Solved: The convention of arbitrarily assigning a zero

Define these terms: system, surroundings, open system, closed system, isolated system, thermal energy, chemical energy, potential energy, kinetic energy, law of conservation of energy.

A gas expands from \(264 \mathrm{~mL}\) to \(971 \mathrm{~mL}\) at constant temperature. Calculate the work done (in joules) by the gas if it expands (a) against a vacuum and (b) against a constant pressure of \(4.00 \mathrm{~atm}\).

Classify each of the following as an open system, a closed system, or an isolated system. (a) Milk kept in a closed thermo flask. (b) A student reading in her dorm room. (c) Air inside a tennis ball.

What is heat? How does heat differ from thermal energy? Under what condition is heat transferred from one system to another?

A gas expands and does P-V work on the surroundings equal to 279 J. At the same time, it absorbs 216 J of heat from the surroundings. What is the change in energy of the system?

Two ideal gases at the same temperature and pressure are placed in two equal volume containers. One container has a fixed volume, while the other is a cylinder fitted with a weightless movable piston like that shown in Figure 6.5. Initially, the gas pressures are equal to the external atmospheric pressure. The gases are then heated with a Bunsen burner. What are the signs of q and w for the gases under these conditions?

For which of the following reactions does \(\Delta H_{r x n}^{\circ}=\Delta H_{f}^{\circ}\)? (a) \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{S}(\text { rhombic }) \rightarrow \mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) (b) \(C(\text { diamond })+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})\) (c) \(H_{2}(g)+C u O(s) \rightarrow H_{2} O(l)+C u(s)\) (d) \(O(g)+O_{2}(g) \rightarrow O_{3}(g)\)

Calculate the work done (in joules) when 1.0 mole of water is frozen at \(0^{\circ} \mathrm{C}\) and 1.0 atm. The volumes of one mole of water and ice at \(0^{\circ} \mathrm{C}\) are 0.0180 L and 0.0196 L, respectively.

A quantity of 0.020 mole of a gas initially at 0.050 L and \(20^{\circ} \mathrm{C}\) undergoes a constant-temperature expansion until its volume is 0.50 L. Calculate the work done (in joules) by the gas if it expands (a) against a vacuum and (b) against a constant pressure of 0.20 atm. (c) If the gas in (b) is allowed to expand unchecked until its pressure is equal to the external pressure, what would its final volume be before it stopped expanding, and what would be the work done?

Calculate the standard enthalpy of formation for diamond, given that \(\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) \(\Delta H^{\circ}=-393.5\ \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{C}(\text { diamond })+\mathrm{O}_{2}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})\) \(\Delta H^{\circ}=-395.4\ \mathrm{kJ} / \mathrm{mol}\)

(a) For most efficient use, refrigerator freezer compartments should be fully packed with food. What is the thermochemical basis for this recommendation? (b) Starting at the same temperature, tea and coffee remain hot longer in a thermal flask than chicken noodle soup. Explain.

Calculate the standard enthalpy change for the fermentation process. (See Problem 3.72.)

Portable hot packs are available for skiers and people engaged in other outdoor activities in a cold climate. The air-permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. The exothermic reaction that produces the heat is a very common one—the rusting of iron: \(4 F e(s)+3 O_{2}(g) \rightarrow 2 F e_{2} O_{3}(s)\) When the outside plastic envelope is removed, \(\mathrm{O}_{2}\) molecules penetrate the paper, causing the reaction to begin. A typical packet contains 250 g of iron to warm your hands or feet for up to 4 hours. How much heat (in kJ) is produced by this reaction? (Hint: See Appendix 3 for \(\Delta H_{f}^{\circ}\) values.)

A person ate 0.50 pound of cheese (an energy intake of 4000 kJ). Suppose that none of the energy was stored in his body. What mass (in grams) of water would he need to perspire in order to maintain his original temperature? (It takes 44.0 kJ to vaporize 1 mole of water.)

The total volume of the Pacific Ocean is estimated to be \(7.2 \times 10^{8}\ \mathrm{km}^{3}\). A medium-sized atomic bomb produces \(1.0 \times 10^{15}\ \mathrm{J}\) of energy upon explosion. Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by \(1^{\circ} \mathrm{C}\).

A 19.2-g quantity of dry ice (solid carbon dioxide) is allowed to sublime (evaporate) in an apparatus like the one shown in Figure 6.5. Calculate the expansion work done against a constant external pressure of 0.995 atm and at a constant temperature of \(22^{\circ} \mathrm{C}\). Assume that the initial volume of dry ice is negligible and that \(\mathrm{CO}_{2}\) behaves like an ideal gas.

The enthalpy of combustion of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) is commonly used as the standard for calibrating constant-volume bomb calorimeters; its value has been accurately determined to be -3226.7 kJ/mol. When 1.9862 g of benzoic acid are burned in a calorimeter, the temperature rises from \(21.84^{\circ} \mathrm{C}\) to \(25.67^{\circ} \mathrm{C}\). What is the heat capacity of the bomb? (Assume that the quantity of water surrounding the bomb is exactly 2000 g.)

The combustion of a 25.0-g gaseous mixture of \(\mathrm{H}_{2}\) and \(\mathrm{CH}_{4}\) releases 2354 kJ of heat. Calculate the amounts of the gases in grams.

Calcium oxide (CaO) is used to remove sulfur dioxide generated by coal-burning power stations: \(2 \mathrm{CaO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CaSO}_{4}(\mathrm{s})\) Calculate the enthalpy change for this process if \(6.6 \times 10^{5}\ \mathrm{g}\) of \(\mathrm{SO}_{2}\) are removed by this process every day.

Glauber's salt, sodium sulfate decahydrate \(\left(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\right)\), undergoes a phase transition (that is, melting or freezing) at a convenient temperature of about \(32^{\circ} \mathrm{C}\): \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\Delta H^{\circ}=74.4\ \mathrm{kJ} / \mathrm{mol}\) As a result, this compound is used to regulate the temperature in homes. It is placed in plastic bags in the ceiling of a room. During the day, the endothermic melting process absorbs heat from the surroundings, cooling the room. At night, it gives off heat as it freezes. Calculate the mass of Glauber's salt in kilograms needed to lower the temperature of air in a room by \(8.2^{\circ} \mathrm{C}\) at 1.0 atm. The dimensions of the room are \(2.80\ m \times 10.6\ m \times 17.2\ m\), the specific heat of air is \(1.2\ \mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\), and the molar mass of air may be taken as 29.0 g/mol.

A balloon \(16 \mathrm{~m}\) in diameter is inflated with helium at \(18^{\circ} \mathrm{C}\). (a) Calculate the mass of \(\mathrm{He}\) in the balloon, assuming ideal behavior. (b) Calculate the work done (in joules) during the inflation process if the atmospheric pressure is \(8.7 \mathrm{kPa}\).

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) can be hydrogenated (reacting with hydrogen) first to ethylene \(\left(C_{2} H_{4}\right)\) and then to ethane \(\left(C_{2} H_{6}\right)\). Starting with one mole of \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\), label the diagram shown here analogous to Figure 6.10. Use the data in Appendix 3.

Calculate the \(\Delta H^{\circ}\) for the reaction \(F e^{3+}(a q)+3 O H^{-}(a q) \rightarrow F e(O H)_{3}(s)\)

An excess of zinc metal is added to 50.0 mL of a 0.100 M \(\mathrm{AgNO}_{3}\) solution in a constant-pressure calorimeter like the one pictured in Figure 6.9. As a result of the reaction \(Z n(s)+2 \mathrm{Ag}^{+}(a q) \rightarrow Z n^{2+}(a q)+2 A g(s)\) the temperature rises from \(19.25^{\circ} \mathrm{C}\) to \(22.17^{\circ} \mathrm{C}\). If the heat capacity of the calorimeter is \(98.6\ \mathrm{J} /{ }^{\circ} \mathrm{C}\), calculate the enthalpy change for the above reaction on a molar basis. Assume that the density and specific heat of the solution are the same as those for water, and ignore the specific heats of the metals.

(a) A person drinks four glasses of cold water \(\left(3.0^{\circ} \mathrm{C}\right)\) every day. The volume of each glass is \(2.5 \times 10^{2}\ m L\). How much heat (in kJ) does the body have to supply to raise the temperature of the water to \(37^{\circ} \mathrm{C}\), the body temperature? (b) How much heat would your body lose if you were to ingest \(8.0 \times 10^{2}\ \mathrm{g}\) of snow at \(0^{\circ} \mathrm{C}\) to quench thirst? (The amount of heat necessary to melt snow is 6.01 kJ/mol.)

A driver's manual states that the stopping distance quadruples as the speed doubles; that is, if it takes 30 ft to stop a car moving at 25 mph then it would take 120 ft to stop a car moving at 50 mph. Justify this statement by using mechanics and the first law of thermodynamics. [Assume that when a car is stopped, its kinetic energy \(\left(\frac{1}{2} m u^{2}\right)\) is totally converted to heat.]

At \(25^{\circ} \mathrm{C}\), the standard enthalpy of formation of HF(aq) is given by - 320.1 kJ/mol; of \(O H^{-}(a q)\), it is -229.6 kJ/mol; of \(F^{-}(a q)\), it is - 329.1 kJ/mol; and of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\), it is -285.8 kJ/mol. (a) Calculate the standard enthalpy of neutralization of HF(aq): \(H F(a q)+O H^{-}(a q) \rightarrow H_{2} O(l)\) (b) Using the value of -56.2 kJ as the standard enthalpy change for the reaction \(H^{+}(a q)+O H^{-}(a q) \rightarrow H_{2} O(l)\) calculate the standard enthalpy change for the reaction \(H F(a q) \rightarrow H^{+}(a q)+F^{-}(a q)\)

Why are cold, damp air and hot, humid air more uncomfortable than dry air at the same temperatures? (The specific heats of water vapor and air are approximately \(1.9\ \mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) and \(1.0\ \mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\), respectively.)

From the enthalpy of formation for \(\mathrm{CO}_{2}\) and the following information, calculate the standard enthalpy of formation for carbon monoxide (CO). \(\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) \(\Delta H^{\circ}=-283.0\ \mathrm{kJ} / \mathrm{mol}\) Why can't we obtain it directly by measuring the enthalpy of the following reaction? \(C(\text { graphite })+\frac{1}{2} O_{2}(g) \rightarrow C O(g)\)

A 46-kg person drinks 500 g of milk, which has a "caloric" value of approximately 3.0 kJ/g. If only 17 percent of the energy in milk is converted to mechanical work, how high (in meters) can the person climb based on this energy intake? (Hint: The work done in ascending is given by mgh, where m is the mass (in kilograms), g the gravitational acceleration \(\left(9.8\ \mathrm{m} / \mathrm{s}^{2}\right)\), and h the height (in meters).]

The height of Niagara Falls on the American side is 51 m. (a) Calculate the potential energy of 1.0 g of water at the top of the falls relative to the ground level. (b) What is the speed of the falling water if all of the potential energy is converted to kinetic energy? (c) What would be the increase in temperature of the water if all the kinetic energy were converted to heat? (See Problem 6.121 for suggestions.)

In the nineteenth century two scientists named Dulong and Petit noticed that for a solid element, the product of its molar mass and its specific heat is approximately \(25\ \mathrm{J} /{ }^{\circ} \mathrm{C}\). This observation, now called Dulong and Petit's law, was used to estimate the specific heat of metals. Verify the law for the metals listed in Table 6.2. The law does not apply to one of the metals. Which one is it? Why?

Determine the standard enthalpy of formation of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) from its standard enthalpy of combustion (-1367.4 kJ/mol).

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(C_{6} H_{6}\right)\) have the same empirical formula. In fact, benzene can be made from acetylene as follows: \(3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{6}(l)\) The enthalpies of combustion for \(\mathrm{C}_{2} \mathrm{H}_{2}\) and \(C_{6} H_{6}\) are - 1299.4 kJ/mol and -3267.4 kJ/mol, respectively. Calculate the standard enthalpies of formation of \(\mathrm{C}_{2} \mathrm{H}_{2}\) and \(C_{6} H_{6}\) and hence the enthalpy change for the formation of \(C_{6} H_{6}\) from \(\mathrm{C}_{2} \mathrm{H}_{2}\).

Ice at \(0^{\circ} \mathrm{C}\) is placed in a Styrofoam cup containing 361 g of a soft drink at \(23^{\circ} \mathrm{C}\). The specific heat of the drink is about the same as that of water. Some ice remains after the ice and soft drink reach an equilibrium temperature of \(0^{\circ} \mathrm{C}\). Determine the mass of ice that has melted. Ignore the heat capacity of the cup. (Hint: It takes 334 J to melt 1g of ice at \(0^{\circ} \mathrm{C}\).)

How much heat is required to decompose 89.7 g of \(\mathrm{NH}_{4} \mathrm{Cl}\)? (Hint: You may use the enthalpy of formation values at \(25^{\circ} \mathrm{C}\) for the calculation.)

After a dinner party, the host performed the following trick. First, he blew out one of the burning candles. He then quickly brought a lighted match to about 1 in above the wick. To everyone's surprise, the candle was relighted. Explain how the host was able to accomplish the task without touching the wick.

A gas company in Massachusetts charges $1.30 for \(15\ f t^{3}\) of natural gas \(\left(\mathrm{CH}_{4}\right)\) measured at \(20^{\circ} \mathrm{C}\) and 1.0 atm. Calculate the cost of heating 200 mL of water (enough to make a cup of coffee or tea) from \(20^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). Assume that only 50 percent of the heat generated by the combustion is used to heat the water; the rest of the heat is lost to the surroundings.

Calculate the internal energy of a Goodyear blimp filled with helium gas at \(1.2 \times 10^{5}\ \mathrm{Pa}\). The volume of the blimp is \(5.5 \times 10^{3}\ \mathrm{m}^{3}\). If all the energy were used to heat 10.0 tons of copper at \(21^{\circ} \mathrm{C}\), calculate the final temperature of the metal. (Hint: See Section 5.7 for help in calculating the internal energy of a gas. \(1 \text { ton }=9.072 \times 10^{5}\ \mathrm{g}\).)

Decomposition reactions are usually endothermic, whereas combination reactions are usually exothermic. Give a qualitative explanation for these trends.

Acetylene \(\left(C_{2} H_{2}\right)\) can be made by reacting calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) with water. (a) Write an equation for the reaction. (b) What is the maximum amount of heat (in joules) that can be obtained from the combustion of acetylene, starting with 74.6 g of \(\mathrm{CaC}_{2}\)?

The average temperature in deserts is high during the day but quite cool at night, whereas that in regions along the coastline is more moderate. Explain.

When 1.034 g of naphthalene \(\left(C_{10} H_{8}\right)\) are burned in a constant-volume bomb calorimeter at 298 K, 41.56 kJ of heat are evolved. Calculate \(\Delta U\) and \(\Delta H\) for the reaction on a molar basis.

From a thermochemical point of view, explain why a carbon dioxide fire extinguisher or water should not be used on a magnesium fire.

Calculate the \(\Delta U\) for the following reaction at 298 K: \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

Lime is a term that includes calcium oxide (CaO, also called quicklime) and calcium hydroxide \(\mathrm{Ca}(\mathrm{OH})_{2}\), also called slaked lime]. It is used in the steel industry to remove acidic impurities, in air-pollution control to remove acidic oxides such as \(\mathrm{SO}_{2}\), and in water treatment. Quicklime is made industrially by heating limestone \(\left(\mathrm{CaCO}_{3}\right)\) above \(2000^{\circ} \mathrm{C}\): \(\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(g)\) \(\Delta H^{\circ}=177.8\ \mathrm{kJ} / \mathrm{mol}\) Slaked lime is produced by treating quicklime with water: \(\mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) \(\Delta H^{\circ}=-65.2\ \mathrm{kJ} / \mathrm{mol}\) The exothermic reaction of quicklime with water and the rather small specific heats of both quicklime \(0.946\ \mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) and slaked lime \(\left(1.20\ \mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) make it hazardous to store and transport lime in vessels made of wood. Wooden sailing ships carrying lime would occasionally catch fire when water leaked into the hold. (a) If a 500-g sample of water reacts with an equimolar amount of CaO (both at an initial temperature of \(25^{\circ} \mathrm{C}\)), what is the final temperature of the product, \(\mathrm{Ca}(\mathrm{OH})_{2}\)? Assume that the product absorbs all of the heat released in the reaction. (b) Given that the standard enthalpies of formation of CaO and \(\mathrm{H}_{2} \mathrm{O}\) are -635.6 kJ/mol and -285.8 kJ/mol, respectively, calculate the standard enthalpy of formation of \(\mathrm{Ca}(\mathrm{OH})_{2}\).

A 4.117-g impure sample of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) was burned in a constant-volume calorimeter having a heat capacity of \(19.65\ \mathrm{kJ} /{ }^{\circ} \mathrm{C}\). If the rise in temperature is \(3.134^{\circ} \mathrm{C}\), calculate the percent by mass of the glucose in the sample. Assume that the impurities are unaffected by the combustion process. See Appendix 3 for thermodynamic data.

Construct a table with the headings q, w, \(\Delta U\), and \(\Delta H\). For each of the following processes, deduce whether each of the quantities listed is positive (+), negative (-), or zero (0). (a) Freezing of benzene. (b) Compression of an ideal gas at constant temperature. (c) Reaction of sodium with water. (d) Boiling liquid ammonia. (e) Heating a gas at constant volume. (f) Melting of ice.

Metabolic activity in the human body releases approximately \(1.0 \times 10^{4}\ \mathrm{kJ}\) of heat per day. Assuming the body is 50 kg of water, how much would the body temperature rise if it were an isolated system? How much water must the body eliminate as perspiration to maintain the normal body temperature \(\left(98.6^{\circ} \mathrm{F}\right)\)? Comment on your results. The heat of vaporization of water may be taken as 2.41 kJ/g.

The combustion of 0.4196 g of a hydrocarbon releases 17.55 kJ of heat. The masses of the products are \(\mathrm{CO}_{2}=1.419\ \mathrm{g}\) and \(\mathrm{H}_{2} \mathrm{O}=0.290\ \mathrm{g}\). (a) What is the empirical formula of the compound? (b) If the approximate molar mass of the compound is 76 g, calculate its standard enthalpy of formation.

Give an example for each of the following situations: (a) Adding heat to a system raises its temperature, (b) adding heat to a system does not change (raise) its temperature, and (c) a system's temperature is changed even though no heat is added or removed from it.

From the following data, calculate the heat of solution for KI:

Starting at A, an ideal gas undergoes a cyclic process involving expansion and compression, as shown here. Calculate the total work done. Does your result support the notion that work is not a state function?

For reactions in condensed phases (liquids and solids), the difference between \(\Delta H\) and \(\Delta U\) is usually quite small. This statement holds for reactions carried out under atmospheric conditions. For certain geochemical processes, however, the external pressure may be so great that \(\Delta H\) and \(\Delta U\) can differ by a significant amount. A well-known example is the slow conversion of graphite to diamond under Earth's surface. Calculate \((\Delta H-\Delta U)\) for the conversion of 1 mole of graphite to 1 mole of diamond at a pressure of 50,000 atm. The densities of graphite and diamond are \(2.25\ \mathrm{g} / \mathrm{cm}^{3}\) and \(3.52\ \mathrm{g} / \mathrm{cm}^{3}\), respectively.

The diagrams shown on p. 273 represent various physical and chemical processes. (a) \(2 A(g) \rightarrow A_{2}(g)\). (b) \(M X(s) \rightarrow M^{+}(a q)+X^{-}(a q)\). (c) \(A B(g)+C(g) \rightarrow A C(g)+B(g)\). (d) \(B(l) \rightarrow B(g)\). Predict whether the situations shown are endothermic or exothermic. Explain why in some cases no clear conclusions can be made.

Which of the following standard enthalpy of formation values is not zero at \(25^{\circ} \mathrm{C}\)? \(\mathrm{Na}(\mathrm{s}),\ \mathrm{Ne}(g),\ \mathrm{CH}_{4}(g),\ \mathrm{S}_{8}(s),\ \mathrm{Hg}(l),\ \mathrm{H}(g)\).

Which is the more negative quantity at \(25^{\circ} \mathrm{C}\): \(\Delta H_{f}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) or \(\Delta H_{f}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)?

The \(\Delta H_{\mathrm{f}}^{\circ}\) values of the two allotropes of oxygen, \(\mathrm{O}_{2}\) and \(\mathrm{O}_{3}\), are 0 and \(142.2 \mathrm{~kJ} / \mathrm{mol}\), respectively, at \(25^{\circ} \mathrm{C}\). Which is the more stable form at this temperature?

Predict the value of \(\Delta H_{f}^{\circ}\) (greater than, less than, or equal to zero) for these elements at \(25^{\circ} \mathrm{C}\): (a) \(B r_{2}(g) ; B r_{2}(l)\). (b) \(I_{2}(g) ; I_{2}(s)\).

In general, compounds with negative \(\Delta H_{f}^{\circ}\) values are more stable than those with positive \(\Delta H_{f}^{\circ}\) values. \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{l})\) has a negative \(\Delta H_{f}^{\circ}\) (see Table 6.4). Why, then, does \(\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{l})\) have a tendency to decompose to \(H_{2} O(l)\) and \(O_{2}(g)\)?

Suggest ways (with appropriate equations) that would enable you to measure the \(\Delta H_{f}^{\circ}\) values of \(A g_{2} O(s)\) and \(\mathrm{CaCl}_{2}(\mathrm{s})\) from their elements. No calculations are necessary.

Calculate the heat of decomposition for this process at constant pressure and \(25^{\circ} \mathrm{C}\): \(\mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) (Look up the standard enthalpy of formation of the reactant and products in Table 6.4.)

The standard enthalpies of formation of ions in aqueous solutions are obtained by arbitrarily assigning a value of zero to \(H^{+}\) ions; that is, \(\Delta H_{f}^{0}\left[H^{+}(a q)\right]=0\). (a) For the following reaction \(HCI(g)\ \xrightarrow{H_{2}O}\ H^{+} (aq)+Cl^{-}(aq)\) \(\Delta H^{\circ}=-74.9\ \mathrm{kJ} / \mathrm{mol}\) calculate \(\Delta H_{f}^{\circ}\) for the \(C l^{-}\) ions. (b) Given that \(\Delta H_{f}^{\circ}\) for \(\mathrm{OH}^{-}\) ions is - 229.6 kJ/mol, calculate the enthalpy of neutralization when 1 mole of a strong monoprotic acid (such as HCl) is titrated by 1 mole of a strong base (such as KOH) at \(25^{\circ} \mathrm{C}\).

Calculate the heats of combustion for the following reactions from the standard enthalpies of formation listed in Appendix 3: (a) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (b) \(2 \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

Methanol, ethanol, and n-propanol are three common alcohols. When 1.00 g of each of these alcohols is burned in air, heat is liberated as shown by the following data: (a) methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\), – 22.6 kJ; (b) ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\), -29.7 kJ; (c) n-propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\), -33.4 kJ. Calculate the heats of combustion of these alcohols in kJ/mol.

Calculate the heats of combustion for the following reactions from the standard enthalpies of formation listed in Appendix 3: (a) \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (b) \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g})+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{SO}_{2}(g)\)

The standard enthalpy change for the following reaction is 436.4 kJ/mol: \(H_{2}(g) \rightarrow H(g)+H(g)\) Calculate the standard enthalpy of formation of atomic hydrogen (H).

From the standard enthalpies of formation, calculate \(\Delta H_{r x n}^{\circ}\) for the reaction \(\mathrm{C}_{6} \mathrm{H}_{12}(\mathrm{l})+9 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) For \(C_{6} H_{12}(l),\ \Delta H_{f}^{\circ}=-151.9 \mathrm{~kJ} / \mathrm{mol}\).

Pentaborane-9, \(\text{B}_5\text{H}_9\), is a colorless, highly reactive liquid that will burst into flame when exposed to oxygen. The reaction is \(2\text{B}_5\text{H}_9(l)+12\text{O}_2(g)\rightarrow 5\text{B}_2\text{O}_3(s)+9\text{H}_2\text{O}(l)\) Calculate the kilojoules of heat released per gram of the compound reacted with oxygen. The standard enthalpy of formation of \(\text{B}_5\text{H}_9\) is 73.2 kJ/mol.

Determine the amount of heat (in kJ) given off when \(1.26 \times 10^{4}\ \mathrm{g}\) of ammonia are produced according to the equation \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)\) \(\Delta H_{r x n}^{\circ}=-92.6\ \mathrm{kJ} / \mathrm{mol}\) Assume that the reaction takes place under standard state conditions at \(25^{\circ} \mathrm{C}\).

At \(850^{\circ} \mathrm{C}, \mathrm{CaCO}_{3}\) undergoes substantial decomposition to yield \(\mathrm{CaO}\) and \(\mathrm{CO}_{2}\). Assuming that the \(\Delta H_{\mathrm{f}}^{\circ}\) values of the reactant and products are the same at \(850^{\circ} \mathrm{C}\) as they are at \(25^{\circ} \mathrm{C}\), calculate the enthalpy change (in \(\mathrm{kJ}\) ) if \(66.8 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) are produced in one reaction.

From these data, \(\mathrm{S}(\text { rhombic })+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)\) \(\Delta H_{r x n}^{\circ}=-296.06 \mathrm{~kJ} / \mathrm{mol}\) \(S(\text { monoclinic })+O_{2}(g) \rightarrow \mathrm{SO}_{2}(g)\) \(\Delta H_{r x n}^{\circ}=-296.36\ \mathrm{kJ} / \mathrm{mol}\) calculate the enthalpy change for the transformation \(S(\text { rhombic }) \rightarrow S(\text { monoclinic })\) (Monoclinic and rhombic are different allotropic forms of elemental sulfur.)

From the following data, \(\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(g)\) \(\Delta H_{r x n}^{\circ}=-393.5\ \mathrm{kJ} / \mathrm{mol}\) \(H_{2}(g)+\frac{1}{2} O_{2}(g) \rightarrow H_{2} O(l)\) \(\Delta H_{r x n}^{\circ}=-285.8\ \mathrm{kJ} / \mathrm{mol}\) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})+7 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\Delta H_{r x n}^{\circ}=-3119.6\ \mathrm{kJ} / \mathrm{mol}\) calculate the enthalpy change for the reaction \(2 \mathrm{C}(\text { graphite })+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})\)

From the following heats of combustion, \(\mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H_{r x n}^{\circ}=-726.4\ \mathrm{kJ} / \mathrm{mol}\) \(C(\text { graphite })+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(\mathrm{g})\) \(\Delta H_{r x n}^{\circ}=-393.5\ \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\Delta H_{r x n}^{\circ}=-285.8\ \mathrm{kJ} / \mathrm{mol}\) calculate the enthalpy of formation of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) from its elements: \(\mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})\)

Calculate the standard enthalpy change for the reaction \(2 \mathrm{Al}(\mathrm{s})+\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})\) given that \(2 \mathrm{Al}(\mathrm{s})+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})\) \(\Delta H_{r x n}^{\circ}=-1669.8\ \mathrm{kJ} / \mathrm{mol}\) \(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) \(\Delta H_{r x n}^{\circ}=-822.2\ \mathrm{kJ} / \mathrm{mol}\)

Define the following terms: enthalpy of solution, heat of hydration, lattice energy, heat of dilution.

Why is the lattice energy of a solid always a positive quantity? Why is the hydration of ions always a negative quantity?

Consider two ionic compounds A and B. A has a larger lattice energy than B. Which of the two compounds is more stable?

\(M g^{2+}\) is a smaller cation than \(\mathrm{Na}^{+}\) and also carries more positive charge. Which of the two species has a larger hydration energy (in kJ/mol)? Explain.

Why is it dangerous to add water to a concentrated acid such as sulfuric acid in a dilution process?

Consider the dissolution of an ionic compound such as potassium fluoride in water. Break the process into the following steps: separation of the cations and anions in the vapor phase and the hydration of the ions in the aqueous medium. Discuss the energy changes associated with each step. How does the heat of solution of KF depend on the relative magnitudes of these two quantities? On what law is the relationship based?

Which of the following does not have \(\Delta H_{f}^{\circ}=0\) at \(25^{\circ} \mathrm{C}\)? \(H e(g) \quad F e(s) \quad C l(g) \quad S_{8}(s) \quad O_{2}(g) \quad B r_{2}(l)\)

Calculate the expansion work done when 3.70 moles of ethanol are converted to vapor at its boiling point \(\left(78.3^{\circ} \mathrm{C}\right)\) and 1.0 atm.

The convention of arbitrarily assigning a zero enthalpy value for the most stable form of each element in the standard state at \(25^{\circ} \mathrm{C}\) is a convenient way of dealing with enthalpies of reactions. Explain why this convention cannot be applied to nuclear reactions.

Given the thermochemical equations: \(B r_{2}(l)+F_{2}(g) \rightarrow 2 B r F(g)\) \(\Delta H^{\circ}=-188\ \mathrm{kJ} / \mathrm{mol}\) \(B r_{2}(l)+3 F_{2}(g) \rightarrow 2 B r F_{3}(g)\) \(\Delta H^{\circ}=-768\ \mathrm{kJ} / \mathrm{mol}\) calculate the \(\Delta H_{r x n}^{\circ}\) for the reaction \(B r F(g)+F_{2}(g) \rightarrow B r F_{3}(g)\)

The standard enthalpy change \(\Delta H^{\circ}\) for the thermal decomposition of silver nitrate according to the following equation is +78.67 kJ: \(\mathrm{AgNO}_{3}(s) \rightarrow A g N \mathrm{NO}_{2}(s)+\frac{1}{2} \mathrm{O}_{2}(g)\) The standard enthalpy of formation of \(\mathrm{AgNO}_{3}(\mathrm{s})\) is -123.02 kJ/mol. Calculate the standard enthalpy of formation of \(\mathrm{AgNO}_{2}(s)\).

Hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\), decomposes according to the following reaction: \(3 \mathrm{~N}_{2} \mathrm{H}_{4}(l) \longrightarrow 4 \mathrm{NH}_{3}(g)+\mathrm{N}_{2}(g)\) (a) Given that the standard enthalpy of formation of hydrazine is \(50.42 \mathrm{~kJ} / \mathrm{mol}\), calculate \(\Delta H^{\circ}\) for its decomposition. (b) Both hydrazine and ammonia burn in oxygen to produce \(\mathrm{H}_{2} \mathrm{O}(l)\) and \(\mathrm{N}_{2}(g)\). Write balanced equations for each of these processes and calculate \(\Delta H^{\circ}\) for each of them. On a mass basis (per \(\mathrm{kg}\) ), would hydrazine or ammonia be the better fuel?

A quantity of \(2.00 \times 10^{2}\ \mathrm{mL}\) of 0.862 M HCl is mixed with an equal volume of \(0.431\ M\ B a(O H)_{2}\) in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the HCl and \(B a(O H)_{2}\) solutions is the same at \(20.48^{\circ} \mathrm{C}\), For the process \(H^{+}(a q)+O H^{-}(a q) \rightarrow H_{2} O(l)\) the heat of neutralization is - 56.2 kJ/mol. What is the final temperature of the mixed solution?

A 3.53-g sample of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) was added to 80.0 mL of water in a constant pressure calorimeter of negligible heat capacity. As a result, the temperature of the water decreased from \(21.6^{\circ} \mathrm{C}\) to \(18.1^{\circ} \mathrm{C}\). Calculate the heat of solution \(\left(\Delta H_{\text {soln }}\right)\) of ammonium nitrate.

Consider the reaction \(N_{2}(g)+3 H_{2}(g) \rightarrow 2 N H_{3}(g)\) \(\Delta H_{r x n}^{\circ}=-92.6\ \mathrm{kJ} / \mathrm{mol}\) If 2.0 moles of \(N_{2}\) react with 6.0 moles of \(H_{2}\) to form \(\mathrm{NH}_{3}\), calculate the work done (in joules) against a pressure of 1.0 atm at \(25^{\circ} \mathrm{C}\). What is \(\Delta U\) for this reaction? Assume the reaction goes to completion.

Calculate the heat released when \(2.00 \mathrm{~L}\) of \(\mathrm{Cl}_{2}(g)\) with a density of \(1.88 \mathrm{~g} / \mathrm{L}\) react with an excess of sodium metal at \(25^{\circ} \mathrm{C}\) and 1 atm to form sodium chloride.

Photosynthesis produces glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and oxygen from carbon dioxide and water: \(6 \mathrm{CO}_{2}+6 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+6 \mathrm{O}_{2}\) (a) How would you determine experimentally the \(\Delta H_{r x n}^{\circ}\) value for this reaction? (b) Solar radiation produces about \(7.0 \times 10^{14}\ \mathrm{kg}\) glucose a year on Earth. What is the corresponding \(\Delta H^{\circ}\) change?

A 2.10-mole sample of crystalline acetic acid, initially at \(17.0^{\circ} \mathrm{C}\), is allowed to melt at \(17.0^{\circ} \mathrm{C}\) and is then heated to \(118.1^{\circ} \mathrm{C}\) (its normal boiling point) at 1.00 atm. The sample is allowed to vaporize at \(118.1^{\circ} \mathrm{C}\) and is then rapidly quenched to \(17.0^{\circ} \mathrm{C}\), so that it recrystallizes. Calculate \(\Delta H^{\circ}\) for the total process as described.

Calculate the work done in joules by the reaction \(2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)\) when \(0.34 \mathrm{~g}\) of Na reacts with water to form hydrogen gas at \(0^{\circ} \mathrm{C}\) and \(1.0\) atm.

You are given the following data: \(\mathrm{H}_{2}(g) \rightarrow 2 \mathrm{H}(\mathrm{g}) \quad \Delta H^{\circ}=436.4\ \mathrm{kJ} / \mathrm{mol}\) \(B r_{2}(g) \rightarrow 2 B r(g) \quad \Delta H^{\circ}=192.5\ \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \rightarrow 2 \mathrm{HBr}(g)\) \(\Delta H^{\circ}=-72.4\ \mathrm{kJ} / \mathrm{mol}\) Calculate \(\Delta H^{\circ}\) for the reaction \(H(g)+B r(g) \rightarrow H B r(g)\)

A gaseous mixture consists of 28.4 mole percent of hydrogen and 71.6 mole percent of methane. A 15.6-L gas sample, measured at \(19.4^{\circ} \mathrm{C}\) and 2.23 atm, is burned in air. Calculate the heat released.

When 2.740 g of Ba reacts with \(\mathrm{O}_{2}\) at 298 K and 1 atm to form Bao, 11.14 kJ of heat are released. What is \(\Delta H_{f}^{\circ}\) for BaO?

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) is an organic solvent and is also used as a fuel in some automobile engines. From the following data, calculate the standard enthalpy of formation of methanol: \(2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H_{r x n}^{\circ}=-1452.8\ \mathrm{kJ} / \mathrm{mol}\)

A 44.0-g sample of an unknown metal at \(99.0^{\circ} \mathrm{C}\) was placed in a constant-pressure calorimeter containing 80.0 g of water at \(24.0^{\circ} \mathrm{C}\). The final temperature of the system was found to be \(28.4^{\circ} \mathrm{C}\). Calculate the specific heat of the metal. (The heat capacity of the calorimeter is \(12.4\ \mathrm{J} /{ }^{\circ} \mathrm{C}\).)

Using the data in Appendix 3, calculate the enthalpy change for the gaseous reaction shown here. (Hint: First determine the limiting reagent.)

Producer gas (carbon monoxide) is prepared by passing air over red-hot coke: \(C(s)+\frac{1}{2} O_{2}(g) \rightarrow C O(g)\) Water gas (mixture of carbon monoxide and hydrogen) is prepared by passing steam over red-hot coke: \(C(s)+H_{2} O(g) \rightarrow C O(g)+H_{2}(g)\) For many years, both producer gas and water gas were used as fuels in industry and for domestic cooking. The large-scale preparation of these gases was carried out alternately, that is, first producer gas, then water gas, and so on. Using thermochemical reasoning, explain why this procedure was chosen.

Compare the heat produced by the complete combustion of 1 mole of methane \(\left(\mathrm{CH}_{4}\right)\) with a mole of water gas (0.50 mole \(H_{2}\) and 0.50 mole CO) under the same conditions. On the basis of your answer, would you prefer methane over water gas as a fuel? Can you suggest two other reasons why methane is preferable to water gas as a fuel?

The so-called hydrogen economy is based on hydrogen produced from water using solar energy. The gas is then burned as a fuel: \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) A primary advantage of hydrogen as a fuel is that it is non polluting. A major disadvantage is that it is a gas and therefore is harder to store than liquids or solids. Calculate the volume of hydrogen gas at \(25^{\circ} \mathrm{C}\) and 1.00 atm required to produce an amount of energy equivalent to that produced by the combustion of a gallon of octane \(\left(C_{8} H_{18}\right)\). The density of octane is 2.66 kg/gal, and its standard enthalpy of formation is -249.9 kJ/mol.

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and gasoline (assumed to be all octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\) ) are both used as automobile fuel. If gasoline is selling for \(\$ 4.50\) /gal, what would the price of ethanol have to be in order to provide the same amount of heat per dollar? The density and \(\Delta H_{\mathrm{f}}^{\circ}\) of octane are \(0.7025 \mathrm{~g} / \mathrm{mL}\) and \(-249.9 \mathrm{~kJ} / \mathrm{mol}\) and of ethanol are \(0.7894 \mathrm{~g} / \mathrm{mL}\) and \(-277.0 \mathrm{~kJ} / \mathrm{mol}\), respectively. \(1 \mathrm{gal}=3.785 \mathrm{~L}\).

If energy is conserved, how can there be an energy crisis?

The combustion of what volume of ethane \(\left(C_{2} H_{6}\right)\), measured at \(23.0^{\circ} \mathrm{C}\) and 752 mmHg, would be required to heat 855 g of water from \(25.0^{\circ} \mathrm{C}\) to \(98.0^{\circ} \mathrm{C}\)?

What is \(\Delta U\) for the formation of 1 mole of CO at 1 atm and \(25^{\circ} \mathrm{C}\)? \(C(\text { graphite })+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}(\mathrm{g})\) \(\Delta H=-110.5\ \mathrm{kJ}/\mathrm{mol}\)

These are various forms of energy: chemical, heat, light, mechanical, and electrical. Suggest ways of interconverting these forms of energy.

Aniron bar of mass 869 g cools from 94°C to 5°C. Calculate the heat released (in kilojoules) by the metal.

Which of the following does not have \(\Delta H_{f}^{\circ}=0\) at \(25^{\circ} \mathrm{C}\)? \(N_{2}(g) \quad C u(s) \quad K r(g) \quad H g(s) \quad H_{2}(g) \quad I_{2}(s)\)

Describe the interconversions of forms of energy occurring in these processes: (a) You throw a softball up into the air and catch it. (b) You switch on a flashlight. (c) You ride the ski lift to the top of the hill and then ski down. (d) You strike a match and let it burn down.

A quantity of 1.922 g of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) was burned in a constant-volume bomb calorimeter. Consequently, the temperature of the water rose by 4.20°C. If the heat capacity of the bomb plus water was 10.4 kJ/°C. Calculate the molar heat of combustion of methanol.

Explain why reactions involving reactant compounds with positive \(\Delta H_{f}^{\circ}\) values are generally more exothermic than those with negative \(\Delta H_{f}^{\circ}\) values.

Define these terms: thermochemistry, exothermic process, endothermic process.

A 30.14-g stainless steel ball bearing at 117.82°C is placed in a constant-pressure calorimeter containing 120.0 mL of water at 18.44°C. If the specific heat of the ball bearing is \(0.474\mathrm{\ J}/\mathrm{g}\cdot^{\circ}\mathrm{C}\), calculate the final temperature of the water. Assume the calorimeter to have negligible heat capacity.

Use the data in appendix 3 to calculate the heat of solution for the following process: \(\mathrm{KNO}_{3}(s) \rightarrow \mathrm{K}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)\)

Stoichiometry is based on the law of conservation of mass. On what law is thermochemistry based?

Practice Exercise A quantity of \(4.00 \times 10^{2}\ \mathrm{mL}\) of \(0.600\ \mathrm{M}\ \mathrm{HNO}_{3}\) is mixed with \(4.00 \times 10^{2}\ \mathrm{mL}\) of \(0.300\ \mathrm{M\ Ba}(\mathrm{OH})_{2}\) in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of both solutions is the same at \(18.46^{\circ} \mathrm{C}\). What is the final temperature of the solution? (Use the result in Example 6.8 for your calculation.)

Describe two exothermic processes and two endothermic processes.

Calculate the standard enthalphy of formation of carbon disulfide \(\left(C S_{2}\right)\) from its elements given that \(C(\text { graphite })+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) \(S(\text { rhombic })+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g)\) \(\mathrm{CS}_{2}(l)+3 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g)\) \(\Delta H_{r x n}^{\circ}=-393.5 \mathrm{~kJ} / \mathrm{mol}\) \(\Delta H_{r x n}^{\circ}=-296.4 \mathrm{~kJ} / \mathrm{mol}\) \(\Delta H_{r x n}^{\circ}=-1073.6 \mathrm{~kJ} / \mathrm{mol}\)

Decomposition reactions are usually endothermic, whereas combination reactions are usually exothermic. Give a qualitative explanation for these trends.

Practice Exercise Benzene \(\left(C_{6} H_{6}\right)\) burns in air to produce carbon dioxide and liquid water. Calculate the heat released in kilojoules) per gram of the compound reacted with oxygen. The standard enthalpy of formation of benzene is 49.04 kJ/mol.

On what law is the first law of thermodynamics based? Explain the sign conventions in the equation \(\Delta U=q+w\).

Explain what is meant by a state function. Give two examples of quantities that are state functions and two that are not.

The internal energy of an ideal gas depends only on its temperature. Do a first-law analysis of this process. A sample of an ideal gas is allowed to expand at constant temperature against atmospheric pressure. (a) Does the gas do work on its surroundings? (b) Is there heat exchange between the system and the surroundings? If so, in which direction? (c) What is \(\Delta U\) for the gas for this process?

Consider these changes. (a) \(\mathrm{Hg}(l) \longrightarrow \mathrm{Hg}(g)\) (b) \(3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{O}_{3}(g)\) (c) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)\) At constant pressure, in which of the reactions is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

A gas expands in volume from 26.7 mL to 89.3 mL at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum, (b) against a constant pressure of 1.5 atm, and (c) against a constant pressure of 2.8 atm.

A sample of nitrogen gas expands in volume from \(1.6 \mathrm{~L}\) to \(5.4 \mathrm{~L}\) at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of \(0.80 \mathrm{~atm}\), and (c) against a constant pressure of \(3.7 \mathrm{~atm}\).

A gas expands and does \(P-V\) work on the surroundings equal to \(325 \mathrm{~J}\). At the same time, it absorbs \(127 \mathrm{~J}\) of heat from the surroundings. Calculate the change in energy of the gas.

The work done to compress a gas is 74 J. As a result, 26 J of heat is given off to the surroundings. Calculate the change in energy of the gas.

Calculate the work done when 50.0 g of tin dissolves in excess acid at 1.00 atm and 25°C: \(\mathrm{Sn}(\mathrm{s})+2\mathrm{H}^+(\mathrm{aq})\rightarrow\mathrm{Sn}^{2+}(\mathrm{aq})+\mathrm{H}_2(\mathrm{g})\) Assume ideal gas behavior.

Calculate the work done in joules when 1.0 mole of water vaporizes at 1.0 atm and \(100^{\circ} \mathrm{C}\). Assume that the volume of liquid water is negligible compared with that of steam at \(100^{\circ} \mathrm{C}\), and ideal gas behavior.

Define these terms: enthalpy, enthalpy of reaction. Under what condition is the heat of a reaction equal to the enthalpy change of the same reaction?

In writing thermochemical equations, why is it important to indicate the physical state (that is, gaseous, liquid, solid, or aqueous) of each substance?

Explain the meaning of this thermochemical equation: \(4\mathrm{NH}_3(\mathrm{g})+5\mathrm{O}_2\rightarrow4\mathrm{NO}(\mathrm{g})+6\mathrm{H}_2\mathrm{O}\Delta\mathrm{H}=-904\mathrm{\ kJ}/\mathrm{mol}\)

The first step in the industrial recovery of zinc from the zinc sulfide ore is roasting, that is, the conversion of ZnS to ZnO by heating \(2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g)\) \(\Delta H=-879\ \mathrm{kJ}/\mathrm{mol}\) Calculate the heat evolved (in kJ) per gram of ZnS roasted

Consider this reaction: \(2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+3 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+2 \mathrm{CO}_{2}(g)\) \(\Delta H=-1452.8\ \mathrm{kJ} / \mathrm{mol}\) What is the value of \(\Delta H\) if (a) the equation is multiplied throughout by 2, (b) the direction of the reaction is reversed so that the products become the reactants and vice versa, (c) water vapor instead of liquid water is formed as the product?

Determine the amount of heat (in kJ) given off when \(1.26 \times 10^{4}\ \mathrm{g}\) of \(\mathrm{NO}_{2}\) are produced according to the equation \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\) \(\Delta H=-114.6\ \mathrm{kJ} / \mathrm{mol}\)

Consider the reaction \(\begin{aligned}2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow & 2\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \\\Delta H &=483.6 \mathrm{~kJ} / \mathrm{mol}\end{aligned}\) If \(2.0\) moles of \(\mathrm{H}_{2} \mathrm{O}(g)\) are converted to \(\mathrm{H}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) against a pressure of \(1.0\) atm at \(125^{\circ} \mathrm{C}\), what is \(\Delta U\) for this reaction?

Consider the reaction \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) \(\Delta H=-184.6 \mathrm{~kJ} / \mathrm{mol}\) If 3 moles of \(\mathrm{H}_{2}\) react with 3 moles of \(\mathrm{Cl}_{2}\) to form HCI, calculate the work done (in joules) against a pressure of 1.0 atm at \(25^{\circ} \mathrm{C}\). What is \(\Delta U\) for this reaction? Assume the reaction goes to completion.

What is the difference between specific heat and heat capacity? What are the units for these two quantities? Which is the intensive property and which is the extensive property?

Define calorimetry and describe two commonly used calorimeters. In a calorimetric measurement, why is it important that we know the heat capacity of the calorimeter? How is this value determined?

Consider the following data: When these two metals are placed in contact, which of the following will take place? (a) Heat will flow from Al to Cu because Al has a larger specific heat. (b) Heat will flow from Cu to Al because Cu has a larger mass. (c) Heat will flow from Cu to Al because Cu has a larger heat capacity. (d) Heat will flow from Cu to Al because Cu is at a higher temperature. (e) No heat will flow in either direction.

A piece of silver of mass 362 g has a heat capacity of 85.7 J/°C. What is the specific heat of silver?

A 6.22-kg piece of copper metal is heated from 20.5°C to 324.3°C. Calculate the heat absorbed (in kJ) by the metal.

A sheet of gold weighing 10.0 g and at a temperature of \(18.0^{\circ} \mathrm{C}\) is placed flat on a sheet of iron weighing 20.0 g and at a temperature of \(55.6^{\circ} \mathrm{C}\). What is the final temperature of the combined metals? Assume that no heat is lost to the surroundings. (Hint: The heat gained by the gold must be equal to the heat lost by the iron. The specific heats of the metals are given in Table 6.2.)

Calculate the amount of heat liberated (in kJ) from 366 g of mercury when it cools from 77.0°C to 12.0°C.

To a sample of water at \(23.4^{\circ} \mathrm{C}\) in a constant-pressure calorimeter of negligible heat capacity is added a 12.1-g piece of aluminum whose temperature is \(81.7^{\circ} \mathrm{C}\). If the final temperature of water is \(24.9^{\circ} \mathrm{C}\), calculate the mass of the water in the calorimeter. (Hint: See Table 6.2.)

A 0.1375-g sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of \(3024\ \mathrm{J} /{ }^{\circ} \mathrm{C}\). The temperature increases by \(1.126^{\circ} \mathrm{C}\). Calculate the heat given off by the burning Mg, in kJ/g and in kJ/mol.

A quantity of 85.0 mL of 0.900 M HCl is mixed with 85.0 mL of 0.900 M KOH in a constant-pressure calorimeter that has a heat capacity of \(325\ \mathrm{J} /{ }^{\circ} \mathrm{C}\). If the initial temperatures of both solutions are the same at \(18.24^{\circ} \mathrm{C}\), what is the final temperature of the mixed solution? The heat of neutralization is -56.2 kJ/mol. Assume the density and specific heat of the solutions are the same as those for water.

What is meant by the standard-state condition?

How are the standard enthalpies of an element and of a compound determined?

What is meant by the standard enthalpy of a reaction?

Write the equation for calculating the enthalpy of a reaction. Define all the terms.

State Hess’s law. Explain, with one example, the usefulness of Hess’s law in thermochemistry.

Describe how chemists use Hess’s law to determine the \(\Delta H_{f}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

A 20.3-g sample of an unknown metal and a 28.5-g sample of copper, both at \(80.6^{\circ} \mathrm{C}\), are added to 100 g of water at \(11.2^{\circ} \mathrm{C}\) in a constant-pressure calorimeter of negligible heat capacity. If the final temperature of the metals and water is \(13.7^{\circ} \mathrm{C}\), determine the specific heat of the unknown metal.

For most biological processes, \(\Delta H \approx \Delta U\). Explain.

Estimate the potential energy expended by an average adult male in going from the ground to the top floor of the Empire State Building using the staircase.

The fastest serve in tennis is about 150 mph. Can the kinetic energy of a tennis ball traveling at this speed be sufficient to heat 1 mL of water by \(30^{\circ} \mathrm{C}\)?

It has been estimated that 3 trillion standard cubic feet of methane is released into the atmosphere every year. Capturing that methane would provide a source of energy, and it would also remove a potent greenhouse gas from the atmosphere (methane is 25 times more effective at trapping heat than an equal number of molecules of carbon dioxide). Standard cubic feet is measured at \(60^{\circ} \mathrm{F}\) and 1 atm. Determine the amount of energy that could be obtained by combustion of the methane that escapes each year.

What are the units for energy commonly employed in chemistry?

Calculate the heat evolved when 266 g of white phosphorus \(\left(P_{4}\right)\) burns in air according to the equation \(P_{4}(s)+5 O_{2}(g) \rightarrow P_{4} O_{10}(s)\) \(\Delta H=-3013 \mathrm{~kJ} / \mathrm{mol}\)

Which of the constant-pressure processes shown here has the smallest difference between \(\Delta U\) and \(\Delta H\)? (a) \(\text { water } \rightarrow \text { water vapor }\) (b) \(\text { water } \rightarrow \text { ice }\) (c) \(\text { ice } \rightarrow \text { water vapor }\)

A truck initially traveling at 60 km per hour is brought to a complete stop at a traffic light. Does this change violate the law of conservation of energy? Explain.

The heat of vaporization of a liquid \(\left(\Delta H_{v a p}\right)\) is the energy required to vaporize 1.00 g of the liquid at its boiling point. In one experiment, 60.0 g of liquid nitrogen (boiling point \(-196^{\circ} \mathrm{C}\)) are poured into a Styrofoam cup containing \(2.00 \times 10^{2} g\) of water at \(55.3^{\circ} \mathrm{C}\). Calculate the molar heat of vaporization of liquid nitrogen if the final temperature of the water is \(41.0^{\circ} \mathrm{C}\).

Explain the cooling effect experienced when ethanol is rubbed on your skin, given that \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{l}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{g}) \quad \Delta \mathrm{H}^{\circ}=42.2\ \mathrm{kJ} / \mathrm{mol}\)

Biomass plants generate electricity from waste material such as wood chips. Some of these plants convert the feedstock to ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) for later use as a fuel. (a) How many grams of ethanol can be produced from 1.0 ton of wood chips, if 85 percent of the carbon is converted to \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)? (b) How much energy would be released by burning the ethanol obtained from 1.0 ton of wood chips? (Hint: Treat the wood chips as cellulose.)

Suppose an automobile carried hydrogen gas in its fuel tank instead of gasoline. At what pressure would the hydrogen gas need to be kept for the tank to contain an equivalent amount of chemical energy as a tank of gasoline?

A press release announcing a new fuel-cell car to the public stated that hydrogen is "relatively cheap" and "some stations in California sell hydrogen for $5 a kilogram. A kg has the same energy as a gallon of gasoline, so it's like paying $5 a gallon. But you go two to three times as far on the hydrogen." Analyze this claim.

We hear a lot about how the burning of hydrocarbons produces the greenhouse gas \(\mathrm{CO}_{2}\), but what about the effect of increasing energy consumption on the amount of oxygen in the atmosphere required to sustain life. The figure shows past and projected energy world consumption. (a) How many moles of oxygen would be required to generate the additional energy expenditure for the next decade? (b) What would be the resulting decrease in atmospheric oxygen?

A 1-g sample of A1 and a 1-g sample of Fe are heated from \(40^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\). Which metal has absorbed a greater amount of heat?

Can the total energy output of the sun in one second be sufficient to heat all of the ocean water on Earth to its boiling point?