Tutorial 5 - Kinetics Tutorial Questions PDF

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REACTION KINETICS TUTORIAL EXAMPLES Prof Anita Jones You should attempt all questions in Part I BEFORE the Examples Class and consult the answers (on Learn) AFTER attempting them. Then, in the Examples Class you will be able to concentrate on the parts you found difficult. When you have completed the questions in Part I and checked your answers, move on to the questions in Part II. You may not have time to finish these questions during the Examples Class. If you need help after the Examples Class, email Prof Jones ([email protected]). Answers to Part II will be available on Learn after the Examples Class.

Part I Rates and Rate Laws 1. In the reaction 2A+B 2C+3D, the initial rate of formation of C was found to be 1.0 mol L-1 s-1 at 298 K. Calculate the initial rates of consumption of A and B, and the initial rate of formation of D. 2. Using the method of initial rates, the rate of the reaction between haemoglobin (Hb) and carbon monoxide (CO) was studied at 293 K The following data were collected. -6

-3

Run [Hb]0/10 mol dm 1 4.42 2 2.21 3 2.21

-6

-3

[CO]0/10 mol dm 2.00 2.00 3.00

-6

-3 -1

Initial Rate /10 mol dm s 1.24 0.62 0.93

(a) Determine the order of the reaction with respect to Hb and the order with respect to CO. (b) Write down the rate law for the reaction (c) Calculate the rate constant for the reaction.

Integrated Rate Laws and Half-life 3. For the first-order reaction A → 3B + C, the concentration of A was measured as a function of time. The initial concentration of A was 0.015 mol L-1, and after 3 minutes [A] decreased to 0.010 mol L-1. (a) (b) (c) (d)

Calculate the rate constant for the reaction. Calculate the concentration of A after 5 minutes reaction time. Calculate the concentration of B after 5 minutes reaction time. Calculate the half-life of the reaction.

4. The following data were obtained for the hydrolysis of a sugar in aqueous solution at 298 K. Time/minutes 0 60 130 180 Sugar conc. / 103 mol m-3 1.000 0.807 0.630 0.531 (a) By drawing a graph, show that the reaction is first order in sugar concentration. (b) Determine the rate constant for the reaction.

1

5.

239

Pu is formed in nuclear reactors from 238U, by neutron capture.239Pu is a very long-lived radioactive isotope; it decays with a half-life of 2.4×104 years to form 235U, with the emission of -particles.

(a) Calculate the rate constant for the 239Pu decay process. (b) How long will it take for the radioactivity of 239Pu to fall to 1/8 of its initial value? (c) How long will it take for the radioactivity of 239Pu to fall to 1% of its initial value?

Temperature-dependence of Reaction Rate 6. The reaction 2N2 O5 →2NO2 +O2 was studied at several temperatures and the following values for the rate constant were measured. T /°C 0 25 35 45 55 65 k /s-1 7.87 x 10-7 3.46 x 10-5 1.35 x 10-4 4.98 x 10-4 1.50 x 10-3 4.87 x 10-3 By drawing a graph, determine the activation energy of the reaction. 7. A cook finds that it takes 30 minutes to cook potatoes at 100 oC in an open pan and only 12 minutes to cook them in a pressure cooker at 110 oC. Estimate the activation energy for cooking potatoes, which involves the conversion of cellulose into starch. ________________________________________________________________________________________

Part II Rates and Rate Laws 8. For the reaction A+2B+C→2D+E the following data were collected. Experiment [A]0 /mmol L-1 [B]0 /mmol L-1 1 2 3 4 5 (a) (b) (c) (d)

2.06 0.87 0.50 1.00 1.60

3.05 3.05 0.50 0.50 2.00

[C]0 /mmol L-1 4.00 4.00 0.50 1.00 3.00

-d[A]0/dt /mmol L-1 s-1 3.7 0.66 0.013 0.072 -

Write the rate law for the reaction. What is the overall order of the reaction? Determine the value of the rate constant. For experiment 5, use the data to predict the initial rate of formation of D.

Integrated Rate Laws and Half-life 9. For the reaction A→2B+C the rate constant was measured to be 4.5×10-3 L mol-1 s-1. (a) What is the order of the reaction? (b) If the initial concentration of A is 0.45 mol L-1, calculate the time taken for the concentration of B to increase to 0.45 mol L-1.

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10. The kinetics of the gas-phase decomposition of ethanal at 540oC were investigated by measuring the concentration of ethanal ([A]) and the reaction rate, -d[A]/dt, as a function of time, during a single run in a closed vessel. The following results were obtained. Time / s [A] / 10-3 mol dm-3 -d[A] / 10-5 mol dm-3s-1 dt

0 50 15.00 10.78 11.68 6.05

100 200 300 8.43 5.87 4.50 3.69 1.79 1.05

(a) Using a graphical method, determine the order of reaction with respect to [A]. (b) Having established the order, make a linear plot using the appropriate integrated rate law to obtain an accurate value for the rate constant. 11. In a second experiment, the kinetics of the gas-phase decomposition of ethanal at 540oC were investigated using the method of initial rates. The initial rate of disappearance of ethanal was measured as a function of the initial concentration, [A]0, using a fresh sample of ethanal each time. The following results were obtained. [A]0 / 10-3 mol dm-3 -d[A]0 / 10-5 mol dm-3s-1 dt

15.00 12.00 11.68 8.36

9.00 6.00 3.00 5.43 2.95 1.05

(a) Using a graphical method, determine the order of reaction with respect to the initial ethanal concentration. (b) Suggest why the order of reaction measured in this experiment is different from that found in the experiment in question 10. 12. The radioactive decay of 14C has a half-life of 5730years. An archaeological sample is found to contain wood in which the concentration of 14C is 66% of that found in living trees. What is the age of the sample?

Temperature-dependence of Reaction Rate 13. The thermal denaturation of haemoglobin has an activation energy of 350 kJ mol-1. What is the change in the rate of denaturation when the temperature is raised from 37oC to 43oC? 14. Catalase is an enzyme that catalyses the decomposition of hydrogen peroxide. Catalase reduces the activation energy of the reaction from 76 kJ mol-1 to 8 kJ mol-1. Determine the factor by which the rate of decomposition of hydrogen peroxide, at body temperature (37oC), is increased in the presence of the enzyme.

Reaction Mechanism 15. One pathway for the destruction of ozone in the atmosphere is 2O3 → 3O2. A proposed mechanism for this reaction is:

(a) Identify the intermediate in this reaction. (b) Show that this mechanism is consistent with the measured rate law: (c) [O3 ]2 Rate = 𝑘 [O2 ] 3

16. When the rate of the reaction 2NO+O2 →2NO2 was studied, it was found that the rate doubled when the O2 concentration alone was doubled, and the rate quadrupled when the NO concentration alone was doubled. The following two alternative mechanisms were proposed for this reaction. For each mechanism determine the predicted rate law, and hence deduce which mechanism accounts for the experimental observations. Mechanism 1 k1   NO O2  NO3 

fast equilibriu m

k1

k2 NO NO3  2NO2

slow

Mechanism 2 k1 2NO  N2 O2 k2

O2  N2 O2  N2 O4 k3

N2 O4  2NO2

slow fast fast

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