CHM 096 TUTORIAL 1

(Chemical Kinetics)

1. Express the rate of reaction in terms of change in concentration of each of the reactants and products for:

a) 3O2(g) 2O3(g)

b) N2(g) + 3H2(g) 2NH3(g)

2. The reaction rate for a certain reaction is written in terms of the concentration of reactants and products:

Rate = ½ d[N2O

5] = ¼ d[NO

2] = d[O

2]

dt dt dt

Write a balanced equation for the reaction.

3. Consider the reaction: C2H4(g) + 3O2(g) 2CO2(g) + 2H2O(l)

a) When [C2H4] is decreasing at 0.25 mol/L.s, how fast is [O2] decreasing?

b) When [CO2] is increasing at 0.15 mol/L.s, how fast is [H2O] increasing?

c) When [O2] is decreasing at 3.6 mol/L.s, how fast is [CO2] increasing?

4. An experiment was carried out to study the rate of decomposition of NOBr by measuring its concentration at regular intervals.

2NOBr(g) 2NO(g) + Br2(g)

Time (s) [NOBr] (mol/L)

0.00 0.0100

2.00 0.0071

4.00 0.0055

6.00 0.0045

8.00 0.0038

10.00 0.0033

a) Calculate the average rate over the entire experiment.b) Calculate the average rate between 2.00 and 4.00 sec.c) Use graphical method to estimate:

i) the initial rateii) the instantaneous rate at 7.00 sec. (a: 0.00067; b: 0.0008 mol/L/s)

5. The rate law for the reaction given below is first order with respect to A2, and second order with respect to B2.

A2 + B2 2AB

a) Write the rate law equation.b) What is the overall reaction order?c) By how much would the rate change if:

i) [A2] is doubled?ii) [B2] is halved?

d) What is the rate of formation of AB if the rate of disappearance of A2 is 6.55 x 10−3 mol/L.s?

(1.31 x102 mol/L/s)6. Give the individual reaction orders for all substances, and the overall reaction order from the rate law

equation : Rate = k[NO2]2[Cl2]

7. By what factor does the rate in Problem 6 change if:

a) [NO2] is tripled?b) [NO2] and [Cl2] are doubled?c) [Cl2] is halved?

8. For the reaction: 4A(g) + 3B(g) 2C(g) the following data were obtained at constant temperature:

Experiment [A]o (mol/L) [B]o (mol/L)Initial rate

(mol/L.min)

1 0.100 0.100 5.00

2 0.300 0.100 45.0

3 0.100 0.200 10.0

4 0.300 0.200 90.0

a) What is the order with respect to A?b) What is the order with respect to B?c) Write the rate law.d) Calculate the rate constant k (using data from experiment 1).e) Derive the unit for k.f) If the reaction is carried out at a higher temperature, how would the value of the rate constant

change?(k = 5 x 103 L2mol2min1)

9. The compound RX3 decomposes according to the equation:

3RX3 R + R2X3 + 3X2

In an experiment, the following data were collected for the decomposition at 100C.

t(s) [RX3](mol L‒1)

0 0.852 0.676 0.418 0.3314 0.16

a) What is the average rate over the entire experiment?b) What is the average rate between the 2nd and the 8th seconds?

(0.049 Ms‒1, 0.057 Ms‒1)

10. The rate of a reaction is expressed in terms of changes in concentration of reactants and products as follows.

Rate = d[A]/dt = d[B]/dt = ⅔d[C]/dt

a) Write a balanced equation for the reaction.b) At a given instant, the reaction rate in terms of [C] is 6.55 x 102 mol/Ls. What is the rate in terms

of [A]?

11. For the reaction: AB(g) A(g) + B(g) ,

rate = k[AB]2, and k = 0.2 L/mol.s

a) How long will it take for [AB] to reach one/third of its initial concentration of 1.50 M?b) What is [AB] after 10.0 s?

(a: 6.67 s; b: 0.375 mol/L)

12. In a first order decomposition reaction, 50% of a compound decomposes in 10.5 min.

a) What is the rate constant of the reaction?

b) How long will it take for 75% of the compound to decompose?(0.0660 min1; 21 min)

13. The following data were collected for the decomposition of NH3 to N2 and H2, which follows a first order rate law: rate = k[NH3].

Time (s): 0.000 1.000 2.000

[NH3] (M): 4.000 3.986 3.974

a) Use graphical method to determine the rate constant.

b) What is the half-life for the reaction?(3 x 103 s1; 2 x 102 s)

14. The rate law for the reaction:

NO2(g) + CO(g) NO(g) + CO2(g)

is rate = k[NO2]2. The following mechanism is proposed:

(I) 2NO2(g) N2(g) + 2O2(g) [slow]

(II) 2CO(g) + O2(g) 2CO2(g) [fast]

(III) N2(g) + O2(g) 2NO(g) [fast]

a) Identify the “intermediates” in the mechanism.b) What are the molecularity and rate law for each elementary steps.c) Is the proposed mechanism consistent with the rate law given?

15. Hydrogen iodide decomposes on heating according to the equation:

2HI(g) H2(g) + I2(g)

The rate constants of the reaction at 227oC and at 327oC are 5.71 x 107 L mol1min1 and 6.6 x 104 L mol1min1 respectively.

a) What is the reaction order?b) Calculate the activation energy for this reaction. (R = 8.31 J mol1K1)

(175.8 kJ mol1)

16. The rate constant of a reaction is 4.7 x 103 s1 at 25oC, and the activation energy is 33.6 kJ/mol. What is the value of k at 750C?

(0.033 s1)

17. For the reaction: A2 + B2 2AB , H = 55 kJ/mol, and Ea(fwd) = 215 kJ/mol.

a) Draw an energy profile diagram.b) Calculate Ea(rev).c) Sketch a possible transition state for the reaction.

18. Consider the one-step reaction:

NO(g) + Cl2(g) NOCl(g) + Cl(g)

a) Given that Ea(fwd) = 86 kJ/mol, and Ea(rev) = 3 kJ/mol, is the reaction endothermic or exothermic?b) Draw the energy profile diagram.c) Sketch the possible transition state. (atom sequence for NOCl is Cl—N—O)

19. a) Is collision frequency the only factor affecting rate? Explain.b) For a reaction with a given Ea, how does an increase in temperature, T affect the rate?c) For a reaction at a given temperature, T, how does a decrease in Ea affect the rate?

20. The proposed mechanism for a reaction is:

(I) A(g) + B(g) ⇌ X(g) [fast]

(II) X(g) + C(g) Y(g) [slow]

(III) Y(g) D(g) [fast]

a) Identify the “intermediates” in the mechanism.b) Write the overall equation for the reaction.c) What are the molecularity and rate law for each elementary steps.d) Which is the rate determining step?e) Derive the rate law for the reaction, based on the given mechanism.

21. The following data were measured for a certain reaction:

A + B C + D

Initial Concentrations (mol/dm3)

[A]o [B]o Initial Rate (mol/dm3.s)

0.10 0.10 1.23 x10−5

0.10 0.20 2.46x10−5

0.20 0.10 4.92 x10−5

a) Determine the rate law for this reaction.b) Calculate the value of rate constant, k.

22. The experimental rate law for the reaction: CO + NO2 NO + CO2 , is: rate = k[NO2]2. The mechanism for the reaction is given as:

2NO2 NO3 + NO (slow)NO3 + CO NO2 + CO2 (fast)

a) Why the term [CO] dose not appear in the experimental rate law?b) Identify the reaction intermediate.c) Is the mechanism consistent with the experimental rate law? Give two reasons to justify your

answer.