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Problem 39b
(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?
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?
- 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 42
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 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?
- 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 45
Problem 46
From the following data for the first-order gas-phase isomerization of CH3NC to CH3CN at 215°C, calculate the first-order 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.
Problem 47c
Consider the data presented in Exercise 14.19. (c) What is the half-life for the reaction?
- Consider the data presented in Exercise 14.20. (a) Determine whether the reaction is first order or second order.
Problem 48
Problem 49a,c
The gas-phase decomposition of NO2, 2 NO2(g) → 2 NO(g) + O2(g), is studied at 383°C, giving the following data:
Time (s) [NO2] (M)
0.0 0.100
5.0 0.017
10.0 0.0090
15.0 0.0062
20.0 0.0047
(a) Is the reaction first order or second order with respect to the concentration of NO2?
(c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO2.
Problem 50a
Sucrose 1C12H22O112, commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6. At 23 C and in 0.5 M HCl, the following data were obtained for the disappearance of sucrose: Time (min) 3C12H22o11 4 1M2 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 (a) Is the reaction first order or second order with respect to 3C12H22O114?
Problem 51a
(a) What factors determine whether a collision between two molecules will lead to a chemical reaction?
Problem 51b
(b) Does the rate constant for a reaction generally increase or decrease with an increase in reaction temperature?
- (a) In which of the following reactions would you expect the orientation factor to be least important in leading to the reaction: NO + O → NO2 or H + Cl → HCl? (b) Does the orientation factor depend on temperature?
Problem 52
Problem 53
Calculate the fraction of atoms in a sample of argon gas at 400 K that has an energy of 10.0 kJ or greater.
Problem 54
(a) The activation energy for the isomerization of methyl isonitrile (Figure 14.6) is 160 kJ>mol. Calculate the fraction of methyl isonitrile molecules that has an energy equal to or greater than the activation energy at 500 K. (b) Calculate this fraction for a temperature of 520 K. What is the ratio of the fraction at 520 K to that at 500 K?
Problem 55a
The gas-phase reaction Cl(g) + HBr(g) → HCl(g) + Br(g) has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (a) Sketch the energy profile for the reaction, and label Ea and ΔE.
Problem 55b
The gas-phase reaction Cl(g) + HBr(g) → HCl(g) + Br(g) has an overall energy change of -66 kJ. The activation energy for the reaction is 7 kJ. (b) What is the activation energy for the reverse reaction?
- For the elementary process N2O5(g) → 2NO2(g) + NO3(g), the activation energy (Ea) and overall ΔE are 154 kJ/mol and 136 kJ/mol, respectively. (a) Sketch the energy profile for this reaction, and label Ea and ΔE.
Problem 56
Problem 57c
Indicate whether each statement is true or false. (c) Increasing the reaction temperature increases the fraction of successful collisions between reactants.
Problem 58a
Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction at different temperatures, you can calculate the overall enthalpy change for the reaction.
Problem 58b
Indicate whether each statement is true or false. (b) Exothermic reactions are faster than endothermic reactions.
Problem 58c
Indicate whether each statement is true or false. (c) If you double the temperature for a reaction, you cut the activation energy in half.
Problem 59
Based on their activation energies and energy changes and assuming that all collision factors are the same, rank the following reactions from slowest to fastest. (a) Ea = 45 kJ>mol; E = -25 kJ>mol (b) Ea = 35 kJ>mol; E = -10 kJ>mol (c) Ea = 55 kJ>mol; E = 10 kJ>mol
- (a) A certain first-order reaction has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 75.5 kJ/mol? (b) Another first-order reaction also has a rate constant of 2.75 * 10^-2 s^-1 at 20 _x001E_C. What is the value of k at 60 _x001E_C if Ea = 125 kJ/mol?
Problem 61
- Understanding the high-temperature behavior of nitrogen oxides is essential for controlling pollution generated in automobile engines. The decomposition of nitric oxide (NO) to N2 and O2 is second order with a rate constant of 0.0796 M-1s-1 at 737 _x001E_C and 0.0815 M-1s-1 at 947 _x001E_C. Calculate the activation energy for the reaction.
Problem 62