Brown - Chemistry: The Central Science 14th Edition - Chapter 14

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Ch.14 - Chemical Kinetics

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Brown 14th Edition

Ch.14 - Chemical Kinetics

Problem 31
Consider the following reaction: CH3Br(aq) + OH-(aq) → CH3OH(aq) + Br-(aq). The rate law for this reaction is first order in CH3Br and first order in OH-. When [CH3Br] is 5.0 * 10^-3 M and [OH-] is 0.050 M, the reaction rate at 298 K is 0.0432 M/s. (c) What would happen to the rate if the concentration of OH- were tripled? (d) What would happen to the rate if the concentration of both reactants were tripled?
Problem 32a
The reaction between ethyl bromide (C₂H₅Br) and hydroxide ion in ethyl alcohol at 330 K, C₂H₅Br(alc) + OH^-(alc) → C₂H₅OH(l) + Br^-(alc), is first order each in ethyl bromide and hydroxide ion. When [C₂H₅Br] is 0.0477 M and [OH^-] is 0.100 M, the rate of disappearance of ethyl bromide is 1.7×10^-7 M/s. (a) What is the value of the rate constant?
Problem 32b
The reaction between ethyl bromide (C₂H₅Br) and hydroxide ion in ethyl alcohol at 330 K, C₂H₅Br(alc) + OH^-(alc) → C₂H₅OH(l) + Br^-(alc), is first order each in ethyl bromide and hydroxide ion. When [C₂H₅Br] is 0.0477 M and [OH^-] is 0.100 M, the rate of disappearance of ethyl bromide is 1.7×10^-7 M/s. (b) What are the units of the rate constant?
Problem 32c
The reaction between ethyl bromide (C₂H₅Br) and hydroxide ion in ethyl alcohol at 330 K, C₂H₅Br(alc) + OH^-(alc) → C₂H₅OH(l) + Br^-(alc), is first order each in ethyl bromide and hydroxide ion. When [C₂H₅Br] is 0.0477 M and [OH^-] is 0.100 M, the rate of disappearance of ethyl bromide is 1.7×10^-7 M/s. (c) How would the rate of disappearance of ethyl bromide change if the solution were diluted by adding an equal volume of pure ethyl alcohol to the solution?
Problem 33a
The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl^- + I^- → OI^- + Cl^- . This rapid reaction gives the following rate data:
[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)
1.5 * 10-3 1.5 * 10-3
1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(a) Write the rate law for this reaction.
Problem 33b
The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl - + I - ¡OI - + Cl - . This rapid reaction gives the following rate data:
[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)
1.5 * 10-3 1.5 * 10-3
1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4
(b) Calculate the rate constant with proper units.
Problem 33c
The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: OCl^- + I^- → OI^- + Cl^- . This rapid reaction gives the following rate data:
[OCl₄^-] (M) [I^-] (M) Initial Rate (M,s)
1.5 * 10-3 1.5 * 10-3
1.36 * 10-4 3.0 * 10-3 1.5 * 10-3 2.72 * 10-4
1.5 * 10-3 3.0 * 10-3 2.72 * 10-4 (c) Calculate the rate when [OCl^-] = 2.0 * 10-3 M and [I^-] = 5.0 * 10 - 4 M.
Problem 34
The reaction 2 ClO2(aq) + 2 OH-(aq) → ClO3-(aq) + ClO2-(aq) + H2O(l) was studied with the following results: Experiment [ClO2] (M) [OH-] (M) Initial Rate (M/s) 1 0.060 0.030 0.0248 2 0.020 0.030 0.00276 3 0.020 0.090 0.00828. (c) Calculate the rate when [ClO2] = 0.100 M and [OH-] = 0.050 M.
Problem 35b
The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):
Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)
1 0.250 0.250 0.2130
2 0.250 0.125 0.1065
3 0.200 0.100 0.0682
4 0.350 0.100 0.1193
5 0.175 0.100 0.0596
(b) What is the overall order of the reaction?
Problem 35c
The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):
Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)
1 0.250 0.250 0.2130
2 0.250 0.125 0.1065
3 0.200 0.100 0.0682
4 0.350 0.100 0.1193
5 0.175 0.100 0.0596
(c) Calculate the rate constant with proper units?
Problem 35d
The following data were measured for the reaction BF₃(g) + NH₃(g) → F₃BNH₃(g):
Experiment [BF₃] (M) [NH₃] (M) Initial Rate (M/s)
1 0.250 0.250 0.2130
2 0.250 0.125 0.1065
3 0.200 0.100 0.0682
4 0.350 0.100 0.1193
5 0.175 0.100 0.0596
(d) What is the rate when [BF₃] = 0.100 M and [NH₃] = 0.500 M?
Problem 36
The following data were collected for the rate of disappearance of NO in the reaction 2 NO(g) + O2(g) → 2 NO2(g): Experiment [NO] (M) [O2] (M) Initial Rate (M/s) 1 0.0126 0.0125 1.41 * 10^-2 2 0.0252 0.0125 5.64 * 10^-2 3 0.0252 0.0250 1.13 * 10^-1 (d) What is the rate of disappearance of NO when [NO] = 0.0750 M and [O2] = 0.0100 M? (e) What is the rate of disappearance of O2 at the concentrations given in part (d)?
Problem 37
Consider the gas-phase reaction between nitric oxide and bromine at 273 _x001E_C: 2 NO(g) + Br2(g) → 2 NOBr(g). The following data for the initial rate of appearance of NOBr were obtained: Experiment [NO] (M) [Br2] (M) Initial Rate (M/s) 1 0.10 0.20 24 2 0.25 0.20 150 3 0.10 0.50 60 4 0.35 0.50 735 (c) How is the rate of appearance of NOBr related to the rate of disappearance of Br2? (d) What is the rate of disappearance of Br2 when [NO] = 0.075 M and [Br2] = 0.25 M?
Problem 37b
Consider the gas-phase reaction between nitric oxide and bromine at 273°C: 2 NO(g) + Br₂(g) → 2 NOBr(g). The following data for the initial rate of appearance of NOBr were obtained:
Experiment [NO] (M) [Br₂] (M) Initial Rate (M/s)
1 0.10 0.20 24
2 0.25 0.20 150
3 0.10 0.50 60
4 0.35 0.50 735
(b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets.
Problem 38
Consider the reaction of peroxydisulfate ion S2O8^2- with iodide ion I^- in aqueous solution: S2O8^2- (aq) + 3 I^- (aq) → 2 SO4^2- (aq) + I3^- (aq). At a particular temperature, the initial rate of disappearance of S2O8^2- varies with reactant concentrations in the following manner: Experiment S2O8^2- [M] I^- [M] Initial Rate [M/s] 1 0.018 0.036 2.6 * 10^-6 2 0.027 0.036 3.9 * 10^-6 3 0.036 0.054 7.8 * 10^-6 4 0.050 0.072 1.4 * 10^-5 (b) What is the average value of the rate constant for the disappearance of S2O8^2- based on the four sets of data? (c) How is the rate of disappearance of S2O8^2- related to the rate of disappearance of I^-? (d) What is the rate of disappearance of I^- when [S2O8^2-] = 0.025 M and [I^-] = 0.050 M?
Problem 38a
Consider the reaction of peroxydisulfate ion (S₂O₈^2-) with iodide ion (I^-) in aqueous solution:
S₂O₈^2-(aq) + 3 I^-(aq) → 2 SO₄^2-(aq) + I₃^-(aq)
At a particular temperature, the initial rate of disappearance of S₂O₈^2- varies with reactant concentrations in the following manner:
Experiment [S₂O₈^2-] (M) [I^-] (M) Initial Rate (M/s)
1 0.018 0.036 2.6 × 10^-6
2 0.027 0.036 3.9 × 10^-6
3 0.036 0.054 7.8 × 10^-6
4 0.050 0.072 1.4 × 10^-5
(a) Determine the rate law for the reaction and state the units of the rate constant.
Problem 39a
(a) For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?
Problem 39b
(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?
Problem 40b
The decomposition of sodium bicarbonate (baking soda), NaHCO₃(s), into Na₂CO₃(s), H₂O(l), and CO₂(g) at constant pressure requires the addition of 85 kJ of heat per two moles of NaHCO₃. (b) Draw an enthalpy diagram for the reaction.
Problem 41a
(a) The gas-phase decomposition of SO₂Cl₂, SO₂Cl₂(g) → SO₂(g) + Cl₂(g), is first order in SO₂Cl₂. At 600 K the half-life for this process is 2.3 × 10⁵ s. What is the rate constant at this temperature?
Problem 41b
(b) At 320°C the rate constant is 2.2 × 10^-5 s^-1. What is the half-life at this temperature?
Problem 42
Molecular iodine, I2(g), dissociates into iodine atoms at 625 K with a first-order rate constant of 0.271 s-1. (b) If you start with 0.050 M I2 at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form I2?
Problem 43a
As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO₂Cl₂) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10^-2 s^-1. (a) If we begin with an initial SO₂Cl₂ pressure of 450 torr, what is the partial pressure of this substance after 60 s?
Problem 43b
As described in Exercise 14.41, the decomposition of sulfuryl chloride (SO₂Cl₂) is a first-order process. The rate constant for the decomposition at 660 K is 4.5 × 10^-2 s^-1. (b) At what time will the partial pressure of SO₂Cl₂ decline to one-tenth its initial value?
Problem 44
The first-order rate constant for the decomposition of N2O5, 2 N2O5(g) → 4 NO2(g) + O2(g), at 70 °C is 6.82 * 10-3 s-1. Suppose we start with 0.0250 mol of N2O5(g) in a volume of 2.0 L. (b) How many minutes will it take for the quantity of N2O5 to drop to 0.010 mol?
Problem 44a
The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (a) How many moles of N₂O₅ will remain after 5.0 min?
Problem 44c
The first-order rate constant for the decomposition of N₂O₅, 2 N₂O₅(g) → 4 NO₂(g) + O₂(g), at 70°C is 6.82×10^-3 s^-1. Suppose we start with 0.0250 mol of N₂O₅(g) in a volume of 2.0 L. (c) What is the half-life of N₂O₅ at 70°C?
Problem 45
The reaction SO2Cl2(g) → SO2(g) + Cl2(g) is first order in SO2Cl2. Using the following kinetic data, determine the magnitude and units of the first-order rate constant: Time (s) Pressure SO2Cl2 (atm) 0 1.000 2500 0.947 5000 0.895 7500 0.848 10,000 0.803
Problem 46
From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the firstorder rate constant and half-life for the reaction: Time (s) Pressure CH3nC (torr) 0 502 2000 335 5000 180 8000 95.5 12,000 41.7 15,000 22.4
Problem 47a
Consider the data presented in Exercise 14.19. (a) By using appropriate graphs, determine whether the reaction is first order or second order.