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chemistry
physical chemistry

General Chemistry 9th edition Darrell Ebbing, Steven D. Gammon - Solutions

A reaction of the form aA → Products is second order with a half-life of 425 s. What is the rate constant of the reaction if the initial concentration of A is 5.99 × 103 mol/L?
In the presence of excess thiocyanate ion, SCN, the following reaction is first order in chromium(III) ion, Cr3+; the rate constant is 2.0 × 106/s. Cr3+(aq) + SCN(aq) → Cr(SCN)2+(aq) If 85.0% reaction is required to obtain a noticeable color from the formation of the Cr(SCN)2+ ion, how many
The rate of a reaction is quadrupled when the concentration of one reactant is doubled. What is the order of the reaction with respect to this reactant?
In the presence of excess thiocyanate ion, SCN, the following reaction is first order in iron(III) ion, Fe3+; the rate constant is 1.27/s. Fe3+(aq) + SCN(aq) → Fe(SCN)2+(aq) If 90.0% reaction is required to obtain a noticeable color from the formation of the Fe(SCN)2+ ion, how many seconds are
It is found that a gas undergoes a zero-order decomposition reaction in the presence of a nickel catalyst. If the rate constant for this reaction is 8.1 × 102 mol/(L∙s), how long will it take for the concentration of the gas to change from an initial concentration of 0.10 M to 1.0 × 102 M?
The reaction A → B + C is found to be zero order. If it takes 4.3 × 102 seconds for an initial concentration of A to go from 0.50 M to 0.25 M, what is the rate constant for the reaction?
Chlorine dioxide oxidizes iodide ion in aqueous solution to iodine; chlorine dioxide is reduced to chlorite ion. 2ClO2(aq)+ 2I(aq) →2ClO2(aq) + I2(aq) The order of the reaction with respect to ClO2 was determined by starting with a large excess of I, so that its concentration was essentially
Methyl acetate, CH3COOCH3, reacts in basic solution to give acetate ion, CH3COO, and methanol, CH3OH. CH3COOCH3(aq) + OH(aq) → CH3COO(aq) + CH3OH(aq) The overall order of the reaction was determined by starting with methyl acetate and hydroxide ion at the same concentrations, so [CH3COOCH3] =
Sketch a potential-energy diagram for the reaction of nitric oxide with ozone. NO(g)+ O3(g) → NO2(g) + O2(g) The activation energy for the forward reaction is 10 kJ; the ΔHo is 200 kJ. What is the activation energy for the reverse reaction? Label your diagram appropriately.
Sketch a potential-energy diagram for the decomposition of nitrous oxide. N2O(g) → N2(g) + O(g) The activation energy for the forward reaction is 251 kJ; the ΔHo is +167 kJ. What is the activation energy for the reverse reaction? Label your diagram appropriately.
In a series of experiments on the decomposition of dinitrogen pentoxide, N2O5, rate constants were determined at two different temperatures. At 35oC, the rate constant was 1.4 × 104/s; at 45oC, the rate constant was 5.0 × 104/s. What is the activation energy for this reaction? What is the value
The reaction 2NOCl(g) → 2NO(g) + Cl2(g) has rate-constant values for the reaction of NOCl of 9.3 × 106/s at 350 K and 6.9 × 104/s at 400 K. Calculate activation energy for the reaction. What is the rate constant at 435 K?
The rate of a particular reaction triples when the temperature is increased from 25oC to 35oC. Calculate the activation energy for this reaction.
A rate law is one-half order with respect to a reactant. What is the effect on the rate when the concentration of this reactant is doubled?
The rate of a particular reaction quadruples when the temperature is increased from 25oC to 35oC. Calculate the activation energy for this reaction.
The following values of the rate constant were obtained for the decomposition of nitrogen dioxide at various temperatures. Plot the logarithm of k versus 1/T and from the graph obtain the energy of activation. Temperature (oC) k (L/mol∙s) 320…… 0.527 330…… 0.776 340……
The following values of the rate constant were obtained for the decomposition of hydrogen iodide at various temperatures. Plot the logarithm of k versus 1/T and from the graph obtain the energy of activation. Temperature (oC) k (L/mol∙s) 440………. 2.69 × 103 460………. 6.21 ×
Nitrogen monoxide, NO, is believed to react with chlorine according to the following mechanism:Identify any reaction intermediate. What is the overall equation?
The decomposition of ozone is believed to occur in two steps:Identify any reaction intermediate. What is the overall reaction?
Write a rate equation, showing the dependence of rate on reactant concentrations, for each of the following elementary reactions. a. O3 → O2 + O b. NOCl2 + NO → 2NOCl
Write a rate equation, showing the dependence of rate on reactant concentrations, for each of the following elementary reactions. a. CS2 → CS + S b. CH3Br + OH → CH3OH + Br
The isomerization of cyclopropane, C3H6, is believed to occur by the mechanism shown in the following equations:Here C3H6* is an excited cyclopropane molecule. At low pressure, Step 1 is much slower than Step 2. Derive the rate law for this mechanism at low pressure. Explain.
The reaction A(g) → B(g) + C(g) is known to be first order in A(g). It takes 25 s for the concentration of A(g) to decrease by one-half of its initial value. How long does it take for the concentration of A(g) to decrease to one-fourth of its initial value? to one-eighth of its initial value?
The thermal decomposition of nitryl chloride, NO2Cl,2NO2Cl(g) †’ 2NO2(g) + Cl2(g)is thought to occur by the mechanism shown in the following equations:What rate law is predicted by this mechanism?
The reaction H2(g) + I2(g) †’ 2HI(g) may occur by the following mechanism:What rate law is predicted by the mechanism?
Ozone decomposes to oxygen gas.2O3(g) †’ 3O2(g)A proposed mechanism for this decomposition isWhat is the rate law derived from this mechanism?
The following is a possible mechanism for a reaction involving hydrogen peroxide in aqueous solution; only a small amount of sodium bromide was added to the reaction mixture. H2O2 + Br → BrO + H2O H2O2 + BrO → Br + H2O + O2 What is the overall reaction? What species is acting as a catalyst?
Consider the following mechanism for a reaction in aqueous solution and indicate the species acting as a catalyst: Explain why you believe this species is a catalyst. What is the overall reaction? What substance might be added to the reaction mixture to give the catalytic activity? Obtain the
A study of the decomposition of azomethane, CH3NNCH3(g) → C2H6(g)+ N2(g) gave the following concentrations of azomethane at various times: Time [CH3NNCH3] 0 min………. 1.50 × 102 M 10 min………. 1.29 × 102 M 20 min………. 1.10 × 102
Nitrogen dioxide decomposes when heated. 2NO2(g) → 2NO(g) + O2(g) During an experiment, the concentration of NO2 varied with time in the following way: Time [NO2] 0.0 min………. 0.1103 M 1.0 min………. 0.1076 M 2.0 min………. 0.1050 M 3.0 min……….
You can write the rate law for the decomposition of azomethane aswhen n is the order of the reaction. When you divide the rates at various times by the concentrations raised to the correct power n, you should get the same number (the rate constant k). Verify that the decomposition of azomethane is
Use the technique described in Problem 13.97 to verify that the decomposition of nitrogen dioxide is second order. That is, divide each average rate in a time interval (obtained in Problem 13.96) by the square of the average concentration in that interval. Note that each calculation gives nearly
Methyl acetate reacts in acidic solution. The rate law is first order in methyl acetate in acidic solution, and the rate constant at 25oC is 1.26 × 104/s. How long will it take for 65% of the methyl acetate to react?
A gas is enclosed in a system similar to that shown in Figure 18.2. More weights are added to the piston, giving a total mass of 2.20 kg. As a result, the gas is compressed and the weights are lowered 0.250 m. At the same time, 1.50 J of heat evolves from (leaves) the system. What is the change in
Use the data from Table 18.2 to obtain the equilibrium constant Kp at 25oC for the reactionThat values of ˆ†Gof are needed for CaCO3 and CaO, even though the substances do not appear in Kp = PCO2.
Calculate the solubility product constant for Mg(OH)2 at 25oC. The ∆Gof values (in kJ/mol) are as follows: Mg2+ (aq), 454.8; OH(aq), 157.3; Mg(OH)2(s), 833.7.
The thermodynamic equilibrium constant for the vaporization of wateris Kp = PH2O. Use thermodynamic data to calculate the vapor pressure of water at 45oC. Compare your answer with the value given in Appendix B.
To what temperature must magnesium carbonate be heated to decompose it to MgO and CO2 at 1 atm? Is this higher or lower than the temperature required to decompose CaCO3? Values of ∆Hof (in kJ/mol) are as follows: MgO(s), 601.2; MgCO3(s), 1111.7. Values of So (in J/K) are as follows: MgO(s),
Consider the combustion (burning) of methane, CH4, in oxygen. CH4(g) + 2O2(g) →CO2(g) + 2H2O(l) The heat of reaction at 25oC and 1.00 atm is 890.2 kJ. What is the change in volume when 1.00 mol CH4 reacts with 2.00 mol O2? (You can ignore the volume of liquid water, which is insignificant
Liquid ethanol, C2H5OH(l), at 25oC has an entropy of 161 J/(mol • K). If the heat of vaporization, ∆Hvap, at 25oC is 42.6 kJ/mol, what is the entropy of the vapor in equilibrium with the liquid at 25oC?
Predict the sign of ∆So for each of the following reactions. a. CaCO3(s) → CaO(s) + CO2(g) b. CS2(l) → CS2(g) c. 2Hg(l) + O2(g) → 2HgO(s) d. 2Na2O2(s) + 2H2O(l) → 4NaOH(aq) + O2(g
Calculate the change of entropy, ∆So, for the reaction given in Example 18.2a. The standard entropy of glucose, C6H12O6(s), is 212 J/(mol•K). See Table 18.1 for other values.
Calculate ∆Go for the following reaction at 25oC. Use data given in Tables 6.2 and 18.1. CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
Calculate ∆Go at 25oC for the following reaction, using values of ∆Gof.CaCO3(s) → CaO(s) + CO2(g)
Which of the following reactions are spontaneous in the direction written? See Table 18.2 for data. a. C(graphite) + 2H2(g) → CH4(g) b. 2H2(g) + O2(g) → 2H2O(l ) c. 4HCN(g) + 5O2(g) → 2H2O(l) + 4CO2(g) + 2N2(g) d. Ag + (aq) + I(aq) → AgI(s)
Give the expression for K for each of the following reactions.a.b. c.
The following reaction is spontaneous in the direction given.A(g) + B(g)→ C(g) + D(g)Suppose you are given a vessel containing an equilibrium mixture of A, B, C, and D, and you increase the concentration of C by increasing its partial pressure.a. How is the value of ∆Go affected by the addition
Consider the decomposition of dinitrogen tetroxide, N2O4, to nitrogen dioxide, NO2: N2O4(g) → 2NO2(g) How would you expect the spontaneity of the reaction to behave with temperature change?
What is a spontaneous process? Give three examples of spontaneous processes. Give three examples of nonspontaneous processes.
The reactionC6H6(l) + Br2(l) → C6H5Br(l) + HBr(g)the products have a lower energy than the reactants.a. Predict the sign of the entropy change for this reaction. Explain.b. Predict whether reactants or products would predominate in an equilibrium mixture. Why?c. How can you account for the fact
When 1.000 g of gaseous butane, C4H10, is burned at 25oC and 1.00 atm pressure, H2O(l) and CO2(g) are formed with the evolution of 49.50 kJ of heat.a. Calculate the molar enthalpy of formation of butane. (Use enthalpy of formation data for H2O and CO2.)b. ∆Gof of butane is 17.2 kJ/mol. What is
When 1.000 g of ethylene glycol, C2H6O2, is burned at 25oC and 1.00 atmosphere pressure, H2O(l) and CO2(g) are formed with the evolution of 19.18 kJ of heat.a. Calculate the molar enthalpy of formation of ethylene glycol. (It will be necessary to use data from Appendix C.)b. ∆Gof of ethylene
a. Calculate K1 at 25C for phosphoric acid:b. Which thermodynamic factor is the most significant in accounting for the fact that phosphoric acid is a weak acid? Why?
a. Calculate K1 at 25oC for sulfurous acid:b. Which thermodynamic factor is the most significant in accounting for the fact that phosphoric acid is a weak acid? Why?
The direct reaction of iron(III) oxide, Fe2O3, to give iron and oxygen gas is a nonspontaneous reaction; normally, iron combines with oxygen to give rust (the oxide). Yet we do change iron(III) oxide, as iron ore, into iron metal. How is this possible? Explain.
Adenosine triphosphate (ATP) is often referred to as a biological €œenergy€ source. What does this mean? Explain how ATP is used in biological organisms to produce proteins from amino acids.
Consider the reaction in which hydrazine vapor decomposes to its elements:Use data from Appendix C to answer the following questions. a. What is the standard enthalpy change for this reaction at 25oC? b. Calculate the standard entropy change at 25oC. Does the sign of the entropy change agree with
Consider the reaction for the formation of H2O(g) from its elements. Use the data in Appendix C to answer the following questions. a. What is the standard enthalpy of formation of H2O(g) at 25oC? b. What is the standard entropy of formation of H2O(g) at 25oC? c. Use these values to calculate the
Acetone, CH3COCH3, is a fragrant liquid that is used as a solvent for lacquers, paint removers, and nail polish remover. It burns in oxygen to give carbon dioxide and water: CH3COCH3(l) + 4O2(g) →3CO2(g) + 3H2O(l) If the standard free-energy change for this reaction is 1739 kJ/mol, what is the
Give an example of a chemical reaction used to obtain useful work.
Cobalt chloride hexahydrate, CoCl2 6H2O, is a bright pink compound, but in the presence of very dry air it loses water vapor to the air to produce the light blue anhydrous salt CoCl2. Calculate the standard free-energy change for the reaction at 25oC:Here are some thermodynamic data at 25oC: What
An experimenter placed 1.000 mol of H2 and 1.000 mol of I2 in a 1.000-L flask. The substances reacted to produce hydrogen iodide:When the contents of the flask came to equilibrium at 458oC, the experimenter found that it contained 0.225 mol H2, 0.225 mol I2, and 1.550 mol HI. a. Calculate the
Hydrogen gas and iodine vapor react to produce hydrogen iodide gas:Calculate the free-energy change ˆ†G for the following two conditions, at 25oC. Which one is closer to equilibrium? Explain. a. The partial pressures of H2(g), I2(g), and HI(g) are each 1/3 atm. b. The partial pressures of
Silver carbonate, Ag2CO3, is a light yellow compound that decomposes when heated to give silver oxide and carbon dioxide:A researcher measured the partial pressure of carbon dioxide over a sample of silver carbonate at 220oC and found that it was 1.37 atm. Calculate the partial pressure of
Sulfur is produced in volcanic gases by the reaction of hydrogen sulfide with sulfur dioxide:A particular sample of volcanic gas at 1.00 atm has a partial pressure of sulfur dioxide of 89 mmHg. If this gas at 1170oC also contains hydrogen sulfide and water vapor in equilibrium with rhombic sulfur,
Adenosine triphosphate, ATP, is used as a free-energy source by biological cells. (See the essay on page 750.) ATP hydrolyzes in the presence of enzymes to give ADP: ATP(aq) + H2O(l) → ADP(aq) + H2PO4 (aq); ∆Go 30.5 kJ/mol at 25oC Consider a hypothetical biochemical reaction of molecule A to
A car has been fitted with an internal combustion engine that uses propane as a fuel. C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g) What is the maximum work that you can obtain from 1.00 kg of propane, C3H8? Suppose the car is driving uphill. What is the maximum height, in miles, that the car could go to,
Hydrogen bromide dissociates into its gaseous elements, H2 and Br2, at elevated temperatures. Calculate the percent dissociation at 375oC and 1.00 atm. What would be the percent dissociation at 375oC and 10.0 atm? Use data from Appendix C and any reasonable approximation to obtain K.
Hydrogen gas and iodine gas react to form hydrogen iodide. If 0.500 mol H2 and 1.00 mol I2 are placed in a closed 10.0-L vessel, what is the mole fraction of HI in the mixture when equilibrium is reached at 205oC? Use data from Appendix C and any reasonable approximations to obtain K.
A 20.0-L vessel is filled with 1.00 mol of ammonia, NH3. What percent of ammonia dissociates to the elements if equilibrium is reached at 345oC? Use data from Appendix C and make any reasonable approximation to obtain K.
How is the concept of coupling of reactions useful in explaining how a nonspontaneous change could be made to occur?
A 25.0-L vessel is filled with 0.0100 mol CO and 0.0300 mol H2. How many moles of CH4 and how many moles of H2O are produced when equilibrium is reached at 785oC? Use data from Appendix C and make any reasonable approximation to obtain K.
Ka for acetic acid at 25.0oC is 1.754 × 105. At 50.0oC, Ka is 1.633 × 105. What are ∆Ho and ∆So for the ionization of acetic acid?
Ksp for silver chloride at 25.0oC is 1.782 × 1010. At 35.0oC, Ksp is 4.159 × 1010. What are ∆Ho and ∆So for the reaction?
Explain how the free energy changes as a spontaneous reaction occurs. Show by means of a diagram how G changes with the extent of reaction.
Explain how an equilibrium constant can be obtained from thermal data alone (that is, from measurements of heat only).
Discuss the different sign combinations of ∆Ho and ∆So that are possible for a process carried out at constant temperature and pressure. For each combination, state whether the process must be spontaneous or not, or whether both situations are possible. Explain.
Consider a reaction in which ∆Ho and ∆So are positive. Suppose the reaction is nonspontaneous at room temperature. How would you estimate the temperature at which the reaction becomes spontaneous?
Thermodynamics and Spontaneous Processes Consider a sample of water at 25oC in a beaker in a room at 50oC.a. What change do you expect to observe in the water sample? Would this be a spontaneous process or not?b. What are the enthalpy and entropy changes for this change in the water sample? (Just
You place the substance A(g) in a container. Consider the following reaction under standard conditions to produce the substance B(g):For this reaction as written, the equilibrium constant is a very large, positive number.a. When A(g) reacts to give B(g), does the standard free energy (Go) of the
For each of the following statements, indicate whether it is true or false. a. A spontaneous reaction always releases heat. b. A spontaneous reaction is always a fast reaction. c. The entropy of a system always increases for a spontaneous change. d. The entropy of a system and its surroundings
Which of the following are spontaneous processes? a. A cube of sugar dissolves in a cup of hot tea. b. A rusty crowbar turns shiny. c. Butane from a lighter burns in air. d. A clock pendulum, initially stopped, begins swinging. e. Hydrogen and oxygen gases bubble out from a glass of pure water.
For each of the following series of pairs, indicate which one of the pair has the greater quantity of entropy.a. 1.0 mol of carbon dioxide gas at 20oC, 1 atm, or 2.0 mol of carbon dioxide gas at 20oC, 1 atmb. 1.0 mol of butane liquid at 20oC, 10 atm, or 1.0 mol of butane gas at 20oC, 10 atmc. 1.0
Predict the sign of the entropy change for each of the following processes. a. A drop of food coloring diffuses throughout a glass of water. b. A tree leafs out in the spring. c. Flowers wilt and stems decompose in the fall. d. A lake freezes over in the winter. e. Rainwater on the pavement
Hypothetical elements A(g) and B(g) are introduced into a container and allowed to react according to the reaction A(g) 2B(g) ±£ AB2(g). The container depicts the reaction mixture after equilibrium has been attained.a. Is the value of ˆ†S for the reaction positive, negative, or zero?b. Is the
Here is a simple experiment. Take a rubber band and stretch it. (Is this a spontaneous process? How does the Gibbs free energy change?) Place the rubber band against your lips; note how warm the rubber band has become. (How does the enthalpy change?) According to polymer chemists, the rubber band
Hypothetical elements X(g) and Y(g) are introduced into a container and allowed to react according to the reaction: X(g) Y(g) ±£ XY(g). The container depicts the reaction mixture after equilibrium has been attained.Next, the volume of the container is doubled by rapidly moving the plunger
State the second law of thermodynamics.
Describe how you would expect the spontaneity (G) for each of the following reactions to behave with a change of temperature.temperature.a. Phosgene, COCl2, the starting material for the preparation of polyurethane plastics, decomposes as follows: COCl2(g) → CO(g) + Cl2(g)b. Chlorine adds to
A gas is cooled and loses 82 J of heat. The gas contracts as it cools, and work done on the system equal to 29 J is exchanged with the surroundings. What are q, w, and ∆U?
An ideal gas is cooled isothermally (at constant temperature). The internal energy of an ideal gas remains constant during an isothermal change. If q is 76 J, what are ∆U and w?
What is ∆U when 1.00 mol of liquid water vaporizes at 100oC? The heat of vaporization, Hovap, of water at 100oC is 40.66 kJ/mol.
What is ∆U for the following reaction at 25oC? 2H2(g) + O2(g) → 2H2O(l)
Chloroform, CHCl3, is a solvent and has been used as an anesthetic. The heat of vaporization of chloroform at its boilingpoint (61.2oC) is 29.6 kJ/mol. What is the entropy change when 1.20 mol CHCl3 vaporizes at its boiling point?
Diethyl ether (known simply as ether), (C2H5)2O, is a solvent and anesthetic. The heat of vaporization of diethyl ether at its boiling point (35.6oC) is 26.7kJ/mol. What is the entropy change when 1.34 mol (C2H5)2O vaporizes at its boiling point?
The enthalpy change when liquid methanol, CH3OH, vaporizes at 25oC is 38.0 kJ/mol. What is the entropy change when 1.00 mol of vapor in equilibrium with liquid condenses to liquid at 25oC? The entropy of this vapor at 25oC is 255 J/(mol•K). What is the entropy of the liquid at this temperature?
The heat of vaporization of carbon disulfide, CS2, at 25oC is 27.2 kJ/mol. What is the entropy change when 1.00 mol of vapor in equilibrium with liquid condenses to liquid at 25oC? The entropy of this vapor at 25oC is 243 J/(mol • K). What is the entropy of the liquid at this temperature?
Predict the sign of S, if possible, for each of the following reactions. If you cannot predict the sign for any reaction, state why.a. C2H2(g) + 2H2(g) → C2H6(g)b. N2(g) + O2(g) → 2NO(g)c. 2C2H2(g) + 3O2(g) → 4CO(g) 2H2O(g)d. 2C(s) + O2(g) → 2CO(g)
The entropy change ∆S for a phase transition equals ∆H/T, where ∆H is the enthalpy change. Why is it that the entropy change for a system in which a chemical reaction occurs spontaneously does not equal ∆H/T?
Predict the sign of ∆So, if possible, for each of the following reactions. If you cannot predict the sign for any reaction, state why.a. N2H4(l) → N2(g) + 2H2O(g)b. C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l)c. P4(s) + 5O2(g) P4O10(s)d. 2NaHCO3(s) → Na2CO3(s) + H2O(g) + CO2(g)

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