202 CHAPTER 5 Thermochemistry

Exercises Visualizing Concepts

5.1 Two positively charged spheres, each with a charge of 2.0 X 10-5 C, a mass of 1.0 kg, and separated by a distance of 1.0 cm, are held in place on a frictionless track. (a) What is the electrostatic potential energy of this system? (b) If the spheres are released, will they move toward or away from each other? (c) What speed will each sphere attain as the distance between the spheres approaches infinity? [Section 5.1]

5.2 The accompanying photo shows a pipevine swallowtail cat­ erpillar climbing up a twig. (a) As the caterpillar climbs, its potential energy is increasing. What source of energy has been used to effect this change in potential energy? (b) If the caterpillar is the system, can you predict the sign of q as the caterpillar climbs? (c) Does the caterpillar do work in climb­ ing the twig? Explain. (d) Does the amount of work done in climbing a 12-inch section of the twig depend on the speed of the caterpillar's climb? (e) Does the change in potential en­ ergy depend on the caterpillar's speed of climb? [Section 5.1]

5.3 Consider the accompanying energy diagram. (a) Does this diagram represent an increase or decrease in the internal en­ ergy of the system? (b) What sign is given to 6.E for this pro­ cess? (c) If there is no work associated with the process, is it exothermic or endothermic? [Section 5.2]

5.4 The contents of the closed box in each of the following il­ lustrations represent a system, and the arrows show the changes to the system during some process. The lengths of the arrows represent the relative magnitudes of q and w. (a) Which of these processes is endothermic? (b) For which of these processes, if any, is 6.E < O? (c) For which process, if any, does the system experience a net gain in internal en­ ergy? [Section 5.2]

(i)

5.5 Imagine that you are climbing a mountain. (a) I distance you travel to the top a state function? (b) I change in elevation between your base camp and the a state function? [Section 5 .2] ·;

5.6 The diagram shows four states of a system, each wit" ferent-internal energy, E. (a) Which of the states oft· tern has the greatest internal energy? (b) In terms oft" values, write two expressions for the difference in i~ energy between State A and State B. (c) Write an expr. for the difference in energy between State C and SU (d) Suppose there is another state of the system, sfk and its energy relative to State A is 6.E = 6.E1 + 6.E4.

would State Ebe on the diagram? [Section 5.2]

1

Products

1 '.4 !I,.

5.7 kl

el ;;:, .:; eo " " QJ QJ

" I ] .:; QJ r ·i

Reactants

q

w w

(ii) (iii)

State B.

,:, '

/

State'C ·

State D

State A

You may have noticed that when you compress the a a bicycle pump, the body of the pump gets warmer. Assuming the pump and the air in it comprise the sys, what is the sign of w when you compress the air? (b) is the sign of q for this process? (c) Based on your answe parts (a) and (b), can you determine the sign of 6.E for c pressing the air in the pump? If not, what would you ex for the sign of 6.E? What is your reasoning? [Section 5.

5.8 Imagine a container placed in a tub of water, as depict the accompanying diagram. (a) If the contents of the i; tainer are the system and heat is able to flow through· container walls, what qualitative changes will occur in·. temperatui:es of the system and in its surroundings? Frorn' system's perspective, is the process exothermic or endotl mic? (b) If neither the volume nor the pressure of the syst changes during the process, how is the change in internal ergy related to the change in enthalpy? [Sections 5.2 and

'In the accompanying cylinder diagram, a chemical process ·occurs at constant temperature and pressure. (a) Is the sign , f w indicated by this change positive or negative? (b) If he process is endothermic, does the internal energy of the hstem within the cylinder increase or decrease during the ':j:hange and is tiE positive or negative? [Sections 5.2 and 5.3] I f 'i:J.

Reaction

· .. The gas-phase reaction shown, between N2 and 02, was run l in an apparatus designed to maintain a constant pressure. > (a) Write a balanced chemical equation for the reaction de­ , picted and predict whether w is positive, negative, or zero.

) 1,(b) Using data from Appendix C, determine tiH for the for­ mation of one mole of the product. [Sections 5.3 and 5,7]

p

Consider the two diagrams that follow, (a) Based on (i), write an equation showing how tiHA is related to b.Hu and b.Hc,

hi, (b) Based on (ii), write an equation relating M{z to the other , enthalpy changes in the diagram. (c) The equations you ob­ ' ., tainecl in parts (a) and (b) are based on what law? (d) Would T · similar relationships hold fol' the work involved in each

Process? [Section 5.6]

t

Exercises 203

(i) (ii)

5.12 Consider the conversion of compound A into compound B: A ---> B. For both compounds A and B, tiff,° > 0. (a) Sketch an enthalpy diagram for the reaction that is analogous to Figure 5.23. (b) Suppose the overall reaction is exothermic. What can you conclude? [Section 5.7]

The Nature of Chemical Energy {Section 5.1} 5.13 (a) What is the electrostatic potential energy (in joules) be­

tween an electron and a proton that are separated by 53 pm? (b) What is the change in potential energy if the distance separating the electron and proton is increased to 1.0 nm? (c) Does the potential energy of the two particles increase or decrease when the distance is increased to 1.0 nm?

5.14 (a) What is the electrostatic potential energy (in joules) be­ tween two protons that are separated by 62 pm? (b) What is the change in potential energy if the distance separating the two is increased to 1.0 nm? (c) Does the potential en­ ergy of the two particles increase or decrease when the dis­ tance is increased to 1.0 nm? -----

5.15 (a) The electrostatic force (not energy) of attraction between two oppositely charged objects is given by the equation F = K(Q1Q2/d2) where K = 8,99 x 109N-m2/C2, Q1 and Qz are the charges of the two objects in Coulombs, and dis the distance separating the two objects in meters. What is the electrostatic force of attraction (in Newtons) between an electron and a proton that are separated by 1.00 x 102 pm? (b) The force of gravity acting between two objects is given by the equation F = G(m1m2/d2), where G is the gravita­ tional constant, G = 6.674 X 10-11N-m2/kg2, m1 and m2 are the masses of the two objects, and dis the distance separat­ ing them. What is the gravitational force of attraction (in Newtons) between the electron and proton? (c) How many times larger is the electrostatic force of attraction?

5.16 Use the equations given in Problem 5.15 to calculate: (a) The electrostatic force of repulsion for two protons separated by 75 pm, (b) The gravitational force of attraction for two protons separated by 75 pm. (c) If allowed to move, will the

---~p_r_otons be repelled or attracted to one another? 5.17 A sodium ion, Na+, with a charge of 1.6 x 10-19 C and a chlo­

ride ion, c1-, with charge of -1.6 x 10-19 C, are separated by a distance of 0.50 nm. How much work would be required to increase the separation of the two ions to an infinite distance?

5.18 ~ magnesium ion, Mg2+, with a charge of 3.2 x 10-19 Canel an oxide ion, 02-, with a charge of -3.2 x 10-19 C, are separated by a distance of 0.35 nm. How much work would be required to

____ in_c_rease the separation of the two ions to an infinite distance? 5. 19 Identify the force present and explain whether work is being

performed in the following cases: (a) You lift a pencil off the top of a desk. (b) A spring is compressed to half its normal length.

5.20 Identify the force present and explain whether work is clone when (a) a positively charged particle moves in a circle at a fixed distance from a negatively charged particle, (b) an iron nail is pulled off a magnet.

204 CHAPTER 5 Thermochemistry

The First Law of Thermodynamics (Section 5.2)

5.21 (a) Which of the following cannot leave or enter a closed sys­ tem: heat, work, or matter? (b) Which cannot leave or enter an isolated system? (c) What do we call the part of the uni­ verse that is not part of the system?

5.22 In a thermodynamic study, a scientist focuses on the proper­ ties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the appara­ tus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? (b) If the in­ let and outlet were closed, what type of system would it be?

Out

5.23 (a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal en­ ergy of a system? (c) By what means can the internal energy of a closed system increase?

5.24 (a) Write an equation that expresses the first Jaw of thermo­ dynamics in terms of heat and work. (b) Under what condi­

____ t_io_ns will the quantities q and w be negative numbers? 5.25 Calculate !lE and determine whether the process is endother­

mic or exothermic for the following cases: (a) q = 0.763 k] and w = -840 J. (b) A system releases 66.1 k] of heat to its surroundings while the surroundings do 44.0 kJ of work on the system. ' ·

5.26 For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by re­ moving 0.655 kJ of heat. It shrinks on cooling, and the atmo­ sphere does 382 J of work on the balloon. (b) A 100.0-g bar of gold is heated from 25 °C to 50 °C during which it absorbs 322 J of heat. Assume the volume of the gold bar remains constant.

5.27 A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

. I Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case

5.28

(2) the piston is fixed so that it cannot move. (a) In Wh{~ case does the gas have the higher temperature after additi of the electrical energy? (b) Identify the sign (positive, ne~~' tive, or zero) of q and win each case? (c) In which case is s.;, for the system (the gas in the cylinder) larger? , Consider a system consisting of two oppositely chai,g~~ spheres hanging by strings and separated by a distance·!,; as shown in the accompanying illustration. Suppose t~~ are separated to a larger distance r2, by moving them apa~t­ (a) What change, if any, has occurred in the potential ene~gy, of the system? (b) What effect, if any, does this process ha& on the value of !lE? (c) What can you say about q and w<f,@ this process?

5.29 I'\

(a)_ What is meant by the term state function? (b) Give an'.@':· ample of a quantity that is a state function and one tl not. (c) Is the volume of a system a state function? W why not?

5.30 Indicate which of the following is independent of the by which a change occurs: (a) the change in potentia ergy when a book is transferred from table to shelf, (b) heat evolved when a cube of sugar is oxidized to C02(g) H20(g), (c) the work accomplished in burning a gallo gasoline. ·

Enthalpy (Section 5.3 and 5.4) 5.31 During a normal breath, our lungs expand about 0.5'.~

against an external pressure of 1.0 atm. How much wod~~ involved in this process (in J)? '

5.32 How much work (in J) is involved in a chemical reactio the volume decreases from 5,00 to 1.26 L against a const pressure of 0.857 atm? (a) Why is the change in enthalpy usually easier to meas than the change in internal energy? (b) His a state functf but q is not a state function. Explain. (c) For a given pi • at constant pressure, i'lH is positive. Is the process endotl?, mic or exothermic? · (a) Under what condition will the enthalpy change<(', process equal the amount of heat transferred into or 0tlff@. the system? (b) During a constant-pressure process, the ~1!; tern releases heat to the surroundings. Does the enthalp%@ the system increase or decrease during the process? (c) I\a constant-pressure process, i'lH = 0. What can you conclU'{ about !lE, q, and w? · .

---- 'l(l 5.35 Assume that the following reaction occurs at consta'

pressure: · 2Al(s) + 3 Cl2(g) ---> 2AlCJ3(s)

(a) If you are given i'lH for the reaction, what additiO~ information do you need to determine b.E for the process?' . (b) Which quantity is larger for this reaction? (c) Expiai~ your answer to part (b).

5.33

5.34

+

r 1 r 2

1. Ii ,i :/1

Exercises 205

6 suppose thatthe g~s-phasereaction 2 NO(g) + 02(g) ~ · 2 NOz(g) were earned out ma constant-volume con tamer

· at constant temperature. (a) Would the measured heat · change represent 6.H or 6.E? (b) If there is a difference, which 1 quantity is larger for this reaction? (c) Explain your answer to part(b).

7,;A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in Figure 5.4. When the gas undergoes a particular chemical reaction, it absorbs 824 J of heat from

.. its surroundings and has 0.65 kJ of P-V work done on it by its surroundings. What are the values of 6.H and 6.E for this process?

, A gas is confined to a cylinder under constant atmospheric · ·! pressure, as illustrated in Figure 5.4. When 0.49 kJ of heat is [. added to the gas, it expands and does 214 J of work on the

surroundings. What are the values of Mi and 6.E for this iJ;(process?

, [I'he complete combustion of ethanol, C2HsOH(I), to form H20(g) and C02(g) at constant pressure releases 1235 kJ of heat per mole of C2HsOH. (a) Write a balanced thermochem­ ical equation for this reaction. (b) Draw an enthalpy diagram

.. for the reaction. . The decomposition of Ca(OH)z(s) into CaO(s) and H20(g) :· at constant pressure requires the addition of 109 kJ of heat per mole of Ca(OH)z. (a) Write a balanced thermochemical

· equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

· 1 Ozone, 03(g), is a form of elemental oxygen that plays an im­ ':, portant role in the absorption of ultraviolet radiation in the " stratosphere. It decomposes to 02(g) at room temperature

and pressure according to the following reaction: . {),

2 03(g) --:-' 3 Oz(g) MI= -284.6 kJ

t(a) What is the enthalpy change for this reaction per mole of03(g)?

(b) Which has the higher enthalpy under these conditions, 2 03(g) or 3 02(g)?

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) 1 mo! C02(s) or

i i) mo! C02(g) at the same temperature, (b) 2 mo! of hydrogen n; atoms or 1 mo! of H2, (c) 1 mo! H2(g) and 0.5 mo! 02(g) at 11,,25 °C or 1 mo! H20(g) at 25 °C, (d) 1 mo! N2(g) at 100 °C or

· 1 mo! N2(g) at 300 °c. ~; Consider the following reaction: h 2 Mg(s) + 02(g) --> 2 MgO(s) 6.H = -1204 kJ

Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 3.55 g of

Mg(s) reacts at constant pressure. (c) How many grams of MgO are produced during an

enthalpy change of -234 k]? /• . (d) How many kilojoules of heat are absorbed when 40.3 g

of MgO(s) is decomposed into Mg(s) and 02(g) at con­ stant pressure?

· 11: Consider the following reaction:

2 CH30H(g) --> 2 CH4(g) + 02(g) 6.H = + 252.8 kJ (a) ls this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 24.0 g of CI-!301-l(g) is decomposed by this reaction at constant pressure. (c) For a given sample of CI-!30!-I, the enthalpy change during the

' reaction is 82.1 kJ. How many grams of methane gas are produced? (d) How many kilojoules of heat are released When 38.5 g of CH4(g) reacts completely with 02(g) to form CH30H(g) at constant pressure?

5.45 When solutions containing silver ions and chloride ions are mixed, silver chloride precipitates

Ag'(aq) + Ci-(aq) --> AgCl(s) Mi= -65.5 kJ

(a) Calculate 6.H for the production of 0.450 mo! of AgCl by this reaction. (b) Calculate Mi for the production of 9.00 g of AgCL (c) Calculate 6.H when 9.25 x 10-4 mo! of AgCl dis­ solves in water.

5.46 At one time, a common means of forming small quantities of oxygen gas in the laboratory was to heat KCI03:

2 KC!03(s) - 2 KC!(s) + 3 02(g) 6.H = -89.4 kJ

For this reaction, calculate 6.H for the formation of (a) 1.36 mol of 02 and (b) 10.4 g of KCL (c) The decomposition of KCI03 proceeds spontaneously when it is heated. Do you think that the reverse reaction, the formation of KC!03 from KC! and 0~, is likely to be feasible under ordinary conditions?

___ E_·x~plain your answer. 5.47 Consider the combustion of liquid methanol, CH30H(I):

CH30H(I) + i 02(g) - C02(g) + 2 H20(1) 6.H = - 726.5 kJ

(a) What is the enthalpy change for the reverse reaction? (b) Balance the forward reaction with whole-number co­ efficients. What is 6.H for the reaction represented by this equation? (c) Which is more likely to be thermodynami­ cally favored, the forward reaction or the reverse reaction? .(d) If the reaction were written to produce H20(g) instead of H20(1), would you expect the magnitude of 6.H to in­ crease, decrease, or stay the same? Explain .

5.48 Consider the decomposition of liquid benzene, C6H6(1), to gaseous acetylene, C2H2(g):

C6H6(1) - 3 C2Hz(g) 6.H = +630 kJ (a) What is the enthalpy change for the reverse reaction?

(b) What is 6.H for the formation of 1 mo! of acetylene? (c) Which is more likely to be thermodynamically favored,

the forward reaction or the reverse reaction? (d) If C6H6(g) were consumed instead of C6H6(1), would you

expect the magnitude of 6.H to increase, decrease, or stay.the same? Explain.

Calorimetry (Section 5.5) 5.49 (a) What are the units of molar heat capacity? (b) What are

the units of specific heat? (c) If you know the specific heat of copper, what additional information do you need to calcu­ late the heat capacity of a particular piece of copper pipe?

5.50 Two solid objects, A and B, are placed in boiling water and al­ lowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing 1000 g water at l0.0°C. Object A increases the water temperature by 3.50 °C; B increases the water temperature by 2.60 °C. (a) Which object has the larger heat capacity? (b) What can

___ y~o_u say about the specific heats of A and B? 5.51 (a) What is the specific heat of liquid water? (b) What is the

molar heat capacity of liquid water? (c) What is the heat ca­ pacity of 185 g of liquid water? (d) How many kJ of heat are needed to raise the temperature of 10.00 kg of liquid water from 24.6 to 46.2 °C?

5.52 (a) Which substance in Table 5.2 requires the smallest amount of energy to increase the temperature of 50.0 g of that substance by 10 K? (b) Calculate the energy needed for this temperature change.

206 CHAPTER 5 Thermochemistry

5.53 The specific heat of octane, C8H18(1), is 2.22]/g-K. (a) How many J of heat are needed to raise the temperature of 80.0 g of octane from 10.0 to 25.0 °C? (b) Which will require more heat, increasing the temperature of 1 mo! of C8I-I18(1) by a certain amount or increasing the temperature of 1 mo! of H20(1) by the same amount?

5.54 Consider the data about gold metal in Exercise 5.26(b). (a) Based on the data, calculate the specific heat of Au(s). (b) Suppose that the same amount of heat is added to two 10.0-g blocks of metal, both initially at the same tem­ perature. One block is gold metal, and one is iron metal. Which block will have the greater rise in temperature after the addition of the heat? (c) What is the molar heat capac-

___ i~ty~of Au(s)? 5.55 When a 6.50-g sample of solid sodium hydroxide dissolves

in 100.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 21.6 to 37.8 °C. (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate t,,H (in kJ/mol NaOI-I) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

5.56 (a) When a 4.25-g sample of solid ammonium nitrate dis­ solves in 60.0 g of water in a coffee-cup calorimeter (Figure 5.18), the temperature drops from 22.0 to 16.9 °C. Calculate t,,H (in kJ/mol NH4N03) for the solution process:

NH4N03(s) - NH/(aq) + N03-(aq)

Assume that the specific heat of the solution is the same as that of pure water. (b) Is this process endothermic or exothermic? ----

5.57 A 2.200-g sample of quinone (C6H402) is burned in a bomb calorimeter whose total heat capacity is 7.854 kJ j°C. The tem­ perature of the calorimeter increases from 23.44 to 30.5 7 °C. What is the heat of combustion per gram of quinone? Per mole of quinone?

5.58 A 1.800-g sample of phenol (C6H50H) was burned in a bomb calorimeter whose total heat capacity is 11.66 kJ j°C. The temperature of the calorimeter plus contents increased from 21.36 to 26.37 °C. (a) Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol? Per mole of

--~p~h_enol? 5.59 Under constant-volume conditions, the heat of combustion

of glucose (C6H1206) is 15.57 kJ/g. A 3.500-g sample of glu­ cose is burned in a bomb calorimeter. The temperature of the calorimeter increases from 20.94 to 24.72 °C. (a) What is the total heat capacity of the calorimeter? (b) If the size of the glucose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

5.60 Under constant-volume conditions, the heat of combustion of benzoic acid (C6H5COOH) is 26.38 kJ/g. A 2.760-g sample of benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.60 to 29.93 °C. (a) What is the total heat capacity of the calorimeter? (b) A 1.440-g sample of a new organic substance is combusted in the same calorime­ ter. The temperature of the calorimeter increases from 22.14 to 27 .09 °C. What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Hess's Law (Section 5.6) 5.61 Can you use an approach similar to Hess's law to calculate

the change in internal energy, t,,E, for an overall reaction by summing the I',,£ values of individual reactions that add up to give the desired overall reaction?

5.62 Consider the following hypothetical reactions:

A -----., B M-1 = + 30 kJ 13 -----., C t,,H = + 60 kJ

(a) Use Hess's law to calculate the enthalpy change fo reaction A -----., C.

(b) Construct an enthalpy diagram for substances A, ____ C, and show how Hess's law applies. 5.63 Calculate the enthalpy change for the reaction

P405(s) + 2 Oz(g) - P4010(s) given the following enthalpies of reaction:

P4(s) + 3 02(g) -----., P406(s) P4(s) + 5 02(g) -----., P4010(s)

5.64 From the enthalpies of reaction

2 C(s) + 02(g) -----., 2 CO(g) 2 C(s) + 02(g) + 4 H2(g) -----., 2 CH30H(g)

calculate t,,H for the reaction

CO(g) + 2 Hz(g) -----> CH30H(g)

5.65 From t_he enthalpies of reaction

H2(g) + F2(g) -----., 2 HF(g) C(s) + 2 F2(g) -----., CF4(g)

2 C(s) + 2 H2(g) -----., C2H4(g)

t,,H = -537kJ t,,H = -680kJ t,,H = +52.3 kJ

calculate l',,H for the reaction of ethylene with F2:

C2H4(g) + 6 Fz(g) -----., 2 CF4(g) + 4 HF(g) 5.66 Given'the data

Nz(g) + 02(g) -----., 2 NO(g) 2 NO(g) + 02(g) -----., 2 NOz(g)

2 N20(g) -----., 2 N2(g) + Oz(g)

t,,H= +180.7 t,,H = -113)

use Hess's law to calculate t,,H for the reaction N20(g) + N02(g) -----> 3 NO(g)

Enthaipies of Formation (Section 5.7) 5.67 (a) What is meant by the term standard conditions wit .·

erence to enthalpy changes? (b) What is meant by the, enthalpy of formation? (c) What is meant by the term sta enthalpy of formation?

5.68 (a) What is the value of the standard enthalpy of form of an element in its most stable form? (b) Write the ch cal equation for the reaction whose enthalpy change i standard enthalpy of formation of sucrose (table su C12H22011(s), t,,H/[C12H22011(s)]. '.

---- 5.69 For each of the following compounds, write a balanced

mochemical equation depicting the formation of one of the compound from its elements in their standard st and then look up t,,H0r for each substance in Appendi (a) N02(g), (b) S03(g), (c) NaBr(s), (d) Pb(N03)z(s).

5.70 Write balanced equations that describe the formation of following compounds from elements in their standard st and then look up the standard enthalpy of formatio each substance in Appendix C: (a) H202(g), (b) CaCO (c) POCl3(1), (d) C2H50H(I).

' 5.71 The following is known as the thermite reaction:

2 Al(s) + Fe203(s) -----., Al203(s) + 2 Fe(s)

This highly exothermic reaction is used for welding mas units, such as propellers for large ships. Using standard thalpies of formation in Appendix C, calculate t,,H0 for reaction.

Exercises 207

2 Many portable gas heaters and grills use propane, C3H8(g), as ' a fuel. Using standard enthalpies of formation, calculate the .. quantity of heat produced when 10.0 g of propane is com­

, pletely combusted in air under standard conditions. Using values from Appendix C, calculate the standard en­

, thalpy change for each of the following reactions: } (a) 2 S02(g) + Oz(g) ----> 2 S03(g)

(b) Mg(OH)z(s) ----> MgO(s) + H20(/) \,

, (c) N204(g) + 4 Hz(g) ----> Nz(g) + 4 H20(g) .,. (d) SiCl4(1) + 2 H20(/) ----> Si02(s) + 4 HCl(g) Using values from Appendix C, calculate the value of t,,H0 for each of the following reactions: (a) CaO(s) + 2 HCl(g) ----> CaCl2(s) + H20(g) (b) 4 FeO(s) + 02(g) ----> 2 Fe203(s) (c) 2 CuO(s) + NO(g) ----> Cu20(s) + N02(g) (d) 4 NH3(g) + Oz(g) ----> 2 N2H4(g) + 2 I-120(/) Complete combustion of 1 mol of acetone (C3H60) liberates 1790 kJ:

C3H60(1) + 4 02(g) ---:--> 3 C02(g) + 3 I-120(/) M-I0 = -1790kJ

Using this information together with the standard en­ . r thalpies of formation of 02(g), C02(g), and I-120(1) from ,,. Appendix C, calculate the standard enthalpy of formation of

· acetone.

5.80 Methanol (CH30H) is used as a fuel in race cars. (a) Write a balanced equation for the combustion of liquid methanol in air. (b) Calculate the standard enthalpy change for the reac­ tion, assuming H20(g) as a product. (c) Calculate the heat produced by combustion per liter of methanol. Methanol has a density of 0.791 g/mL. (d) Calculate the mass of CO2 produced per kJ of heat emitted.

1,, ,I

;6 Calcium carbide (CaC2) reacts with water to form acetylene , (C2H2) and Ca(OH)z. From the following enthalpy of reac­ tion data and data in Appendix C, calculate !',,Hf° for CaC2(s): CaC2(s) + 2 I-120(/) ----> Ca(OH)z(s) + C2H2(g)

sn: = -127.2kJ Gasoline is composed primarily of hydrocarbons, includ­ ing many with eight carbon atoms, called octanes. One of

·,. · the cleanest-burning octanes is a compound called 2,3,4- trimethylpentane, which has the following structural formula:

The complete combustion of one mole of this com­ pound to C02(g) and H20(g) leads to t,,H° = -5064.9 k]. (a) Write a balanced equation for the combustion of 1 mol of C8H18(1). (b) By using the information in this problem and data in Table 5.3, calculate /',,Hf° for 2,3,4-trimethylpentane. Diethyl ether, C4H100(/), a flammable compound that was once used as a surgical anesthetic, has the structure

The complete combustion of 1 mo! of C4H100(1) to C02(g) and H20(1) yields t,,H° = -2723.7 k]. (a) Write a balanced equation for the combustion of 1 mol of C4I-l100(1). (b) By using the information in this problem and data in Table 5.3, calculate t:,H/ for diethyl ether. Ethanol (C2H50H) is blended with gasoline as an automo­ bile fuel. (a) Write a balanced equation for the combustion of liquid ethanol in air. (b) Calculate the standard enthalpy change for the reaction, assuming H20(g) as a product. (c) Calculate the heat produced per liter of ethanol by com­ bustion of ethanol under constant pressure. Ethanol has a density of 0.789 g/mL. (cl) Calculate the mass of CO2 pro­ duced per kJ of heat emitted.

Bond Enthalpies {Section 5.8) 5.81 Without doing any calculations, predict the sign of t:,H for

each of the following reactions: (a) NaCl(s) ----> Na+(g) + Ci-(g) (b) 2 1-l(g) ----> I-lz(g) (c) Na(g) ----> Na+(g) + e­ (cl) I2(s) ----> lz(/)

5.82 Without doing any calculations, predict the sign of t:,H for each of the following reactions: (a) 2 N02(g) ----> N204(g) (b) 2 F(g) ----> Fz(g) (c) Mg2+(g) + 2 Ci-(g) ----> MgCl2(s) (cl) HBr(g) ----> H(g) + Br(g)

5.83 Use bond enthalpies in Table 5.4 to estimate Mi for each of the following reactions: (a) H - H(g) + Br- Br(g) ----> 2 H - Br(g) (b)

H I

2H-C-O-H + 30=0 -- 20=C=O + 4H-0-H I H

5.84 Use bond enthalpies in Table 5.4 to estimate t,,H for each of the following reactions: (a)

Br I

Br-C-H + Cl-Cl -- I Br

Br I

Br-C-Cl + Cl-H I Br

(b)

H I

H-C-H + 2 O=O -- O=C=O + 2 H-0-H I H

5.85 (a) Use enthalpies of formation given in Appendix C to cal­ culate t,,H for the reaction Br2(g) ----> 2 Br(g), and use this value to estimate the bond enthalpy D(Br- Br). (b) How large is the difference between the value calculated in part (a) ~nd the value given in Table 5.4?

5.86 (a) The nitrogen atoms in an N2 molecule are held together by a triple bond; use enthalpies of formation in Appen­ dix C to estimate the enthalpy of this bond, D(N=N). (b) Consider the reaction between hydrazine and hydrogen to produce ammonia, N2H4(g) + H2(g) ----> 2 NH3(g). Use en­ thalpies of formation and bond enthalpies to estimate the en­ thalpy of the nitrogen- nitrogen bond in N2H4. (c) Based on your answers to parts (a) and (b), would you predict that the nitrogen-nitrogen bond in hydrazine is weaker than, similar to, or stronger than the bond in N2?

208 CHAPTER 5 Thermochemistry

5.87

5.88

Consider the reaction 2H2(g) + 02(g) - 2H20(1). (a) Use the bond enthalpies in Table 5.4 to estimate /',./-J for this reaction, ignoring the fact that water is in the liquid state. (b) Without doing a calculation, predict whether your estimate in part (a) is more negative or less negative than the true reaction enthalpy. (c) Use the enthalpies of formation in Appendix C to determine the true reaction enthalpy.

Consider the reaction H2(g) + 12(s) ---,, 2 HI(g). (a) Use the bond enthalpies in Table 5.4 to estimate 6.J-J for this reaction, ignoring the fact that iodine is in the solid state. (b) Without doing a calculation, predict whether your estimate in part (a) is more negative or less negative than the true reaction en­ thalpy. (c) Use the enthalpies of formation in Appendix C to determine the true reaction enthalpy.

Foods and Fuels (Section 5.9) 5.89 (a) What is meant by the term fuel value? (b) Which is a greater

source of energy as food, 5 g of fat or 9 g of carbohydrate? (c) The metabolism of glucose produces C02(g) and H20(1). How does the human body expel these reaction products?

5.90 (a) Which releases the most energy when metabolized, 1 g of car­ bohydrates or 1 g of fat? (b) A particular chip snack food is com­ posed of 12% protein, 14% fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How

____ m_a_ny grams of protein provide the same fuel value as 25 g of fat? 5.91 (a) A serving of a particular ready-to-serve chicken noodle

soup contains 2.5 g fat, 14 g carbohydrate, and 7 g protein. Estimate the number of Calories in a serving. (b) According to its nutrition label, the same soup also contains 690 mg of sodium. Do you think the sodium contributes to the caloric content of the soup? ·

5.92 A pound of plain M&M®candies contains 96 g fat, 320 g carbo­ hydrate, and 21 g protein. What is the fuel value in kJ in a 42-g

____ (_ab_out 1.5 oz) serving? How many Calories does it provide? 5.93 The heat of combustion of fructose, C6H1206, is

-2812 kJ/mol. If a fresh golden delicious apple weighing 4.23 oz (120 g) contains 16.0 g of fructose, what caloric con­ tent does the fructose contribute to the apple?

5.94 The heat of combustion of ethanol, C2H50J-I(I), is -1367 kJ/mol. A batch of Sauvignon Blanc wine contains 10.6% ethanol by mass. Assuming the density of the wine to

be 1.0 g/mL, what is the caloric content clue to the alcoll', (ethanol) in a 6-oz glass of wine (177 mL)? .,:;\Qi

_5_._9_5_1--h-e standard enthalpies of formation of gaseous Pl; pyne (C3H4), propylene (C3J-l6), and propane (C3H8f~te + 185.4, +20.4, and -103.8 kJ/mol, respectively. (a) Calcul~t; the heat evolved per mole on combustion of each substarjc.~l yield C02(g) and H20(g). (b) Calculate the heat evolvec1~g combustion of 1 kg of each substance. (c) Which is the rn 11

efficient fuel in terms of heat evolved per unit mass? , It is interesting to compare the "fuel value" of a hy~fo­ carbon in a hypothetical world where oxygen is not,\."iil combustion agent. The enthalpy of formation of Cl\(g,)-" -679.9 kJ/mol. Which of the following two reactions is fl\'i more exothermic? i'i

5.96

CJ-I4(g) -1- 2 Oz(s) ---,, C02(S) + 2 H20(g)

CH4(g) -1- 4 Fz(s) ---,, CF4(g) -1- 4 HF(g)

5.97 At the encl of 2012, global population was about 7.0 bill people. What mass of glucose in kg would be need~ provide 1500 Cal/person/day of nourishment to the glo population for one year? Assume that glucose is metabo!' entirely to C02(g) and J-120(1) according to the folio thermochemical equation:

C6I-l1z05(s) + 6 Oz(S) ---,, 6 C02(s) + 6 H20(/) . I

6.J-1° = -280811!

5.98 The automobile fuel called E85 consists of 85% ethanol a 15% gasoline. E85 can be used in the so-called flex-fuel v.e cles (FFVs), which can use gasoline, ethanol, or a mix as fu Assume that gasoline consists of a mixture of octanes (di ent isomers of C8J-I18), that the average heat of combus of C8H18(/) is 5400 kJ/mol, and that gasoline has an av density of 0. 70 g/mL. The density of ethanol is 0. 79 g/m By using the information given as well as data in Appen compare the energy produced by combustion of 1.0 L of line and of 1.0 L of ethanol. (b) Assume that the density heat of combustion of E85 can be obtained by using 85 the values for ethanol and 15% of the values for gasoline. much energy could be released by the combustion of 1.0 E85? ( c) How many gallons of E85 would be needed to pro the same energy as 10 gal of gasoline? ( d) If gasoline costs f per gallon in the United States, what is the break-even pric gallon of E85 if the same amount of energy is to be deliver

Additional Exercises 5.99 The air bags that provide protection in automobiles in the

event of an accident expand because of a rapid chemical re­ action. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of q and win this process?

5.100 An aluminum can of a soft drink is placed in a freezer. Later, you find that the can is split open and its contents have fro­ zen. Work was done on the can in splitting it open. Where did the energy for this work come from?

5.101 Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expan­ sion of the gas? (b) Why or why not? (c) Can you determine the value of 6.E for the process?

5.102

A

1 atm

B

Evacuated

A sample of gas is contained in a cylinder-and-piston ai:, rangement. It undergoes the change in state shown in tll6

drawing. (a) Assume first that the cylinder and piston al perfect thermal insulators that do not allow heat to be traJJ·, ferred. What is the value of q for the state change? wnat iS the sign of w for the state change? What can be said about ti for the state change? (b) Now assume that the cylinder and piston are made up of a thermal conductor such as a metiil, During the state change, the cylinder gets warmer to th touch. What is the sign of q for the state change in this cas~l

Additional Exercises 209

oescribe the difference in the state of the system at the end of the process in the two cases. What can you say about the

1 relative values of nE?

!'1 ' ftimestone stalactites and stalagmites are formed in caves by the following reaction:

'.-(aq) + 2 HC03-(aq) ---" CaC03(s) + C02(g) + H20(/)

if 1 rnol of CaC03 forms at 298 K under 1 atm pressure, the 'reaction performs 2.47 kJ of P-V work, pushing back the atmo­ .sphere as the gaseous CO2 forms. At the same time, 38.95 kJ 'of heat is absorbed from the environment. What are the values of tsl] and of !:i.E for this reaction? :consider the systems shown in Figure 5.10.An one case the battery becomes completely discharged by running the cur­ .rent through a heater, and in the other case by running a fan. :Both processes occur at constant pressure. In both cases the change in state of the system is the same: The battery goes from being fully charged to being fully discharged. Yet in one case the heat evolved is large, and in the other it is small. Is ,the enthalpy change the same in the two cases? If not, how ,can enthalpy be considered a state function? If it is, what can .you say about the relationship between enthalpy change .and q in this case, as compared with others that we have

·,considered? ~' A house is designed to have passive solar energy features. ., Brickwork incorporated into the interior of the house acts ,. as a heat absorber. Each brick weighs approximately 1.8 kg. , The specific heat of the brick is 0.85 J /g-K. How many bricks ,1must be incorporated into the interior of the house to pro­ )~vide the same total heat capacity as 1. 7 x 103 gal of water?

· .A coffee-cup calorimeter of the type shown in Figure 5.18 i, contains 150.0 g of water at 25.1 °C. A 121.0-g block of cop­ ;·,. per metal is heated to 100.4 °c by putting it in a beaker of

boiling water. The specific heat of Cu(s) is 0.385 J/g-K. The Cu is added to the calorimeter, and after a time the contents

, of the cup reach a constant temperature of 30.1 °C. (a) De­ ., termine the amount of heat, inJ, lost by the copper block.

(b) Determine the amount of heat gained by the water. The specific heat of water is 4.18]/g-K. (c) The difference be­ tween your answers for (a) and (b) is due to heat loss through the Styrofoam® cups and the heat necessary to raise the tem­ perature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise

, the temperature of the apparatus (the cups and the stopper) . by l K. Calculate the heat capacity of the calorimeter in J/K. · (d)What would be the final temperature of the system if all

i the heat lost by the copper block were absorbed by the water in the calorimeter? (a) When a 0.235-g sample of benzoic acid is combusted in a bomb calorimeter (Figure 5.19), the temperature rises l.642 °c. When a 0.265-g sample of caffeine, C8H10N402,

is burned, the temperature rises 1.525 °C. Using the value 26.38 kJ/g for the heat of combustion of benzoic acid, cal­ culate the heat of combustion per mole of caffeine at constant volume. (b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

5.108 Meals-ready-to-eat (MREs) are military meals that can be heated on a flameless heater. The heat is produced by the fol­ lowing reaction:

(a) Calculate the standard enthalpy change for this reaction. (b) Calculate the number of grams of Mg needed for this re­ action to release enough energy to increase the temperature of 75 mL of water from 21 to 79 °C.

5.109 Burning methane in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), CO(g), and C02(g). (a) Write three balanced equa­ tions for the reaction of methane gas with oxygen to produce these three products. In each case assume that H20(1) is the only other product. (b) Determine the standard enthalpies for the reactions in part (a). (c) Why, when the oxygen supply is adequate, is C02(g) the predominant carbon-containing product of the combustion of methane?

5.110 We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethylene:

2 CH4(g) - C2H4(g) + Hz(g) Calculate the nH0 for this reaction using the following ther­ mochemical data:

CH4(g) + 2 02(g) ---" C02(g) + 2 H20( I) C2H4(g) + Hz(g) ---" C2H5(g) 2 Hz(g) + Oz(g) ---" 2 H20(/)

2 C2H5(g) + 7 Oz(g)---" 4 C02(g) + 6 H20(/)

str = -890.3 kJ !:i.H° = -136.3 kJ D.H° = -571.6 kJ sir = -3120.8 kJ

5.111 From the following data for three prospective fuels, calculate which could provide the most energy per unit volume:

Fuel

Density. at 20'C (g/cm3)

Molar Enthalpy of Combustion (kJ/mol)

. Niiroethail·e 01HgNOi('/i\'lil .,,fi1 •}ln.lrbsz.:) th, r",oit . .!.!,1,368''1 · , "}, ·.:, .-' .... .., .(. ... -~ '• . -~ '., ',\ , .. , .. ~ Ethanol, C2H50H(/) 0. 789 -136 7 Methylhydrazine, CH6N2(1) ,,;,,i,~1.0!87411J!1f·i. 1·· ,,,~ 1'3'0V 1

~! ' ••

5.112 The hydrocarbons acetylene (C2H2) and benzene (C6H6) have the same empirical formula. Benzene is an "aromatic" hydrocarbon, one that is unusually stable because of its struc­ ture. (a) By using data in Appendix C, determine the standard enthalpy change for the reaction 3 C2Hz(g) ---" C5H5(/). (b) Which has greater enthalpy, 3 mol of acetylene gas or 1 mol of liquid benzene? (c) Determine the fuel value, in kJ / g, for acetylene and benzene.

5.113 Ammonia (NH3) boils at -33 °C; at this temperature it has a density of 0.81 g/cm3. The enthalpy of formation of NH3(g) is -46.2 kJ/mol, and the enthalpy of vaporization of NI-!3(/) is 23.2 kJ/mol. Calculate the enthalpy change when 1 L of liquid NI-!3 is burned in air to give N2(g) and I-I20(g). How does this compare with nH for the complete combustion of 1 L of liquid methanol, CI-!30H(I)? For CH301-l(/), the clen­ sity at250C is 0.792g/cm3, and nH! = -239kJ/mol.