7. Consider the reaction:

BrO3- + 5 Br- + 6 H+ 3 Br2 + 3 H2O



[1]a. How might you define the rate of the reaction?





rate = -d[BrO3-] / dt = -d[Br-] / 5dt = -d[H+] / 6dt = d[Br2] / 3dt = d[H2O] / 3dt





[1]b. How does the rate of disappearance of BrO3- anion compare with the rate of appearance of Br2 molecules?



Br2 molecules appear 3 times as fast as BrO3- ions disappear.









[6]c. The following initial rate data were obtained. Assuming that the rate equation has the format: Rate = k [BrO3-]x [Br-]y [H+]z,

Find k, x, y, and z.





Experiment #
[BrO3-] initial

(mol/L)

[Br-] initial

(mol/L)

[H+] initial

(mol/L)

Initial rate

(mol/L.s)

1 0.10 0.10 0.10 1.2 x 10-3
2 0.20 0.10 0.10 2.4 x 10-3
3 0.10 0.30 0.10 3.6 x 10-3
4 0.20 0.10 0.20 9.6 x 10-3



From 1 and 2: x = 1 (double conc leads to double rate)

From 1 and 3: y = 1 (triple conc leads to triple rate)

From 2 and 4: z = 2 (double cons leads to quadruple rate)



So rate = k [BrO3-] [Br-] [H+]2



from which k = 12 L3 mol-3 s-1.





So Rate = 12 L3 mol-3 s-1 [BrO3-] [Br-] [H+]2.



[2]8. Use the half life relation to estimate whether the following process is 0th , 1st or 2nd order: State why you choose the answer you do.



[reactant] (M) 1.00 0.75 0.60 0.50 0.37 0.25
time (s) 0.0 83.0 147.4 200.0 286.9 400.0




Time to first half life (to 0.5 M) = 200 seconds.

Time from 0.5 M to 0.25 M (second half life) = 200 seconds.



The half life is thus constant which is true if the process is 1st order.



























[4]9. The half life for cobalt-60 is 5.26 years. Calculate what fraction of a sample of cobalt-60 will remain 12 years after it was formed. Radioisotopes decompose following first order kinetics.





For first order reactions:

ln (a / (a - x)) = kt, and t = (ln 2) / k



For cobalt-60, k = (ln 2) / 5.26 yrs = 0.1318 yrs-1.



So in this case: ln (initial amount / final amount) = 0.1318 yrs-1 * 12 yrs = 1.581.



Leading to (initial amount / final amount) = 4.860.



Fraction required = (final amount / initial amount) = 0.206.



















[4]10. Calculate Ea for a reaction having k = 2.61 x 10-5 at 190 C

and k = 3.02 x 10-3 at 250 C.





ln k = ln A - Ea / RT

from which:

ln (k2 / k1) = Ea (T1-1 - T2-1) / R



In this case:

ln (2.61 x 10-5 / 3.02 x 10-3) = Ea (523-1 - 463-1) / R



From which Ea = 159 kJ.











11. A possible mechanism for a gas-phase reaction is:

step 1 Ce4+ + Mn2+ Ce3+ + Mn3+ fast

step 2 Ce4+ + Mn3+ Ce3+ + Mn4+ slow

step 3 Mn4+ + Tl+ Mn2+ + Tl3+ fast



[2]a. Write the balanced equation for the reaction.



2 Ce4+ + Tl+ 2 Ce3+ + Tl3+





[2]b. Indicate any intermediates in the reaction:



Mn3+, Mn4+. These two ions are formed in a step and react in a later step.





[2]c. Is a catalyst involved, if so, what is it?



Yes, Mn2+. This ion is used in a step and reformed in a later step.





[4]d. Write the theoretical rate law (in terms of measurable concentrations) for the reaction.



From the rds: rate = k [Ce4+] [Mn3+]



but the [Mn3+] is not directly measurable.



Use the approximation that the first, fast step is an equilibrium:



K = [Ce3+] [Mn3+] [Ce4+]-1 [ Mn2+]-1, from which [Mn3+] = K [Ce4+] [Mn2+] [Ce3+]-1



and rate = k [Ce4+] K [Ce4+] [Mn2+] [Ce3+]-1 = k' [Ce4+]2 [Mn2+] [Ce3+]-1

Data:



Integrated rate equations: Corresponding half-life equations



0th Order x = kt t = 2k / a

1st Order ln(a / (a-x)) = kt t = (ln 2) / k

2nd Order x / a(a-x) = kt t = 1 / (ak)





Arrhenius equation



ln k = ln A - Ea / RT





Gas constant, R = 8.314 J K-1 mol-1.