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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?
- (c) Which factor is most sensitive to changes in temperature—the frequency of collisions, the orientation factor, or the fraction of molecules with energy greater than the activation energy?
Problem 51
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
- Indicate whether each statement is true or false. (a) If you compare two reactions with similar collision factors, the one with the larger activation energy will be slower. (b) A reaction that has a small rate constant must have a small frequency factor.
Problem 57
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
- The rate of the reaction CH3COOC2H5(aq) + OH-(aq) → CH3COO-(aq) + C2H5OH(aq) was measured at several temperatures, and the following data were collected: Temperature (°C) k (M⁻¹ s⁻¹) 15 0.0521 25 0.101 35 0.184 45 0.332. Calculate the value of Ea by constructing an appropriate graph.
Problem 63
Problem 64
The temperature dependence of the rate constant for a reaction is tabulated as follows: Temperature (K) k 1M 1 s1 2 600 0.028 650 0.22 700 1.3 750 6.0 800 23 Calculate Ea and A.
- What is meant by the term elementary reaction? What is a reaction mechanism? What is meant by the term rate-determining step?
Problem 65
Problem 65b
(b) What is the difference between a unimolecular and a bimolecular elementary reaction?
- (a) Can an intermediate appear as a reactant in the first step of a reaction mechanism? (b) On a reaction energy profile diagram, is an intermediate represented as a peak or a valley?
Problem 66
Problem 67a
What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) Cl2(g) → 2 Cl(g)
Problem 67b
What is the molecularity of each of the following elementary reactions? Write the rate law for each. (b) OCl-(aq + H2O(l) → HOCl(aq) + OH-(aq)
Problem 67c
What is the molecularity of each of the following elementary reactions? Write the rate law for each. (c) NO(g) + Cl2(g) → NOCl2(g)
Problem 68a,b
What is the molecularity of each of the following elementary reactions? Write the rate law for each.
(a) 2 NO(g) → N2O2(g)
(c) SO3(g) → SO2(g) + O(g)