Although we often assume that the heat capacity of a

What if DSuniv was a state function? How would the world be different?

You have an ideal gas in a container fitted with a frictionless, massless piston. What if you add a weight to the top of the piston? We would expect the gas to be compressed at constant temperature. For these to be true, DS would be negative (since the gas is compressed), and DH would be zero (since the process is at constant temperature). This would make DG positive. Does this mean the isothermal compression of the gas is not spontaneous? Defend your answer.

What if the first law of thermodynamics was true but the second law was not? How would the world be different?

For the process A(l) n A(g), which direction is favored by changes in energy probability? Positional probability? Explain your answer. If you wanted to favor the process as written, would you raise or lower the temperature of the system? Explain.

For a liquid, which would you expect to be larger: DSfusion or DSevaporation? Why?

Gas A2 reacts with gas B2 to form gas AB at constant temperature. The bond energy of AB is much greater than that of either reactant. What can be said about the sign of DH? DSsurr? DS? Explain how potential energy changes for this process. Explain how random kinetic energy changes during the process.

What types of experiments can be carried out to determine if a reaction is spontaneous? Does spontaneity have any relationship to the final equilibrium position of a reaction? Explain.

A friend tells you Free energy G and pressure P are directly related by the equation G 5 G8 1 RT ln(P). Also, G is related to the equilibrium constant K in that when Gproducts 5 Greactants, the system is at equilibrium. Therefore it must be true that a system is at equilibrium when all pressures are equal. Do you agree with this friend? Explain.

You remember that DG8 is related to RT ln(K) but cant remember if it is RT ln(K) or 2RT ln(K). Realizing what DG8 and K mean, how can you figure out the correct sign?

Predict the sign of DS for each of the following and explain. a. the evaporation of alcohol b. the freezing of water c. compressing an ideal gas at constant temperature d. heating an ideal gas at constant pressure e. dissolving NaCl in water

Which is larger: DS at constant pressure or DS at constant volume? Provide a conceptual rationale.

Is DSsurr favorable or unfavorable for exothermic reactions? endothermic reactions? Explain

At 1 atm, liquid water is heated above 1008C. For this process which of the following choices (iiv) is correct for DSsurr? DS? DSuniv? Explain each answer. i. greater than zero ii. less than zero iii. equal to zero iv. cannot be determined

High temperatures are favorable to a reaction kinetically but may be unfavorable to a reaction thermodynamically. Explain.

Define the following. a. spontaneous process d. system b. entropy e. surroundings c. positional probability f. universe

Table 10.2 shows the possible arrangements of four molecules in a two-bulbed flask. What are the possible arrangements if there is one molecule in this two-bulbed flask or two molecules or three molecules? For each, what arrangement is most likely?

Consider the following illustration of six molecules of gas in a two-bulbed flask a. What is the most likely arrangement of molecules? How many microstates are there for this arrangement? b. Determine the probability of finding the gas in its most likely arrangement.

Consider the following energy levels, each capable of holding two objects: E = 2 kJ E E = 1 kJ E = 0 XX Draw all the possible arrangements of the two identical particles (represented by X) in the three energy levels. What total energy is most likely, that is, occurs the greatest number of times? Assume that the particles are indistinguishable from each other.

Do Exercise 15 with two particles A and B that can be distinguished from each other

Which of the following processes require energy as they occur? a. Salt dissolves in H2O. b. A clear solution becomes a uniform color after a few drops of dye are added. c. A cell produces proteins from amino acids. d. Iron rusts. e. A house is built. f. A satellite is launched into orbit. g. A satellite falls back to earth.

Which of the following involve an increase in the entropy of the system under consideration? a. melting of a solid e. mixing b. evaporation of a liquid f. separation c. sublimation g. diffusion d. freezing

Describe how the following changes affect the positional probability of a substance. a. increase in volume of a gas at constant T b. increase in temperature of a gas at constant V c. increase in pressure of a gas at constant T

Choose the substance with the larger positional probability in each case. a. 1 mole of H2 (at STP) or 1 mole of H2 (at 1008C, 0.5 atm) b. 1 mole of N2 (at STP) or 1 mole of N2 (at 100 K, 2.0 atm) c. 1 mole of H2O(s) (at 08C) or 1 mole of H2O(l) (at 208C)

In the roll of two dice, what total number is the most likely to occur? Is there an energy reason why this number is favored? Would energy have to be spent to increase the probability of getting a particular number (that is, to cheat)?

Entropy can be calculated by a relationship proposed by Ludwig Boltzmann: S 5 kB ln V where kB 5 1.38 3 10223 J/K and V is the number of ways a particular state can be obtained. (This equation is engraved on Boltzmanns tombstone.) Calculate S for the three arrangements of particles in Table 10.2.

Calculate the energy required to change the temperature of 1.00 kg of ethane (C2H6) from 25.08C to 73.48C in a rigid vessel. (Cv for C2H6 is 44.60 J K21 mol21.) Calculate the energy required for this same temperature change at constant pressure. Calculate the change in internal energy of the gas in each of these processes.

For nitrogen gas the values of Cv and Cp at 258C are 20.8 J K21 mol21 and 29.1 J K21 mol21, respectively. When a sample of nitrogen is heated at constant pressure, what fraction of the energy is used to increase the internal energy of the gas? How is the remainder of the energy used? How much energy is required to raise the temperature of 100.0 g N2 from 25.08C to 85.08C in a vessel having a constant volume?

Consider a rigid, insulated box containing 0.400 mole of He(g) at 20.08C and 1.00 atm in one compartment and 0.600 mole of N2(g) at 100.08C and 2.00 atm in the other compartment. These compartments are connected by a partition that transmits heat. What is the final temperature in the box at thermal equilibrium? [For He(g), Cv 5 12.5 J K21 mol21; for N2(g), Cv 5 20.7 J K21 mol21.]

One mole of an ideal gas is contained in a cylinder with a movable piston. The temperature is constant at 778C. Weights are removed suddenly from the piston to give the following sequence of three pressures: a. P1 5 5.00 atm (initial state) b. P2 5 2.24 atm c. P3 5 1.00 atm (final state) What is the total work (in joules) in going from the initial to the final state by way of the preceding two steps? What would be the total work if the process were carried out reversibly?

One mole of an ideal gas with a volume of 1.0 L and a pressure of 5.0 atm is allowed to expand isothermally into an evacuated bulb to give a total volume of 2.0 L. Calculate w and q. Also calculate qrev for this change of state.

A cylinder with an initial volume of 10.0 L is fitted with a frictionless piston and is filled with 1.00 mole of an ideal gas at 258C. Assume that the surroundings are large enough so that if heat is withdrawn from or added to it, the temperature does not change. a. The gas expands isothermally and reversibly from 10.0 L to 20.0 L. Calculate the work and the heat. b. The gas expands isothermally and irreversibly from 10.0 L to 20.0 L as the external pressure changes instantaneously from 2.46 atm to 1.23 atm. Calculate the work and the heat.

The molar heat capacities for carbon dioxide at 298.0 K are Cv 5 28.95 J K21 mol21 Cp 5 37.27 J K21 mol21 The molar entropy of carbon dioxide gas at 298.0 K and 1.000 atm is 213.64 J K21 mol21. a. Calculate the energy required to change the temperature of 1.000 mole of carbon dioxide gas from 298.0 K to 350.0 K, both at constant volume and at constant pressure. b. Calculate the molar entropy of CO2(g) at 350.0 K and 1.000 atm. c. Calculate the molar entropy of CO2(g) at 350.0 K and 1.174 atm

The molar entropy of helium gas at 258C and 1.00 atm is 126.1 J K21 mol21. Assuming ideal behavior, calculate the entropy of the following. a. 0.100 mole of He(g) at 258C and a volume of 5.00 L b. 3.00 moles of He(g) at 258C and a volume of 3000.0 L

Consider the process A(l) 88n A(g) 758C 1558C which is carried out at constant pressure. The total DS for this process is known to be 75.0 J K21 mol21. For A(l) and A(g), the Cp values are 75.0 J K21 mol21 and 29.0 J K21 mol21, respectively, and are not dependent on temperature. Calculate DHvaporization for A(l) at 1258C (its boiling point).

A sample of ice weighing 18.02 g, initially at 230.08C, is heated to 140.08C at a constant pressure of 1.00 atm. Calculate q, w, DE, DH, and DS for this process. The molar heat capacities (Cp) for solid, liquid, and gaseous water37.5 J K21 mol21, 75.3 J K21 mol21, and 36.4 J K21 mol21, respectivelyare assumed to be temperature-independent. The enthalpies of fusion and vaporization are 6.01 kJ/mol and 40.7 kJ/mol, respectively. Assume ideal gas behavior

Calculate the entropy change for a process in which 3.00 moles of liquid water at 08C is mixed with 1.00 mole of water at 100.8C in a perfectly insulated container. (Assume that the molar heat capacity of water is constant at 75.3 J K21 mol21.)

Entropy has been described as “time’s arrow.” Interpret this view of entropy.

The synthesis of glucose directly from CO2 and H2O and the synthesis of proteins directly from amino acids are both nonspontaneous processes under standard conditions. Yet these processes must occur for life to exist. In light of the second law of thermodynamics, how can life exist

A green plant synthesizes glucose by photosynthesis as shown in the reaction 6CO2(g) 1 6H2O(l) 88n C6H12O6(s) 1 6O2(g) Animals use glucose as a source of energy: C6H12O6(s) 1 6O2(g) 88n 6CO2(g) 1 6H2O(l) If we were to assume that both of these processes occur to the same extent in a cyclic process, what thermodynamic property must have a nonzero value?

Entropy has been described as times arrow. Interpret this view of entropy.

For a gas phase reaction, what do you concentrate on to predict the sign of DS? For a phase change, what do you concentrate on to predict the sign of DS? That is, how are S8solid, S8liquid, and S8gas related to one another? When a solute dissolves in water, what is usually the sign of DS for this process?

What determines DSsurr for a process? To calculate DSsurr at constant pressure and temperature, we use the following equation: DSsurr 5 2DH/T. Why does a minus sign appear in the equation, and why is DSsurr inversely proportional to temperature?

Predict the sign of DSsurr for the following processes. a. H2O(l) 88n H2O(g) b. I2(g) 88n I2(s)

Calculate DSsurr for the following reactions at 258C and 1 atm. a. C3H8(g) 1 5O2(g) 88n 3CO2(g) 1 4H2O(l) DH8 5 22221 kJ b. 2NO2(g) 88n 2NO(g) 1 O2(g) DH8 5 112 kJ

For each of the following pairs of substances, which substance has the greater value of S8 at 258C and 1 atm? a. Cgraphite(s) or Cdiamond(s) b. C2H5OH(l) or C2H5OH(g) c. CO2(s) or CO2(g) d. N2O(g) or He(g) e. HF(g) or HCl(g)

Predict the sign of DS8 for each of the following changes. a. b. AgCl(s) 88n Ag1(aq) 1 Cl2(aq) c. 2H2(g) 1 O2(g) 88n 2H2O(l) d. Na(s) 1 1 2Cl2(g) 88n NaCl(s) e. HCl(g) 88n H1(aq) 1 Cl2(aq) f. KBr(s) 88n K1(aq) 1 Br2(aq)

Predict the sign of DS8 and then calculate DS8 for each of the following reactions. a. 2H2S(g) 1 SO2(g) 88n 3Srhombic(s) 1 2H2O(g) b. 2SO3(g) 88n 2SO2(g) 1 O2(g) c. Fe2O3(s) 1 3H2(g) 88n 2Fe(s) 1 3H2O(g)

Predict the sign of DS8 and then calculate DS8 for each of the following reactions. a. H2 1g2 1 1 2O2 1g2 h H2O1l2 b. 2CH3OH1g2 1 3O2 1g2 h 2CO2 1g2 1 4H2O1g2 c. HCl1g2 h H1 1aq2 1 Cl2 1aq2

For the reaction CS2 1g2 1 3O2 1g2 h CO2 1g2 1 2SO2 1g2 DS8 is equal to 2143 J/K. Use this value and data from Appendix 4 to calculate the value of S8 for CS2(g).

For the reaction C2H2(g) 1 4F2(g) 88n 2CF4(g) 1 H2(g) DS8 is equal to 2358 J/K. Use this value and data from Appendix 4 to calculate the value of S8 for CF4(g).

Ethanethiol (C2H5SH; also called ethyl mercaptan) is commonly added to natural gas to provide the rotten egg smell of a gas leak. The boiling point of ethanethiol is 35C and its heat of vaporization is 27.5 kJ/mol. What is the entropy of vaporization for this substance?

For mercury at 1 atm, the enthalpy of vaporization is 58.51 kJ/mol and the entropy of vaporization is 92.92 J K21 mol21. What is the boiling point of mercury?

The enthalpy of vaporization of ethanol is 38.7 kJ/mol at its boiling point (788C). Determine DSsys, DSsurr, and DSuniv when 1.00 mole of ethanol is vaporized at 788C and 1.00 atm.

For ammonia (NH3) the enthalpy of fusion is 5.65 kJ/mol, and the entropy of fusion is 28.9 J K21 mol21. a. Will NH3(s) spontaneously melt at 200. K? b. What is the approximate melting point of ammonia?

It is quite common for a solid to change from one structure to another at a temperature below its melting point. For example, sulfur undergoes a phase change from the rhombic crystal structure to the monoclinic crystal form at temperatures above 958C. a. Predict the signs of DH and DS for the process Srhombic 88n Smonoclinic. b. Which form of sulfur has the more ordered crystalline structure (has the smaller positional probability)?

As O2(l) is cooled at 1 atm, it freezes at 54.5 K to form solid I. At a lower temperature, solid I rearranges to solid II, which has a different crystal structure. Thermal measurements show that DH for the I 88n II phase transition is 2743.1 J/mol, and DS for the same transition is 217.0 J K21 mol21. At what temperature are solids I and II in equilibrium?

From data in Appendix 4, calculate DH8, DS8, and DG8 for each of the following reactions at 258C. a. CH4(g) 1 2O2(g) 88n CO2(g) 1 2H2O(g) b. 6CO2(g) 1 6H2O(l) 88n C6H12O6(s) 1 6O2(g) Glucose c. P4O10(s) 1 6H2O(l) 88n 4H3PO4(s) d. HCl(g) 1 NH3(g) 88n NH4Cl(s)

The value of DG8 for the reaction 2C4H10(g) 1 13O2(g) 88n 8CO2(g) 1 10H2O(l) is 25490. kJ. Use this value and data from Appendix 4 to calculate the standard free energy of formation for C4H10(g).

Of the functions DH8, DS8, and DG8, which depends most strongly on temperature? When DG8 is calculated at temperatures other than 258C, what assumptions are generally made concerning DH8 and DS8?

For the reaction at 298 K, 2NO2(g) 34 N2O4(g) the values of DH8 and DS8 are 258.03 kJ and 2176.6 J/K, respectively. What is the value of DG8 at 298 K? Assuming that DH8 and DS8 do not depend on temperature, at what temperature is DG8 5 0? Is DG8 negative above or below this temperature?

Consider the reaction Fe2O3 1s2 1 3H2 1g2 h 2Fe1s2 1 3H2O1g2 a. Use DG8f values in Appendix 4 to calculate DG8 for this reaction. b. Is this reaction spontaneous under standard conditions at 298 K? c. The value of DH8 for this reaction is 100. kJ. At what temperatures is this reaction spontaneous at standard conditions? Assume that DH8 and DS8 do not depend on temperature.

Consider the reaction 2POCl3(g) 88n 2PCl3(g) 1 O2(g) a. Calculate DG8 for this reaction. The DG8f values for POCl3(g) and PCl3(g) are 2502 kJ/mol and 2270. kJ/mol, respectively. b. Is this reaction spontaneous under standard conditions at 298 K? c. The value of DS8 for this reaction is 179 J/K. At what temperatures is this reaction spontaneous at standard conditions? Assume that DH8 and DS8 do not depend on temperature.

Consider two reactions for the production of ethanol: C2H4(g) 1 H2O(g) 88n CH3CH2OH(l) C2H6(g) 1 H2O(g) 88n CH3CH2OH(l) 1 H2(g) Which would be more thermodynamically feasible? Why? Assume standard conditions and assume that DH8 and DS8 are temperature-independent.

Using data from Appendix 4, calculate DH8, DS8, and DG8 for the following reactions that produce acetic acid: CH4(g) C + O2(g) CH3C OH( O l) B O CH3OH(g) CO( + g) CH3C OH( O l) B O Which reaction would you choose as a commercial method for producing acetic acid (CH3CO2H)? What temperature conditions would you choose for the reaction? Assume standard conditions and assume that DH8 and DS8 are temperature-independent.

Given the following data: 2C6H6(l) 1 15O2(g) 88n 12CO2(g) 1 6H2O(l) DG8 5 26399 kJ C(s) 1 O2(g) 88n CO2(g) DG8 5 2394 kJ H2(g) 1 1 2O2(g) 88n H2O(l) DG8 5 2237 kJ calculate DG8 for the reaction 6C(s) 1 3H2(g) 88n C6H6(l)

When most biological enzymes are heated, they lose their catalytic activity. The change Original enzyme 88n new form that occurs upon heating is endothermic and spontaneous. Is the structure of the original enzyme or its new form more ordered (has the smaller positional probability)? Explain your answer

For the reaction 2O(g) 88n O2(g) a. predict the signs of DH and DS. b. would the reaction be more spontaneous at high or low temperatures?

Hydrogen cyanide is produced industrially by the following exothermic reaction: 2HCN(g) + 6H2O(g) 1000C Pt-Rh 2NH3(g) + + 3O2(g) 2CH4(g) Is the high temperature needed for thermodynamic or for kinetic reasons?

A reaction at constant T and P is spontaneous as long as DG is negative; that is, reactions always proceed as long as the products have a lower free energy than the reactants. What is so special about equilibrium? Why dont reactions move away from equilibrium?

DG predicts spontaneity for a reaction at constant T and P, whereas DG8 predicts the equilibrium position. Explain what this statement means.

Using thermodynamic data from Appendix 4, calculate DG8 at 258C for the process 2SO2(g) 1 O2(g) 88n 2SO3(g) where all gases are at 1.00 atm pressure. Also calculate DG8 at 258C for this same reaction but with all gases at 10.0 atm pressure

Consider the reaction 2NO2(g) 34 N2O4(g) For each of the following mixtures of reactants and products at 258C, predict the direction in which the reaction will shift to reach equilibrium. Use thermodynamic data in Appendix 4. a. PNO2 5 PN2O4 5 1.0 atm b. PNO2 5 0.21 atm, PN2O4 5 0.50 atm c. PNO2 5 0.29 atm, PN2O4 5 1.6 atm

Using data from Appendix 4, calculate DG for the reaction 2H2S(g) 1 SO2(g) 34 3S(s) 1 2H2O(g) for the following conditions at 258C: PH2S 5 1.0 3 1024 atm PSO2 5 1.0 3 1022 atm PH2O 5 3.0 3 1022 atm

Using data from Appendix 4, calculate DH8, DS8, and K (at 298 K) for the synthesis of ammonia by the Haber process: N2(g) 1 3H2(g) 34 2NH3(g) Calculate DG for this reaction under the following conditions (assume an uncertainty of 61 in all quantities): a. T 5 298 K, PN2 5 PH2 5 200 atm, PNH3 5 50 atm b. T 5 298 K, PN2 5 200 atm, PH2 5 600 atm, PNH3 5 200 atm c. T 5 100 K, PN2 5 50 atm, PH2 5 200 atm, PNH3 5 10 atm d. T 5 700 K, PN2 5 50 atm, PH2 5 200 atm, PNH3 5 10 atm Assume that DH8 and DS8 do not depend on temperature

One of the reactions that destroys ozone in the upper atmosphere is NO(g) 1 O3(g) 34 NO2(g) 1 O2(g) Using data from Appendix 4, calculate DG8 and K (at 298 K) for this reaction.

Hydrogen sulfide can be removed from natural gas by the reaction 2H2S(g) 1 SO2(g) 34 3S(s) 1 2H2O(g) Calculate DG8 and K (at 298 K) for this reaction. Would this reaction be favored at a high or low temperature?

Consider the autoionization of water at 258C: H2O(l) 34 H1(aq) 1 OH2(aq) Kw 5 1.00 3 10214 a. Calculate DG8 for this process at 258C. b. At 40.8C, Kw 5 2.92 3 10214. Calculate DG8 at 40.8C.

How can one estimate the value of K at temperatures other than 258C for a reaction? How can one estimate the temperature where K 5 1 for a reaction? Do all reactions have a specific temperature where K 5 1?

The standard free energies of formation and the standard enthalpies of formation at 298 K for difluoroacetylene (C2F2) and hexafluorobenzene (C6F6) are DG8f (kJ/mol) DH8f (kJ/mol) C2F2(g) 191.2 241.3 C6F6(g) 78.2 132.8 For the following reaction: C6F6(g) 34 3C2F2(g) a. calculate DS8 at 298 K. b. calculate K at 298 K. c. estimate K at 3000. K, assuming DH8 and DS8 do not depend on temperature.

Consider the reaction Fe2O3(s) 1 3H2(g) 88n 2Fe(s) 1 3H2O(g) Assuming DH8 and DS8 do not depend on temperature, calculate the temperature where K 5 1.00 for this reaction

The Ostwald process for the commercial production of nitric acid involves three steps: 4NH3(g) 1 5O2(g) 88888n 4NO(g) 1 6H2O(g) 2NO(g) 1 O2(g) 88888n 2NO2(g) 3NO2(g) 1 H2O(l) 88888n 2HNO3(l) 1 NO(g) a. Calculate DH8, DS8, DG8, and K (at 298 K) for each of the three steps in the Ostwald process (see Appendix 4). b. Calculate the equilibrium constant for the first step at 8258C. Assume that DH8 and DS8 are temperature-independent. c. Is there a thermodynamic reason for the high temperature in the first step assuming standard conditions?

Consider the following reaction at 800. K: N2(g) 1 3F2(g) 88n 2NF3(g) An equilibrium mixture contains the following partial pressures: PN2 5 0.021 atm, PF2 5 0.063 atm, and PNF3 5 0.48 atm. Calculate DG8 for the reaction at 800. K.

Consider the following reaction at 298 K: 2SO2(g) 1 O2(g) 88n 2SO3(g) An equilibrium mixture contains O2(g) and SO3(g) at partial pressures of 0.50 atm and 2.0 atm, respectively. Using data from Appendix 4, determine the equilibrium partial pressure of SO2 in the mixture. Will this reaction be most favored at a high or a low temperature, assuming standard conditions?

For the reaction A(g) 1 2B(g) 34 C(g) the initial partial pressures of gases A, B, and C are all 0.100 atm. Once equilibrium has been established, it is found that [C] 5 0.040 atm. What is DG8 for this reaction at 258C?

Consider the following diagram of free energy (G) versus fraction of A reacted in terms of moles for the reaction 2A(g) 8n B(g). 0 0.33 0.67 Fraction of A reacted 1.00 G Before any A has reacted, PA 5 3.0 atm and PB 5 0. Determine the sign of DG8 and the value of K for this reaction.

Calculate DG8 for H2O(g) 1 1 2O2(g) 34 H2O2(g) at 600. K, using the following data: H2(g) 1 O2(g) 34 H2O2(g) K 5 2.3 3 106 at 600. K 2H2(g) 1 O2(g) 34 2H2O(g) K 5 1.8 3 1037 at 600. K

Cells use the hydrolysis of adenosine triphosphate, abbreviated ATP, as a source of energy. Symbolically, this reaction can be represented as ATP(aq) 1 H2O(l) 88n ADP(aq) 1 H2PO4 2(aq) where ADP represents adenosine diphosphate. For this reaction DG8 5 230.5 kJ/mol. a. Calculate K at 258C. b. If all the free energy from the metabolism of glucose C6H12O6(s) 1 6O2(g) 88n 6CO2(g) 1 6H2O(l) goes into the production of ATP, how many ATP molecules can be produced for every molecule of glucose?

Carbon monoxide is toxic because it bonds much more strongly to the iron in hemoglobin (Hgb) than does O2. Consider the following reactions and approximate standard free energy changes: Hgb 1 O2 88n HgbO2 DG8 5 270 kJ Hgb 1 CO 88n HgbCO DG8 5 280 kJ Using these data, estimate the equilibrium constant value at 258C for the following reaction: HgbO2 1 CO 34 HgbCO 1 O2

One reaction that occurs in human metabolism is + B O H2NCCH2CH2CHCO2H(aq) NH2 H2O(l) A Glutamine HO2CCH2CH2CHCO2H(aq) N + H3(aq) NH2 A Glutamic acid For this reaction DG8 5 14 kJ at 258C. a. Calculate K for this reaction at 258C. b. In a living cell this reaction is coupled with the hydrolysis of ATP. (See Exercise 84.) Calculate DG8 and K at 258C for the following reaction: Glutamic acid(aq) 1 ATP(aq) 1 NH3(aq) 34 Glutamine(aq) 1 ADP(aq) 1 H2PO4 2(aq)

At 25.08C, for the reaction 2NO2(g) 34 N2O4(g) the values of DH8 and DS8 are 258.03 kJ/mol and 2176.6 J K21 mol21, respectively. Calculate the value of K at 25.08C. Assuming DH8 and DS8 are temperatureindependent, estimate the value of K at 100.08C.

Consider the relationship ln1K2 5 2DH RT 1 DS R The equilibrium constant for some hypothetical process was determined as a function of temperature (in kelvins) with the results plotted below. 1000 T(K) ln ( K) 10. 1.0 2.0 3.0 20. 30. 40. From the plot, determine the values of DH8 and DS8 for this process. What would be the major difference in the ln(K) versus 1/T plot for an endothermic process as compared to an exothermic process?

a. Use the equation in Exercise 88 to determine DH8 and DS8 for the autoionization of water: H2O(l) 34 H1(aq) 1 OH2(aq) T (8C) K 0 1.14 3 10215 25 1.00 3 10214 35 2.09 3 10214 40. 2.92 3 10214 50. 5.47 3 10214 b. Estimate the value of DG8 for the autoionization of water at its critical temperature, 3748C.

The equilibrium constant K for the reaction 2Cl(g) 34 Cl2(g) was measured as a function of temperature (in kelvins). A graph of ln(K) versus 1/T for this reaction gives a straight line with a slope of 1.352 3 104 K and a y intercept of 214.51. Determine the values of DH8 and DS8 for this reaction. (See Exercise 88.

The equilibrium constant for a certain reaction decreases from 8.84 to 3.25 3 1022 when the temperature increases from 258C to 758C. Estimate the temperature where K 5 1.00 for this reaction. Estimate the value of DS8 for this reaction. (Hint: Manipulate the equation given in Exercise 88.)

A sample of a monatomic ideal gas at 1.00 atm and 258C expands adiabatically and reversibly from 5.00 L to 12.5 L. Calculate the final temperature and pressure of the gas, the work associated with this process, and the change in internal energy

A sample of 1.75 moles of H2 (Cv 5 20.5 J K21 mol21) at 218C and 1.50 atm undergoes a reversible adiabatic compression until the final pressure is 4.50 atm. Calculate the final volume of the gas sample and the work associated with this process. Assume that the gas behaves ideally.

A 1.50-mole sample of an ideal gas is allowed to expand adiabatically and reversibly to twice its original volume. In the expansion the temperature dropped from 296 K to 239 K. Calculate DE and DH for the gas expansion.

Consider 1.00 mole of CO2(g) at 300. K and 5.00 atm. The gas expands until the final pressure is 1.00 atm. For each of the following conditions describing the expansion, calculate q, w, and DE. Cp for CO2 is 37.1 J K21 mol21, and assume that the gas behaves ideally. a. The expansion occurs isothermally and reversibly. b. The expansion occurs isothermally against a constant external pressure of 1.00 atm. c. The expansion occurs adiabatically and reversibly

Consider 1.00 mole of CO2(g) at 300. K and 5.00 atm. The gas expands until the final pressure is 1.00 atm. For each of the following conditions describing the expansion, calculate DS, DSsurr, and DSuniv. Cp for CO2 is 37.1 J K21 mol21, and assume that the gas behaves ideally. a. The expansion occurs isothermally and reversibly. b. The expansion occurs isothermally against a constant external pressure of 1.00 atm. c. The expansion occurs adiabatically and reversibly

A mixture of hydrogen gas and chlorine gas remains unreacted until it is exposed to ultraviolet light from a burning magnesium strip. Then the following reaction occurs very rapidly: H2 1g2 1 Cl2 1g2 h 2HCl1g2 Explain.

When the environment is contaminated by a toxic or potentially toxic substance (for example, from a chemical spill or the use of insecticides), the substance tends to disperse. How is this consistent with the second law of thermodynamics? In terms of the second law, which requires the least work: cleaning the environment after it has been contaminated or trying to prevent the contamination before it occurs? Explain.

If you calculate a value for DG8 for a reaction using values of DG8f in Appendix 4 and get a negative number, is it correct to say the reaction is always spontaneous? Why or why not?

Given the following illustration, what can be said about the sign of DS for the process of solid NaCl dissolving in water? What can be said for DH about this process? NaCl(s) dissolves

Some water is placed in a coffee cup calorimeter. When 1.0 g of an ionic solid is added, the temperature of the solution increases from 21.58C to 24.28C as the solid dissolves. For the dissolving process, what are the signs for DSsys, DSsurr, and DSuniv?

Using Appendix 4 and the following data, determine S8 for Fe(CO)5(g). Fe1s2 1 5CO1g2 h Fe1CO2 5 1g2 DS 5 ? Fe1CO2 5 1l2 h Fe1CO2 5 1g2 DS 5 107 J/K Fe1s2 1 5CO1g2 h Fe1CO2 5 1l2 DS 5 2677 J/K

Discuss the relationship between wmax and the magnitude and sign of the free energy change for a reaction. Also discuss wmax for real processes.

Human DNA contains almost twice as much information as is needed to code for all the substances produced in the body. Likewise, the digital data sent from Voyager 2 contain one redundant bit out of every two bits of information. The Hubble space telescope transmits three redundant bits for every bit of information. How is entropy related to the transmission of information? What do you think is accomplished by having so many redundant bits of information in both DNA and the space probes?

The enthalpy of vaporization of chloroform (CHCl3) is 31.4 kJ/mol at its boiling point (61.78C). Determine DSsys, DSsurr, and DSuniv when 1.00 mole of chloroform is vaporized at 61.78C and 1.00 atm

Two crystalline forms of white phosphorus are known. Both forms contain P4 molecules, but the molecules are packed together in different ways. The a form is always obtained when the liquid freezes. However, below 276.98C, the a form spontaneously converts to the b form: P4(s, a) 88n P4(s, b) a. Predict the signs of DH and DS for this process. b. Predict which form of phosphorus has the more ordered crystalline structure (has the smaller positional probability).

Monochloroethane (C2H5Cl) can be produced by the direct reaction of ethane gas (C2H6) with chlorine gas or by the reaction of ethylene gas (C2H4) with hydrogen chloride gas. The second reaction gives almost a 100% yield of pure C2H5Cl at a rapid rate without catalysis. The first method requires light as an energy source or the reaction would not occur. Yet DG8 for the first reaction is considerably more negative than DG8 for the second reaction. Explain how this can be so

Acrylonitrile is the starting material used in the manufacture of acrylic fibers (U.S. annual production capacity is more than 2 million pounds). Three industrial processes for the production of acrylonitrile are given below. Using data from Appendix 4, calculate DS8, DH8, and DG8 for each process. For part a, assume that T 5 258C; for part b, T 5 70.8C; and for part c, T 5 700.8C. Assume that DH8 and DS8 do not depend on temperature. a. CH2 CH2(g) CH2 H2O(l) HCN(g) CHCN(g) + P + O Ethylene oxide Acrylonitrile C OG D b. HC HCN(g) CH2 CaCl2 HCl 70C90C CH(g) + CHCN(g) c. 4CH2PCHCH3(g) + 6NO(g) 4CH2PCHCN(g) + 6H2O(g) + N2(g)

In the text the equation DG 5 DG8 1 RT ln(Q) was derived for gaseous reactions where the quantities in Q were expressed in units of pressure. We also can use units of mol/L for the quantities in Qspecifically for aqueous reactions. With this in mind, consider the reaction HF(aq) 34 H1(aq) 1 F2(aq) for which Ka 5 7.2 3 1024 at 258C. Calculate DG for the reaction under the following conditions at 258C: a. [HF] 5 [H1] 5 [F2] 5 1.0 M b. [HF] 5 0.98 M, [H1] 5 [F2] 5 2.7 3 1022 M c. [HF] 5 [H1] 5 [F2] 5 1.0 3 1025 M d. [HF] 5 [F2] 5 0.27 M, [H1] 5 7.2 3 1024 M e. [HF] 5 0.52 M, [F2] 5 0.67 M, [H1] 5 1.0 3 1023 M Based on the calculated DG values, in which direction will the reaction shift to reach equilibrium for each of the five sets of conditions?

Many biochemical reactions that occur in cells require relatively high concentrations of potassium ion (K1). The concentration of K1 in muscle cells is about 0.15 M. The concentration of K1 in blood plasma is about 0.0050 M. The high internal concentration in cells is maintained by pumping K1 from the plasma. How much work must be done to transport 1.0 mole of K1 from the blood to the inside of a muscle cell at 378C (normal body temperature)? When 1.0 mole of K1 is transferred from blood to the cells, do any other ions have to be transported? Why or why not? Much of the ATP (see Exercise 84) formed from metabolic processes is used to provide energy for transport of cellular components. How much ATP must be hydrolyzed to provide the energy for the transport of 1.0 mole of K1?

Consider the following reaction at 358C: 2NOCl(g) mn 2NO(g) 1 Cl2(g) DG8 5 20. kJ If 2.0 atm of NOCl are reacted in a rigid container at 358C, calculate the equilibrium partial pressure of NO.

Consider the reaction H2(g) 1 Br2(g) 34 2HBr(g) where DH8 5 2103.8 kJ. In a particular experiment, 1.00 atm of H2(g) and 1.00 atm of Br2(g) were mixed in a 1.00-L flask at 258C and allowed to reach equilibrium. Then the molecules of H2 were counted by using a very sensitive technique, and 1.10 3 1013 molecules were found. For this reaction, calculate the values of K, DG8, and DS

At 1500 K the process I2(g) 88n 2I(g) 10 atm 10 atm is not spontaneous. However, the process I2(g) 88n 2I(g) 0.10 atm 0.10 atm is spontaneous at 1500 K. Explain

Using the following data, calculate the value of Ksp for Ba(NO3)2, one of the least soluble of the common nitrate salts. Species DG8f Ba21(aq) 2561 kJ/mol NO3 2(aq) 2109 kJ/mol Ba(NO3)2(s) 2797 kJ/mol

Sodium chloride is added to water (at 258C) until it is saturated. Calculate the Cl2 concentration in such a solution. Species DG8(kJ/mol) NaCl(s) 2384 Na1(aq) 2262 Cl2(aq) 2131

What is the pH of a 0.125 M solution of the weak base B if DH8 5 228.0 kJ and DS8 5 2175 J/K for the following equilibrium reaction at 258C? B(aq) 1 H2O(l) 34 BH1(aq) 1 OH2(aq)

Consider the reactions Ni21(aq) 1 6NH3(aq) 88n Ni(NH3)6 21(aq) (1) Ni21(aq) 1 3en(aq) 88n Ni(en)3 21(aq) (2) where en 5 H2NOCH2OCH2ONH2 The DH values for the two reactions are quite similar, yet Kreaction 2 . Kreaction 1. Explain.

The deciding factor on why HF is a weak acid and not a strong acid like the other hydrogen halides is entropy. What occurs when HF dissociates in water as compared to the other hydrogen halides?

The third law of thermodynamics states that the entropy of a perfect crystal at 0 K is zero. In Appendix 4, F2(aq), OH2(aq), and S22(aq) all have negative standard entropy values. How can S8 values be less than zero?

Calculate the entropy change for the vaporization of liquid methane and hexane using the following data: Boiling Point (1 atm) DHvap Methane 112 K 8.20 kJ/mol Hexane 342 K 28.9 kJ/mol Compare the molar volume of gaseous methane at 112 K with that of gaseous hexane at 342 K. How do the differences in molar volume affect the values of DSvap for these liquids?

The standard entropy values (S8) for H2O(l) and H2O(g) are 70. J K21 mol21 and 189 J K21 mol21, respectively. Calculate the ratio of Vg to Vl for water using Boltzmanns equation. (See Exercise 22.)

Calculate the values of DS and DG for each of the following processes at 298 K: H2O(l, 298 K) 88n H2O(g, V 5 1000. L/mol) H2O(l, 298 K) 88n H2O(g, V 5 100. L/mol) The standard enthalpy of vaporization for water at 298 K is 44.02 kJ/mol. Does either of these processes occur spontaneously?

Calculate the changes in free energy, enthalpy, and entropy when 1.00 mole of Ar(g) at 278C is compressed isothermally from 100.0 L to 1.00 L

Consider the isothermal expansion of 1.00 mole of ideal gas at 278C. The volume increases from 30.0 L to 40.0 L. Calculate q, w, DE, DH, DS, and DG for two situations: a. a free expansion b. a reversible expansion

A 1.00-mole sample of an ideal gas in a vessel with a movable piston initially occupies a volume of 5.00 L at an external pressure of 5.00 atm. a. If Pex is suddenly lowered to 2.00 atm and the gas is allowed to expand isothermally, calculate the following quantities for the system: DE, DH, DS, DG, w, and q. b. Show by the second law that this process will occur spontaneously.

One mole of an ideal gas with a volume of 6.67 L and a pressure of 1.50 atm is contained in a vessel with a movable piston. The external pressure is suddenly increased to 5.00 atm and the gas is compressed isothermally (T 5 122 K). Calculate DE, DH, DS, w, q, DSsurr, DSuniv, and DG.

Which of the following reactions (or processes) are expected to have a negative value for DS8? a. SiF6 1aq2 1 H2 1g2 h 2HF1g2 1 SiF4 1g2 b. 4Al1s2 1 3O2 1g2 h 2Al2O3 1s2 c. CO1g2 1 Cl2 1g2 h COCl2 1g2 d. C2H4 1g2 1 H2O1l2 h C2H5OH1l2 e. H2O1s2 h H2O1l2

For rubidium DHvap 8 5 69.0 kJ/mol at 6868C, its boiling point. Calculate DS8, q, w, and DE for the vaporization of 1.00 mole of rubidium at 6868C and 1.00 atm pressure

Given the thermodynamic data below, calculate DS and DSsurr for the following reaction at 258C and 1 atm: XeF6 1g2 h XeF4 1s2 1 F2 1g2 DH8f (kJ/mol) S8 (J K21 mol21) XeF6(g) 2294 300. XeF4(s) 2251 146 F2(g) 0 203

Consider the reaction: H2S1g2 1 SO2 1g2 h 3S1g2 1 2H2O1l2 for which DH is 2233 kJ and DS is 2424 J/K. a. Calculate the free energy change for the reaction (DG) at 393 K. b. Assuming DH and DS do not depend on temperature, at what temperatures is this reaction spontaneous?

The following reaction occurs in pure water: H2O1l2 1 H2O1l2 h H3O1 1aq2 1 OH2 1aq2 which is often abbreviated as H2O1l2 h H1 1aq2 1 OH2 1aq2 For this reaction, DG8 5 79.9 kJ/mol at 258C. Calculate the value of DG for this reaction at 258C when [OH2] 5 0.15 M and [H1] 5 0.71 M.

Consider the dissociation of a weak acid HA (Ka 5 4.5 3 1023) in water: HA1aq2mH1 1aq2 1 A2 1aq2 Calculate DG8 for this reaction at 258C.

Consider the reaction: PCl3 1g2 1 Cl2 1g2mPCl5 1g2 At 258C, DG8 5 292.50 kJ. Which of the following statements is(are) true? a. This is an endothermic reaction. b. DS8 for this reaction is negative. c. If the temperature is increased, the ratio PCl5 PCl3 will increase. d. DG8 for this reaction has to be negative at all temperatures. e. When DG8 for this reaction is negative, then Kp is greater than 1.00

The equilibrium constant for a certain reaction increases by a factor of 6.67 when the temperature is increased from 300.0 K to 350.0 K. Calculate the standard change in enthalpy (DH8) for this reaction (assuming DH8 is temperature-independent)

Consider a 2.00-mole sample of Ar at 2.00 atm and 298 K. a. If the gas sample expands adiabatically and reversibly to a pressure of 1.00 atm, calculate the final temperature of the gas sample assuming ideal gas behavior. b. If the gas sample expands adiabatically and irreversibly against a constant 1.00 atm pressure, calculate the final temperature of the gas sample assuming ideal gas behavior

Consider 1.0 mole of a monatomic ideal gas in a container fitted with a piston. The initial conditions are 5.0 L and P 5 5.0 atm at some constant T. a. If the external pressure is suddenly changed to 2.0 atm, show that expansion of the gas is spontaneous. b. If the external pressure suddenly changes back to 5.0 atm, show that compression of the gas is spontaneous. c. Calculate and compare signs of DG for each case (parts a and b) and discuss why this sign cannot be used to predict spontaneity

One mole of an ideal gas undergoes an isothermal reversible expansion at 258C. During this process, the system absorbs 855 J of heat from the surroundings. When this gas is compressed to the original state in one step (isothermally), twice as much work is done on the system as was performed on the surroundings in the expansion. a. What is DS for the one-step isothermal compression? b. What is DSuniv for the overall process (expansion and compression)?

At least some of what is in the following quoted statement is false. Change the incorrect statements so that they are correct and defend your answer. What is correct in the statements? What is wrong? Discuss a real-world situation that supports your position. The magnitude of DS is always larger than the magnitude of DSsurr. This is so because DS is related to qrev, whereas DSsurr is related to qactual, and the magnitude of qrev is always larger than the magnitude of qactual.

You have a 1.00-L sample of hot water (90.8C) sitting open in a 258C room. Eventually the water cools to 258C, whereas the temperature of the room remains unchanged. Calculate DSuniv for this process. Assume the density of water is 1.00 g/mL over this temperature range and that the heat capacity of water is constant over this temperature range and equal to 75.3 J K21 mol21.

Consider two perfectly insulated vessels. Vessel 1 initially contains an ice cube at 08C and water at 08C. Vessel 2 initially contains an ice cube at 08C and a saltwater solution at 08C. Consider the process H2O(s) n H2O(l). a. Determine the sign of DS, DSsurr, and DSuniv for the process in vessel 1. b. Determine the sign of DS, DSsurr, and DSuniv for the process in vessel 2. (Hint: Think about the effect that a salt has on the freezing point of a solvent.)

If wet silver carbonate is dried in a stream of hot air, the air must have a certain concentration level of carbon dioxide to prevent silver carbonate from decomposing by the reaction Ag2CO3(s) 34 Ag2O(s) 1 CO2(g DH8 for this reaction is 79.14 kJ/mol in the temperature range of 258C1258C. Given that the partial pressure of carbon dioxide in equilibrium with pure solid silver carbonate is 6.23 3 1023 torr at 258C, calculate the partial pressure of CO2 necessary to prevent decomposition of Ag2CO3 at 110.8C

Consider a weak acid HX. If a 0.10 M solution of HX has a pH of 5.83 at 258C, what is DG8 for the acids dissociation reaction at 258C?

Using data from Appendix 4, calculate DH8, DG8, and K (at 298 K) for the production of ozone from oxygen: 3O2(g) 34 2O3(g) At 30 km above the surface of the earth, the temperature is about 230. K and the partial pressure of oxygen is about 1.0 3 1023 atm. Estimate the partial pressure of ozone in equilibrium with oxygen at 30 km above the earths surface. Is it reasonable to assume that the equilibrium between oxygen and ozone is maintained under these conditions? Explain.

One mole of a monatomic ideal gas (for which S8 5 8.00 J K21 mol21 at 273.08C) was heated at a constant pressure of 2.00 atm from 273.08C to 27.08C. Calculate DH, DE, w, q, DS due to the change in volume, DS due to the change in temperature, and DG.

Consider the system A(g) 88n B(g) at 258C. a. Assuming that G8 A 5 8996 J/mol and G8 B 5 11,718 J/mol, calculate the value of the equilibrium constant for this reaction. b. Calculate the equilibrium pressures that result if 1.00 mole of A(g) at 1.00 atm and 1.00 mole of B(g) at 1.00 atm are mixed at 258C. c. Show by calculations that DG 5 0 at equilibrium

Liquid water at 258C is introduced into an evacuated, insulated vessel. Identify the signs of the following thermodynamic functions for the process that occurs: DH, DS, DG, DTwater, DSsurr, DSuniv.

Consider 1.00 mole of an ideal gas that is expanded isothermally at 258C from 2.45 3 1022 atm to 2.45 3 1023 atm in the following three irreversible steps: Step 1: from 2.45 3 1022 atm to 9.87 3 1023 atm Step 2: from 9.87 3 1023 atm to 4.93 3 1023 atm Step 3: from 4.93 3 1023 atm to 2.45 3 1023 atm Calculate q, w, DE, DS, DH, and DG for each step and for the overall process.

Consider 1.00 mole of an ideal gas at 258C. a. Calculate q, w, DE, DS, DH, and DG for the expansion of this gas isothermally and irreversibly from 2.45 3 1022 atm to 2.45 3 1023 atm in one step. b. Calculate q, w, DE, DS, DH, and DG for the same change of pressure as in part a but performed isothermally and reversibly. c. Calculate q, w, DE, DS, DH, and DG for the one-step isothermal, irreversible compression of 1.00 mole of an ideal gas at 258C from 2.45 3 1023 atm to 2.45 3 1022 atm. d. Construct the PV diagrams for the processes described in parts a, b, and c. e. Calculate the entropy change in the surroundings for the processes described in parts a, b, and c.

Consider the reaction 2CO(g) 1 O2(g) 88n 2CO2(g) a. Using data from Appendix 4, calculate K at 298 K. b. What is DS for this reaction at T 5 298 K if the reactants, each at 10.0 atm, are changed to products at 10.0 atm? (Hint: Construct a thermodynamic cycle and consider how entropy depends on pressure.)

Calculate DH8 and DS8 at 258C for the reaction 2SO2(g) 1 O2(g) 88n 2SO3(g) at a constant pressure of 1.00 atm using thermodynamic data in Appendix 4. Also calculate DH8 and DS8 at 2278C and 1.00 atm, assuming that the constantpressure molar heat capacities for SO2(g), O2(g), and SO3(g) are 39.9 J K21 mol21, 29.4 J K21 mol21, and 50.7 J K21 mol21, respectively. (Hint: Construct a thermodynamic cycle, and consider how enthalpy and entropy depend on temperature.)

Although we often assume that the heat capacity of a substance is not temperature-dependent, this is not strictly true, as shown by the following data for ice: Temperature (8C) Cp (J K21 mol21) 2200. 12 2180. 15 2160. 17 2140. 19 2100. 24 260. 29 230. 33 210. 36 0 37 Use these data to calculate graphically the change in entropy for heating ice from 2200.8C to 08C. (Hint: Recall that DST1ST2 5 3 T2 T1 Cp dT T and that integration from T1 to T2 sums the area under the curve of a plot of Cp/T versus T from T1 to T2.)

Consider the following Cp values for N2(g): Cp (J K21 mol21) T (K) 28.7262 300.0 29.2937 400.0 29.8545 500.0 Assume that Cp can be expressed in the form Cp 5 a 1 bT 1 cT2 Estimate the value of Cp for N2(g) at 900. K. Assuming that Cp shows this temperature dependence over the range 100 K to 900 K, calculate DS for heating 1.00 mole of N2(g) from 100. K to 900. K.

Benzene (C6H6) has a melting point of 5.58C and an enthalpy of fusion of 10.04 kJ/mol at 25.08C. The molar heat capacities at constant pressure for solid and liquid benzene are 100.4 J K21 mol21 and 133.0 J K21 mol21, respectively. For the reaction C6H6(l) 34 C6H6(s) calculate DSsys and DSsurr at 10.08C

Impure nickel, refined by smelting sulfide ores in a blast furnace, can be converted into metal from 99.90% to 99.99% purity by the Mond process. The primary reaction involved in the Mond process is Ni(s) 1 4CO(g) 34 Ni(CO)4(g) a. Without referring to Appendix 4, predict the sign of DS8 for the preceding reaction. Explain. b. The spontaneity of the preceding reaction is temperature-dependent. Predict the sign of DSsurr for this reaction. Explain. c. For Ni(CO)4(g), DH8f 5 2607 kJ/mol and S8 5 417 J K21 mol21 at 298 K. Using these values and data in Appendix 4, calculate DH8 and DS8 for the preceding reaction. d. Calculate the temperature at which DG8 5 0 (K 5 1) for the preceding reaction, assuming that DH8 and DS8 do not depend on temperature. e. The first step of the Mond process involves equilibrating impure nickel with CO(g) and Ni(CO)4(g) at about 508C. The purpose of this step is to convert as much nickel as possible into the gas phase. Calculate the equilibrium constant for the preceding reaction at 50.8C. f. In the second step of the Mond process, the gaseous Ni(CO)4 is isolated and heated at 2278C. The purpose of this step is to deposit as much nickel as possible as pure solid (the reverse of the preceding reaction). Calculate the equilibrium constant for the preceding reaction at 2278C. g. Why is temperature increased for the second step of the Mond process? h. The Mond process relies on the volatility of Ni(CO)4 for its success. Only pressures and temperatures at which Ni(CO)4 is a gas are useful. A recently developed variation of the Mond process carries out the first step at higher pressures and a temperature of 1528C. Estimate the maximum pressure of Ni(CO)4(g) that can be attained before the gas will liquefy at 1528C. The boiling point for Ni(CO)4 is 428C, and the enthalpy of vaporization is 29.0 kJ/mol. [Hint: The phase-change reaction and the corresponding equilibrium expression are Ni(CO)4(l) 34 Ni(CO)4(g) K 5 PNi(CO)4 Ni(CO)4(g) will liquefy when the pressure of Ni(CO)4 is greater than the K value.]

The initial state of an ideal gas is 2.00 atm, 2.00 L. The final state is 1.00 atm, 4.00 L. The expansion is accomplished isothermally. a. If the expansion is a free expansion, calculate w, q, DE, and DH. b. If the expansion is done in one step, calculate w, q, DE, and DH. c. If the expansion is done in two steps (with V 5 3.00 L as the intermediate step), calculate w, q, DE, and DH. d. If the expansion is reversible, calculate w, q, DE, and DH. You have the new state of an ideal gas at 1.00 atm, 4.00 L. You take the gas back to conditions of 2.00 atm, 2.00 L. The compression is accomplished isothermally. e. If the compression is done in one step, calculate w, q, DE, and DH. f. If the compression is done in two steps (with V 5 3.00 L as the intermediate step), calculate w, q, DE, and DH. g. If the compression is reversible, calculate w, q, DE, and DH. Explain. Compare your answers for the expansion and compression. Discuss the implications, especially considering the changes to the system and the changes to the surroundings that have occurred even though the system was brought back to its initial state.