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Problem 44
Consider the tabulated data showing the initial rate of a reaction (A → products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction including the value of the rate constant, k.
- The tabulated data were collected for this reaction: 2 NO2(g) + F2(g) → 2 NO2F(g). Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction?
Problem 45
Problem 46
The tabulated data were collected for this reaction: CH3Cl(g) + 3 Cl2(g) → CCl4( g) + 3 HCl(g)
Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction?
Problem 48a
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 48c
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 49
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 51
Problem 52
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 53a
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 -0.0045/s. a. What is the value of the rate constant (k) for this reaction at this temperature?
Problem 54b
This reaction was monitored as a function of time: AB → A + B A plot of 1/[AB] versus time yields a straight line with a slope of +0.55/Ms. b. Write the rate law for the reaction.
- 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 55
- The decomposition of XY is second order in XY and has a rate constant of 7.02 * 10^-3 M^-1 s^-1 at a certain temperature. b. How long will it take for the concentration of XY to decrease to 12.5% of its initial concentration when the initial concentration is 0.100 M? When the initial concentration is 0.200 M? c. If the initial concentration of XY is 0.150 M, how long will it take for the concentration to decrease to 0.062 M? d. If the initial concentration of XY is 0.050 M, what is the concentration of XY after 5.0 * 10^1 s? After 5.50 * 10^2 s?
Problem 56
Problem 56a
The decomposition of XY is second order in XY and has a rate constant of 7.02⨉10-3 M-1• s-1 at a certain temperature. a. What is the half-life for this reaction at an initial concentration of 0.100 M?
Problem 57a
The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration. How long will it take for 10% of the U-238 atoms in a sample of U-238 to decay?
Problem 57b
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 1.5⨉1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms does it contain today?
Problem 58a
The half-life for the radioactive decay of C-14 is 5730 years and is independent of the initial concentration. How long does it take for 25% of the C-14 atoms in a sample of C-14 to decay?
Problem 58b
The half-life for the radioactive decay of C-14 is 5730 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 2255 years?
Problem 59
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 61
The activation energy of a reaction is 56.8 kJ/mol and the frequency factor is 1.5⨉1011/ s. Calculate the rate constant of the reaction at 25 °C.
Problem 63
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 -7445 K. Calculate the activation energy for the reaction.
Problem 65
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 66
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 67
- 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 69
Problem 69a
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 70b
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 71
- If a temperature increase from 20.0 °C to 35.0 °C triples the rate constant for a reaction, what is the value of the activation energy for the reaction?
Problem 72
Problem 73
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 74
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)