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- The oxidation of SO2 to SO3 is accelerated by NO2. The reaction proceeds according to: NO2(g) + SO2(g) → NO(g) + SO3(g) 2 NO(g) + O2(g) → 2 NO2(g) (a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of SO2 by O2 to give SO3. (d) Is this an example of homogeneous catalysis or heterogeneous catalysis?
Problem 79
Problem 80b
The addition of NO accelerates the decomposition of N2O, possibly by the following mechanism: NO1g2 + N2O1g2¡N21g2 + NO21g2 2 NO21g2¡2 NO1g2 + O21g2 (b) Is NO serving as a catalyst or an intermediate in this reaction?
Problem 80c
The addition of NO accelerates the decomposition of N2O, possibly by the following mechanism:
NO(g) + N2O(g) → N2(g) + NO2(g)
2 NO2(g) → 2 NO(g) + O2(g)
(c) If experiments show that during the decomposition of N2O, NO2 does not accumulate in measurable quantities, does this rule out the proposed mechanism?
Problem 81b
Many metallic catalysts, particularly the precious-metal ones, are often deposited as very thin films on a substance of high surface area per unit mass, such as alumina (Al2O3) or silica (SiO2). (b) How does the surface area affect the rate of reaction?
- The enzyme carbonic anhydrase catalyzes the reaction CO2(g) + H2O(l) ↔ HCO3⁻(aq) + H⁺(aq). In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s⁻¹ at 25 _x001E_C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 * 10⁶ s⁻¹ at 25 _x001E_C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.
Problem 85
Problem 86b
The enzyme urease catalyzes the reaction of urea, (NH2CONH2), with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 × 10-5 s-1 at 100°C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 × 104 s-1 at 21°C. (b) If the rate of the catalyzed reaction were the same at 100°C as it is at 21°C, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions?
Problem 86c
The enzyme urease catalyzes the reaction of urea, (NH2CONH2), with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 × 10-5 s-1 at 100°C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 × 104 s-1 at 21°C. (c) In actuality, what would you expect for the rate of the catalyzed reaction at 100°C as compared to that at 21°C?
Problem 87a
The activation energy of an uncatalyzed reaction is 95 kJ/mol. The addition of a catalyst lowers the activation energy to 55 kJ/mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) 25 C
Problem 87b
The activation energy of an uncatalyzed reaction is 95 kJ/mol. The addition of a catalyst lowers the activation energy to 55 kJ/mol. Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (b) 125 °C?
- Suppose that a certain biologically important reaction is quite slow at physiological temperature 137 _x001E_C2 in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a 1 * 10^5-fold increase in the reaction rate?
Problem 88
Problem 89b
Consider the reaction A + B → C + D. Is each of the following statements true or false? (b) If the reaction is an elementary reaction, the rate law is second order.
Problem 89c
Consider the reaction A + B → C + D. Is each of the following statements true or false? (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order.
Problem 91b
The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and [O2] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (b) What is the value of the rate constant?
Problem 91c
The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and [O2] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (c) What are the units of the rate constant?
Problem 91d
The reaction 2 NO(g) + O2(g) → 2 NO2 (g) is second order in NO and first order in O2. When [NO] = 0.040 M, and [O2] = 0.035 M, the observed rate of disappearance of NO is 9.3⨉10-5 M/s. (d) What would happen to the rate if the concentration of NO were increased by a factor of 1.8?
- You perform a series of experiments for the reaction A → B + C and find that the rate law has the form rate = k[A]^x. Determine the value of x in each of the following cases: (a) There is no rate change when [A] is tripled. (b) The rate increases by a factor of 9 when [A] is tripled. (c) When [A] is doubled, the rate increases by a factor of 8.
Problem 92
Problem 93b,c
Consider the following reaction between mercury(II) chloride and oxalate ion:
2 HgCl2(aq) + C2O42-(aq) → 2 Cl-(aq) + 2 CO2(g) + Hg2Cl2(s)
The initial rate of this reaction was determined for several concentrations of HgCl2 and C2O42-, and the following rate data were obtained for the rate of disappearance of C2O42-:
Experiment [HgCl2] (M) [C2O42-] (M) Rate (M/s)
1 0.164 0.15 3.2 × 10-5
2 0.164 0.45 2.9 × 10-4
3 0.082 0.45 1.4 × 10-4
4 0.246 0.15 4.8 × 10-5
(b) What is the value of the rate constant with proper units?
(c) What is the reaction rate when the initial concentration of HgCl2 is 0.100 M and that of C2O42- is 0.25 M if the temperature is the same as that used to obtain the data shown?
- The following kinetic data are collected for the initial rates of a reaction 2X + Z → products: Experiment [X] (M) [Z] (M) Rate (M/s) 1 0.25 0.25 4.0 * 10^1 2 0.50 0.50 3.2 * 10^2 3 0.50 0.75 7.2 * 10^2. (c) What is the reaction rate when the initial concentration of X is 0.75 M and that of Z is 1.25 M?
Problem 94
Problem 95a
The reaction 2 NO2 → 2 NO + O2 has the rate constant k = 0.63 M-1s-1. (a) Based on the units for k, is the reaction first or second order in NO2?
Problem 95b
The reaction 2 NO2 → 2 NO + O2 has the rate constant k = 0.63 M-1s-1.
(b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?
Problem 96
Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?
- A first-order reaction A → B has the rate constant k = 3.2 * 10^-3 s^-1. If the initial concentration of A is 2.5 * 10^-2 M, what is the rate of the reaction at t = 660 s?
Problem 97
- The reaction H₂O₂(aq) → H₂O(l) + 1/2 O₂(g) is first order. At 300 K, the rate constant equals 7.0 * 10⁻⁴ s⁻¹. If the activation energy for this reaction is 75 kJ/mol, at what temperature would the reaction rate be doubled?
Problem 98
Problem 99a,b
Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate?
Problem 99c,d
Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (c) How much of a 1.00-mg sample of each isotope remains after three half-lives? (d) How much of a 1.00-mg sample of each isotope remains after 4 days?
Problem 101a
The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 × 103 M-1 cm-1 at 520 nm.
(a) Calculate the initial concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction.
Problem 101c
The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 × 103 M-1 cm-1 at 520 nm.
(c) Calculate the half-life of the reaction.
Problem 101d
The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 × 103 M-1 cm-1 at 520 nm.
(d) How long does it take for the absorbance to fall to 0.100?
- A colored dye compound decomposes to give a colorless product. The original dye absorbs at 608 nm and has an extinction coefficient of 4.7 * 10^4 M^-1 cm^-1 at that wavelength. You perform the decomposition reaction in a 1-cm cuvette in a spectrometer and obtain the following data: Time (min) Absorbance at 608 nm 0 1.254 30 0.941 60 0.752 90 0.672 120 0.545. From these data, determine the rate law for the reaction 'dye → product' and determine the rate constant.
Problem 102
- Cyclopentadiene (C5H6) reacts with itself to form dicyclopentadiene (C10H12). A 0.0400 M solution of C5H6 was monitored as a function of time as the reaction 2 C5H6 → C10H12 proceeded. The following data were collected: Time (s) | [C5H6] (M) 0.0 | 0.0400 50.0 | 0.0300 100.0 | 0.0240 150.0 | 0.0200 200.0 | 0.0174 Plot [C5H6] versus time, ln[C5H6] versus time, and 1/[C5H6] versus time. (b) What is the value of the rate constant?
Problem 103