Chapter 5

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

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

Consider the reaction \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \quad \Delta H=-92.6 \mathrm{~kJ} / \mathrm{mol}\) When \(2 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) react with \(6 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) to form \(4 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) at 1 atm and a certain temperature, there is a decrease in volume equal to \(98 \mathrm{~L}\). Calculate \(\Delta U\) for this reaction. (The conversion factor is \(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J} .\)

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

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

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

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

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.

Consider the following two reactions: $$ \begin{array}{ll} \mathrm{A} \longrightarrow 2 \mathrm{~B} & \Delta H_{\mathrm{rxn}}^{\circ}=H_{1} \\\ \mathrm{~A} \longrightarrow \mathrm{C} & \Delta H_{\mathrm{rxn}}^{\circ}=H_{2} \end{array} $$ Determine the enthalpy change for the process $$ 2 \mathrm{~B} \longrightarrow \mathrm{C} $$

The standard enthalpy change \(\Delta H^{\circ}\) for the thermal decomposition of silver nitrate according to the following equation is \(+78.67 \mathrm{~kJ}\) : \(\mathrm{AgNO}_{3}(s) \longrightarrow \mathrm{AgNO}_{2}(s)+\frac{1}{2} \mathrm{O}_{2}(g)\) The standard enthalpy of formation of \(\mathrm{AgNO}_{3}(s)\) is \(-123.02 \mathrm{~kJ} / \mathrm{mol} .\) Calculate the standard enthalpy of formation of \(\mathrm{AgNO}_{2}(s)\).

Consider the reaction: \(2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)\) When 2 moles of Na react with water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), the volume of \(\mathrm{H}_{2}\) formed is \(24.5 \mathrm{~L}\). Calculate the work done in joules when \(0.34 \mathrm{~g}\) of Na reacts with water under the same conditions. (The conversion factor is \(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J} .)\)

A 44.0-g sample of an unknown metal at \(99.0^{\circ} \mathrm{C}\) was placed in a constant-pressure calorimeter containing \(80.0 \mathrm{~g}\) 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 \(12.4 \mathrm{~J} /{ }^{\circ} \mathrm{C} .\)

A student mixes \(88.6 \mathrm{~g}\) of water at \(74.3^{\circ} \mathrm{C}\) with \(57.9 \mathrm{~g}\) of water at \(24.8^{\circ} \mathrm{C}\) in an insulated flask. What is the final temperature of the combined water?

You are given the following data: \(\begin{aligned} \mathrm{H}_{2}(g) & \longrightarrow 2 \mathrm{H}(g) & & \Delta H^{\circ}=436.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{Br}_{2}(g) & \longrightarrow 2 \mathrm{Br}(g) & & \Delta H^{\circ}=192.5 \mathrm{~kJ} / \mathrm{mol} \\\ \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) & \longrightarrow 2 \mathrm{HBr}(g) & \Delta H^{\circ} &=-72.4 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) Calculate \(\Delta H^{\circ}\) for the reaction\(\mathrm{H}(g)+\mathrm{Br}(g) \longrightarrow \mathrm{HBr}(g)\).

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 \(\$ 2.20 / \mathrm{gal},\) 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 \(-249.9 \mathrm{~kJ} / \mathrm{mol}\), respectively, and of ethanol are \(0.7894 \mathrm{~g} / \mathrm{mL}\) and \(-277.0 \mathrm{~kJ} / \mathrm{mol}\) respectively \((1 \mathrm{gal}=3.785 \mathrm{~L})\).

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

For which of the following reactions does \(\Delta H_{\mathrm{rxn}}^{\circ}=\Delta H_{\mathrm{f}}^{\circ}\) ? (a) \(\mathrm{H}_{2}(g)+\mathrm{S}(\) rhombic \() \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)\) (b) \(\mathrm{C}(\) diamond \()+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)\) (c) \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{CuO}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cu}(s)\) (d) \(\mathrm{O}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{3}(g)\)

Calculate the work done (in joules) when \(1.0 \mathrm{~mole}\) of water is frozen at \(0^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\). The volumes of 1 mole of water and ice at \(0^{\circ} \mathrm{C}\) are 0.0180 and \(0.0196 \mathrm{~L},\) respectively. (The conversion factor is \(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J} .)\)

A certain gas initially at \(0.050 \mathrm{~L}\) undergoes expansion until its volume is \(0.50 \mathrm{~L}\). 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. (The conversion factor is \(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J} .\) )

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

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 \(-3226.7 \mathrm{~kJ} / \mathrm{mol}\). When \(1.9862 \mathrm{~g}\) 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 \(2000 \mathrm{~g} .\) )

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

Ice at \(0^{\circ} \mathrm{C}\) is placed in a Styrofoam cup containing \(361 \mathrm{~g}\) 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.

A quantity of \(85.0 \mathrm{~mL}\) of \(0.600 \mathrm{M} \mathrm{HCl}\) is mixed with \(85.0 \mathrm{~mL}\) of \(0.600 \mathrm{M} \mathrm{KOH}\) in a constant- pressure calorimeter. The initial temperature of both solutions is the same at \(17.35^{\circ} \mathrm{C}\), and the final temperature of the mixed solution is \(19.02^{\circ} \mathrm{C}\). What is the heat capacity of the calorimeter? Assume that the specific heat of the solutions is the same as that of water and the molar heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol}\).

When \(1.034 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) is burned in a constant-volume bomb calorimeter at \(298 \mathrm{~K}, 41.56 \mathrm{~kJ}\) of heat is evolved. Calculate \(\Delta U\) and \(w\) 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.

The combustion of \(0.4196 \mathrm{~g}\) of a hydrocarbon releases \(17.55 \mathrm{~kJ}\) 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 \(76 \mathrm{~g} / \mathrm{mol}\), calculate its standard enthalpy of formation.

In a constant-pressure calorimetry experiment, a reaction gives off \(21.8 \mathrm{~kJ}\) of heat. The calorimeter contains \(150 \mathrm{~g}\) of water, initially at \(23.4^{\circ} \mathrm{C}\). What is the final temperature of the water? The heat capacity of the calorimeter is negligibly small.

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 its temperature, and (c) a system's temperature changes despite no heat being added to it or removed from it.

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) reaction of sodium with water, (c) boiling of liquid ammonia, (d) melting of ice, (e) expansion of a gas at constant temperature.

A \(3.52-\mathrm{g}\) sample of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) was added to \(80.0 \mathrm{~mL}\) of water in a constant-pressure calorimeter of negligible heat capacity. As a result, the temperature of the solution decreased from \(21.6^{\circ} \mathrm{C}\) to \(18.1^{\circ} \mathrm{C} .\) Calculate the heat of solution \(\left(\Delta H_{\mathrm{soln}}\right)\) in \(\mathrm{kJ} / \mathrm{mol}:\) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) Assume the specific heat of the solution is the same as that of water.

A quantity of \(50.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) is mixed with \(50.0 \mathrm{~mL}\) of \(0.400 \mathrm{M} \mathrm{HNO}_{3}\) in a constant-pressure calorimeter having a heat capacity of \(496 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The initial temperature of both solutions is the same at \(22.4^{\circ} \mathrm{C}\). What is the final temperature of the mixed solution? Assume that the specific heat of the solutions is the same as that of water and the molar heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol}\).

Producer gas (carbon monoxide) is prepared by passing air over red-hot coke: \(\mathrm{C}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}(g)\) Water gas (a mixture of carbon monoxide and hydrogen) is prepared by passing steam over red-hot coke: \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) 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.

Glauber's salt, sodium sulfate decahydrate \(\left(\mathrm{Na}_{2} \mathrm{SO}_{4} .\right.\) \(\left.10 \mathrm{H}_{2} \mathrm{O}\right),\) undergoes a phase transition (i.e., melting or freezing) at a convenient temperature of about \(32^{\circ} \mathrm{C}\) : \(\begin{aligned}{\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(l)}{\Delta H^{\circ}} &=74.4 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) 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 \(8.2^{\circ} \mathrm{C}\). The mass of air in the room is \(605.4 \mathrm{~kg} ;\) the specific heat of air is \(1.2 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).

An excess of zinc metal is added to \(50.0 \mathrm{~mL}\) of a \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) solution in a constant-pressure calorimeter like the one pictured in Figure 5.8 . As a result of the reaction \(\mathrm{Zn}(s)+2 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Zn}^{2+}(a q)+2 \mathrm{Ag}(s)\) 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 given 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 driver's manual states that the stopping distance quadruples as the speed doubles; that is, if it takes \(30 \mathrm{ft}\) to stop a car moving at \(25 \mathrm{mph}\), then it would take \(120 \mathrm{ft}\) to stop a car moving at \(50 \mathrm{mph}\). 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.)

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.

Consider the reaction $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)$$ Under atmospheric conditions (1.00 atm) it was found that the formation of water resulted in a decrease in volume equal to \(73.4 \mathrm{~L}\). Calculate \(\Delta U\) for the process. \(\Delta H=-571.6 \mathrm{~kJ} / \mathrm{mol}\). (The conversion factor is \(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J} .)\)

A 46-kg person drinks \(500 \mathrm{~g}\) of milk, which has a "caloric" value of approximately \(3.0 \mathrm{~kJ} / \mathrm{g}\). 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?

A man ate 0.50 pound of cheese (an energy intake of \(4 \times 10^{3} \mathrm{~kJ}\) ). 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 \(44.0 \mathrm{~kJ}\) to vaporize 1 mole of water.)

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 \(1.9 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) and \(1.0 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\) respectively.

A woman expends \(95 \mathrm{~kJ}\) of energy walking a kilometer. The energy is supplied by the metabolic breakdown of food, which has an efficiency of 35 percent. How much energy does she save by walking the kilometer instead of driving a car that gets \(8.2 \mathrm{~km}\) per liter of gasoline (approximately \(20 \mathrm{mi} / \mathrm{gal}) ?\) The density of gasoline is \(0.71 \mathrm{~g} / \mathrm{mL},\) and its enthalpy of combustion is \(-49 \mathrm{~kJ} / \mathrm{g}\).

The carbon dioxide exhaled by sailors in a submarine is often removed by reaction with an aqueous lithium hydroxide solution. (a) Write a balanced equation for this process.

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) can be made by combining 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 \(74.6 \mathrm{~g}\) of \(\mathrm{CaC}_{2} ?\)

(a) A person drinks four glasses of cold water \(\left(3.0^{\circ} \mathrm{C}\right)\) every day. The volume of each glass is \(2.5 \times 10^{2} \mathrm{~mL}\). 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 your thirst? (The amount of heat necessary to melt snow is \(6.01 \mathrm{~kJ} / \mathrm{mol}\).)

Metabolic activity in the human body releases approximately \(1.0 \times 10^{4} \mathrm{~kJ}\) of heat per day. Assume that a \(55-\mathrm{kg}\) body has the same specific heat as 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 is \(2.41 \mathrm{~kJ} / \mathrm{g}\).)

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.

Lime is a term that includes calcium oxide \((\mathrm{CaO},\) also called quicklime) and calcium hydroxide \(\left[\mathrm{Ca}(\mathrm{OH})_{2}\right.\) 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 \(2000^{\circ} \mathrm{C}:\) \(\begin{aligned} \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) & \Delta H^{\circ}=177.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) Slaked lime is produced by treating quicklime with water: \(\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)_{\Delta H^{\circ}}=-65.2 \mathrm{~kJ} / \mathrm{mol}\) The exothermic reaction of quicklime with water and the rather small specific heats of both quicklime \(\left[0.946 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\right]\) and slaked lime \(\left[1.20 \mathrm{~J} /\left(\mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right)\right]\) 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 500.0 -g sample of water reacts with an equimolar amount of \(\mathrm{CaO}\) (both at an initial temperature of \(\left.25^{\circ} \mathrm{C}\right)\), what is the final temperature of the product, \(\mathrm{Ca}(\mathrm{OH})_{2} ?\) Assume that the product absorbs all the heat released in the reaction. (b) Given that the standard enthalpies of formation of \(\mathrm{CaO}\) and \(\mathrm{H}_{2} \mathrm{O}\) are -635.6 and \(-285.8 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the standard enthalpy of formation of \(\mathrm{Ca}(\mathrm{OH})_{2}\).

A piece of silver with a mass of \(362 \mathrm{~g}\) has a heat capacity of \(85.7 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). What is the specific heat of silver?