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Problem 52a
Indicate the order of reaction consistent with each observation.
a. The half-life of the reaction gets shorter as the initial concentration is increased.
b. A plot of the natural log of the concentration of the reactant versus time yields a straight line.
Problem 52c
Indicate the order of reaction consistent with each observation c. The half-life of the reaction gets longer as the initial concentration is increased.
Problem 53
The tabulated data show the concentration of AB versus time for this reaction: AB( g)¡A( g) + B( g) Time (s) [AB] (M) 0 0.950 50 0.459 100 0.302 150 0.225 200 0.180 250 0.149 300 0.128 350 0.112 400 0.0994 450 0.0894 500 0.0812 Determine the order of the reaction and the value of the rate constant. Predict the concentration of AB at 25 s.
- The tabulated data show the concentration of cyclobutane (C4H8) versus time for this reaction: C4H8 -> 2 C2H4. Time (s) [C4H8] (M) 0 1.000 10 0.894 20 0.799 30 0.714 40 0.638 50 0.571 60 0.510 70 0.456 80 0.408 90 0.364 100 0.326. Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [C4H8] = 0.25 M?
Problem 55
Problem 56
The reaction A¡products was monitored as a function of time. The results are shown here. Time (s) [A] (M) 0 1.000 25 0.914 50 0.829 75 0.744 100 0.659 125 0.573 150 0.488 175 0.403 200 0.318 Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [A] = 0.10 M?
Problem 59a
This reaction was monitored as a function of time: A → B + C A plot of ln[A] versus time yields a straight line with slope -0.0105/s. a. What is the value of the rate constant (k) for this reaction at this temperature?
- a. What is the half-life for the first-order decomposition of SO2Cl2 with a rate constant of 1.42 x 10^-4 s^-1? b. How long will it take for the concentration of SO2Cl2 to decrease to 25% of its initial concentration? c. If the initial concentration of SO2Cl2 is 1.00 M, how long will it take for the concentration to decrease to 0.78 M? d. If the initial concentration of SO2Cl2 is 0.150 M, what is the concentration of SO2Cl2 after 2.00 x 10^2 s? After 5.00 x 10^2 s?
Problem 61
Problem 63b
The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. If a sample of U-238 initially contained 3.2⨉1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms does it contain today?
Problem 64a
The half-life for the radioactive decay of C-14 is 5715 years and is independent of the initial concentration. How long does it take for 25.00% of the C-14 atoms in a sample of C-14 to decay?
Problem 64b
The half-life for the radioactive decay of C-14 is 5715 years and is independent of the initial concentration. If a sample of C-14 initially contains 1.5 mmol of C-14, how many millimoles are left after 2725 years?
Problem 65
The diagram shows the energy of a reaction as the reaction progresses. Label each blank box in the diagram.
a. reactants b. products c. activation energy (Ea) d. enthalpy of reaction (ΔHrxn)
Problem 67
The activation energy of a reaction is 44.2 kJ/mol and the frequency factor is 1.9⨉1011/ s. Calculate the rate constant of the reaction at 25 °C.
Problem 69
The rate constant (k) for a reaction was measured as a function of temperature. A plot of ln k versus 1/T (in K) is linear and has a slope of -7012 K. Calculate the activation energy for the reaction.
Problem 71
The data shown here were collected for the first-order reaction: N2O(g) → N2(g) + O(g) Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
800 3.24⨉10- 5
900 0.00214
1000 0.0614
1100 0.955
Problem 72
The tabulated data show the rate constant of a reaction measured at several different temperatures. Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction.
Temperature (K) Rate Constant (1 , s)
300 0.0134
310 0.0407
320 0.114
330 0.303
340 0.757
- The tabulated data were collected for the second-order reaction: Cl(g) + H2(g) → HCl(g) + H(g). Use an Arrhenius plot to determine the activation barrier and frequency factor for the reaction. Temperature (K) and Rate Constant (L/mol # s) are as follows: 90 K, 0.00357; 100 K, 0.0773; 110 K, 0.956; 120 K, 7.781.
Problem 73
- What is the value of the rate constant at 425 K for a reaction with rate constants of 0.0117/s at 400.0 K and 0.689/s at 450.0 K?
Problem 75
Problem 75a
A reaction has a rate constant of 0.0117/s at 400.0 K and 0.689/s at 450.0 K. a. Determine the activation barrier for the reaction.
Problem 76b
A reaction has a rate constant of 0.000122/s at 27 °C and 0.228/s at 77 °C. b. What is the value of the rate constant at 17 °C?
- If a temperature increase from 10.0 °C to 20.0 °C doubles the rate constant for a reaction, what is the value of the activation energy for the reaction?
Problem 77
Problem 79
Consider these two gas-phase reactions: a. AA(g) + BB(g) → 2 AB(g) b. AB(g) + CD(g) → AC(g) + BD(g) If the reactions have identical activation barriers and are carried out under the same conditions, which one would you expect to have the faster rate?
Problem 80
Which of these two reactions would you expect to have the smaller orientation factor? Explain. a. O(g) + N2(g) → NO( g) + N(g) b. NO(g) + Cl2(g) → NOCl( g) + Cl(g)
- Consider this overall reaction, which is experimentally observed to be second order in X and first order in Y: X + Y → XY. a. Does the reaction occur in a single step in which X and Y collide? b. Is this two-step mechanism valid? 2X →k1/k2 X2 (Fast) X2 + Y →k3 XY + X (Slow)
Problem 82
Problem 83a
Consider this three-step mechanism for a reaction:
Cl2 (g) k1⇌k2 2 Cl (g) Fast
Cl (g) + CHCl3 (g) →k3 HCl (g) + CCl3 (g) Slow
Cl (g) + CCl3 (g) →k4 CCl4 (g) Fast
a. What is the overall reaction?
Problem 83c
Consider this three-step mechanism for a reaction:
Cl2 (g) k1⇌k2 2 Cl (g) Fast
Cl (g) + CHCl3 (g) →k3 HCl (g) + CCl3 (g) Slow
Cl (g) + CCl3 (g) →k4 CCl4 (g) Fast
c. What is the predicted rate law?
- Consider this two-step mechanism for a reaction: Step 1: NO2(g) + Cl2(g) → ClNO2(g) + Cl(g) Slow Step 2: NO2(g) + Cl(g) → ClNO2(g) Fast c. What is the predicted rate law? a. What is the overall reaction?
Problem 84
Problem 85
Many heterogeneous catalysts are deposited on high-surfacearea supports. Why?
Problem 86
Suppose that the reaction A¡products is exothermic and has an activation barrier of 75 kJ/mol. Sketch an energy diagram showing the energy of the reaction as a function of the progress of the reaction. Draw a second energy curve showing the effect of a catalyst.
- Suppose that a catalyst lowers the activation barrier of a reaction from 125 kJ/mol to 55 kJ/mol. By what factor would you expect the reaction rate to increase at 25 °C? (Assume that the frequency factors for the catalyzed and uncatalyzed reactions are identical.)
Problem 87
Problem 88
The activation barrier for the hydrolysis of sucrose into glucose and fructose is 108 kJ/mol. If an enzyme increases the rate of the hydrolysis reaction by a factor of 1 million, how much lower must the activation barrier be when sucrose is in the active site of the enzyme? (Assume that the frequency factors for the catalyzed and uncatalyzed reactions are identical and a temperature of 25 °C.)