40*10-6

0.3528

0.10

5.94*10-5

IV

6.32*10-5

0.7056

0.10

1.27*10-4

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