Chapter 8

Titanium is a metal used in jet engines. Its specific heat is \(0.523 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If \(5.88 \mathrm{~g}\) of titanium absorbs \(4.78 \mathrm{~J}\), what is the change in temperature?

Gold has a specific heat of \(0.129 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). When a \(5.00-\mathrm{g}\) piece of gold absorbs \(1.33\) J of heat, what is the change in temperature?

Stainless steel accessories in cars are usually plated with chromium to give them a shiny surface and to prevent rusting. When \(5.00 \mathrm{~g}\) of chromium at \(23.00^{\circ} \mathrm{C}\) absorbs \(62.5 \mathrm{~J}\) of heat, the temperature increases to \(50.8^{\circ} \mathrm{C}\). What is the specific heat of chromium?

Copper is used in building the integrated circuits, chips, and printed circuit boards for computers. When \(228 \mathrm{~J}\) of heat are absorbed by \(125 \mathrm{~g}\) of copper at \(22.38^{\circ} \mathrm{C}\), the temperature increases to \(27.12^{\circ} \mathrm{C}\). What is the specific heat of copper?

Mercury has a specific heat of \(0.140 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). Assume that a thermometer has 20 (2 significant figures) grams of mercury. How much heat is absorbed by the mercury when the temperature in the thermometer increases from \(98.6^{\circ} \mathrm{F}\) to \(103.2^{\circ} \mathrm{F} ?\) (Assume no heat loss to the glass of the thermometer.)

Urea, \(\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\), is used in the manufacture of resins and glues. When \(5.00 \mathrm{~g}\) of urea is dissolved in \(250.0 \mathrm{~mL}\) of water \((d=1.00 \mathrm{~g} / \mathrm{mL})\) at \(30.0^{\circ} \mathrm{C}\) in a coffee-cup calorimeter, \(27.6 \mathrm{~kJ}\) of heat is absorbed. (a) Is the solution process exothermic? (b) What is \(q_{\mathrm{H}_{2} \mathrm{O}}\) ? (c) What is the final temperature of the solution? (Specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).) (d) What are the initial and final temperatures in \({ }^{\circ} \mathrm{F}\) ?

When \(225 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(25^{\circ} \mathrm{C}\) are mixed with \(85 \mathrm{~mL}\) of water at \(89^{\circ} \mathrm{C}\), what is the final temperature? (Assume that no heat is lost to the surroundings; \(d_{\mathrm{H}_{2} \mathrm{O}}=1.00 \mathrm{~g} / \mathrm{mL}\).)

How many mL of water at \(10^{\circ} \mathrm{C}\) ( 2 significant figures) must be added to \(75 \mathrm{~mL}\) of water at \(35^{\circ} \mathrm{C}\) to obtain a final temperature of \(19^{\circ} \mathrm{C} ?\) (Make the same assumptions as in Question 9.)

When \(35.0 \mathrm{~mL}\) of \(1.43 \mathrm{M} \mathrm{NaOH}\) at \(22.0^{\circ} \mathrm{C}\) is neutralized by \(35.0 \mathrm{~mL}\) of \(\mathrm{HCl}\) also at \(22.0^{\circ} \mathrm{C}\) in a coffee-cup calorimeter, the temperature of the final solution rises to \(31.29^{\circ} \mathrm{C}\). Assume that the specific heat of all solutions is \(4.18 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\), that the density of all solutions is \(1.00 \mathrm{~g} / \mathrm{mL}\), and that volumes are additive. (a) Calculate \(q\) for the reaction. (b) Calculate \(q\) for the neutralization of one mole of \(\mathrm{NaOH}\).

When one mole of KOH is neutralized by sulfuric acid, \(q=-56 \mathrm{~kJ} .\) At \(22.8^{\circ} \mathrm{C}, 25.0 \mathrm{~mL}\) of \(0.500 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is neutralized by \(50.0 \mathrm{~mL}\) of \(0.500 \mathrm{M}\) \(\mathrm{KOH}\) in a coffee-cup calorimeter. What is the final temperature of the solution? (Use the assumptions in Question 11.)

Fructose is a sugar commonly found in fruit. A sample of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), weighing \(4.50 \mathrm{~g}\) is burned in a bomb calorimeter. The heat capacity of the calorimeter is \(2.115 \times 10^{4} \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The temperature in the calorimeter rises from \(23.49^{\circ} \mathrm{C}\) to \(27.71^{\circ} \mathrm{C}\). (a) What is \(q\) for the calorimeter? (b) What is \(q\) when \(4.50 \mathrm{~g}\) of fructose is burned? (c) What is \(q\) for the combustion of one mole of fructose?

Isooctane is a primary component of gasoline and gives gasoline its octane rating. Burning \(1.00 \mathrm{~mL}\) of isooctane \((d=0.688 \mathrm{~g} / \mathrm{mL})\) releases \(33.0 \mathrm{~kJ}\) of heat. When \(10.00 \mathrm{~mL}\) of is ooctane is burned in a bomb calorime- ter, the temperature in the bomb rises from \(23.2^{\circ} \mathrm{C}\) to \(66.5^{\circ} \mathrm{C}\). What is the heat capacity of the bomb calorimeter?

When one mole of caffeine \(\left(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\right)\) is burned in air, \(4.96 \times 10^{3} \mathrm{~kJ}\) of heat is evolved. Five grams of caffeine is burned in a bomb calorimeter. The temperature is observed to increase by \(11.37^{\circ} \mathrm{C}\). What is the heat capacity of the calorimeter in \(\mathrm{J} /{ }^{\circ} \mathrm{C} ?\)

Isooctane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), is a component of gasoline. When \(0.500 \mathrm{~g}\) of isooctane is burned, \(24.06 \mathrm{~kJ}\) of heat is given off. If \(10.00 \mathrm{mg}\) of isooctane is burned in a bomb calorimeter (heat capacity \(=5175 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) initially at \(23.6^{\circ} \mathrm{C}\), what is the temperature of the calorimeter when reaction is complete?

Salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\), is one of the starting materials in the manufacture of aspirin. When \(1.00 \mathrm{~g}\) of salicylic acid burns in a bomb calorimeter, the temperature rises from \(23.11^{\circ} \mathrm{C}\) to \(28.91^{\circ} \mathrm{C}\). The temperature in the bomb calorimeter increases by \(2.48^{\circ} \mathrm{C}\) when the calorimeter absorbs \(9.37 \mathrm{~kJ}\). How much heat is given off when one mole of salicylic acid is burned?

Naphthalene, \(\mathrm{C}_{10} \mathrm{H}_{8}\), is the compound present in moth balls. When one mole of naphthalene is burned, \(5.15 \times 10^{3} \mathrm{~kJ}\) of heat is evolved. A sample of naphthalene burned in a bomb calorimeter (heat capacity \(=9832 \mathrm{~J} /{ }^{\circ} \mathrm{C}\) ) increases the temperature in the calorimeter from \(25.1^{\circ} \mathrm{C}\) to \(28.4^{\circ} \mathrm{C}\). How many milligrams of naphthalene were burned?

Nitrogen oxide (NO) has been found to be a key component in many biological processes. It also can react with oxygen to give the brown gas \(\mathrm{NO}_{2}\). When one mole of NO reacts with oxygen, \(57.0 \mathrm{~kJ}\) of heat is evolved. (a) Write the thermochemical equation for the reaction between one mole of nitrogen oxide and oxygen. (b) Is the reaction exothermic or endothermic? (c) Draw an energy diagram showing the path of this reaction. (Figure \(8.4\) is an example of such an energy diagram.)

Calcium carbide, \(\mathrm{CaC}_{2}\), is the raw material for the production of acetylene (used in welding torches). Calcium carbide is produced by reacting calcium oxide with carbon, producing carbon monoxide as a byproduct. When one mole of calcium carbide is formed, \(464.8 \mathrm{~kJ}\) is absorbed. (a) Write a thermochemical equation for this reaction. (b) Is the reaction exothermic or endothermic? (c) Draw an energy diagram showing the path of this reaction. (Figure \(8.4\) is an example of such an energy diagram.) (d) What is \(\Delta H\) when \(1.00 \mathrm{~g}\) of \(\mathrm{CaC}_{2}(\mathrm{~g})\) is formed? (e) How many grams of carbon are used up when \(20.00 \mathrm{~kJ}\) of heat is absorbed?

In the late eighteenth century Priestley prepared ammonia by reacting \(\mathrm{HNO}_{3}(g)\) with hydrogen gas. The thermodynamic equation for the reaction is $$ \mathrm{HNO}_{3}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{NH}_{3}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H=-637 \mathrm{~kJ} $$ (a) Calculate \(\Delta H\) when one mole of hydrogen gas reacts. (b) What is \(\Delta H\) when \(10.00 \mathrm{~g}\) of \(\mathrm{NH}_{3}(g)\) is made to react with an excess of steam to form \(\mathrm{HNO}_{3}\) and \(\mathrm{H}_{2}\) gases?

In photosynthesis, the following reaction takes place: \(6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 6 \mathrm{O}_{2}(g)+\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \quad \Delta H=2801 \mathrm{~kJ}\) (a) Calculate \(\Delta H\) when one mole of \(\mathrm{CO}_{2}\) reacts. (b) How many kilojoules of energy are liberated when \(15.00 \mathrm{~g}\) of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is burned in oxygen?

Strontium metal is responsible for the red color in fireworks. Fireworks manufacturers use strontium carbonate, which can be produced by combining strontium metal, graphite (C), and oxygen gas. The formation of one mole of \(\mathrm{SrCO}_{3}\) releases \(1.220 \times 10^{3} \mathrm{~kJ}\) of energy. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(10.00 \mathrm{~L}\) of oxygen at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is used by the reaction?

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is an explosive most often used in mine or quarry blasting. It is a powerful explosive because four gases \(\left(\mathrm{N}_{2}\right)\) \(\mathrm{O}_{2}, \mathrm{CO}_{2}\), and steam) are formed when nitroglycerine is detonated. In addition, \(6.26 \mathrm{~kJ}\) of heat is given off per gram of nitroglycerine detonated. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(4.65\) mol of products is formed?

A typical fat in the body is glyceryl trioleate, \(\mathrm{C}_{57} \mathrm{H}_{104} \mathrm{O}_{6}\). When it is metabolized in the body, it combines with oxygen to produce carbon dioxide, water, and \(3.022 \times 10^{4} \mathrm{~kJ}\) of heat per mole of fat. (a) Write a balanced thermochemical equation for the metabolism of fat. (b) How many kilojoules of energy must be evolved in the form of heat if you want to get rid of five pounds of this fat by combustion? (c) How many nutritional calories is this? (1 nutritional calorie = \(1 \times 10^{3}\) calories)

A lead ore, galena, consisting mainly of lead(II) sulfide, is the principal source of lead. To obtain the lead, the ore is first heated in the air to form lead oxide. $$ \mathrm{PbS}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{PbO}(s)+\mathrm{SO}_{2}(g) \quad \Delta H=-415.4 \mathrm{~kJ} $$ The oxide is then reduced to metal with carbon. $$ \mathrm{PbO}(s)+\mathrm{C}(s) \longrightarrow \mathrm{Pb}(s)+\mathrm{CO}(g) \quad \Delta H=+108.5 \mathrm{k}] $$ Calculate \(\Delta H\) for the reaction of one mole of lead(II) sulfide with oxygen and carbon, forming lead, sulfur dioxide, and carbon monoxide.

To produce silicon, used in semiconductors, from sand \(\left(\mathrm{SiO}_{2}\right)\), a reaction is used that can be broken down into three steps: $$ \begin{aligned} \mathrm{SiO}_{2}(s)+2 \mathrm{C}(s) \longrightarrow \mathrm{Si}(s)+2 \mathrm{CO}(g) & & \Delta H=689.9 \mathrm{~kJ} \\ \mathrm{Si}(s)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SiCl}_{4}(g) & & \Delta H=-657.0 \mathrm{~kJ} \\ \mathrm{SiCl}_{4}(g)+2 \mathrm{Mg}(s) \longrightarrow 2 \mathrm{MgCl}_{2}(s)+\mathrm{Si}(s) & & \Delta H=-625.6 \mathrm{~kJ} \end{aligned} $$ (a) Write the thermochemical equation for the overall reaction for the formation of silicon from silicon dioxide; \(\mathrm{CO}\) and \(\mathrm{MgCl}_{2}\) are byproducts. (b) What is \(\Delta H\) for the formation of one mole of silicon? (c) Is the overall reaction exothermic?

Given the following thermochemical equations, $$ \begin{aligned} \mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow & 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & & \Delta H=-1299.5 \mathrm{~kJ} \\ \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) & & \Delta H=-393.5 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & & \Delta H=-285.8 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the decomposition of one mole of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), to its elements in their stable state at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Given the following thermochemical equations $$ \begin{aligned} 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & & \Delta H=-571.6 \mathrm{~kJ} \\ \mathrm{~N}_{2} \mathrm{O}_{5}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l) & & \Delta H=-73.7 \mathrm{~kJ} \\ \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{O}_{2}(g)+\frac{1}{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{HNO}_{3}(l) & & \Delta H=-174.1 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the formation of one mole of dinitrogen pentoxide from its elements in their stable state at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Write thermochemical equations for the decomposition of one mole of the following compounds into the elements in their stable states at \(25^{\circ} \mathrm{C}\) and 1 atm. (a) ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) (b) sodium fluoride \((s)\) (c) magnesium sulfate \((s)\) (d) ammonium nitrate (s)

Write thermochemical equations for the formation of one mole of the following compounds from the elements in their stable states at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). (a) acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) nitrogen dioxide \((g)\) (c) lead(II) bromide (s) (d) phosphorus pentachloride \((g)\)

Given $$ 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) \longrightarrow 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \quad \Delta H^{\circ}=3351.4 \mathrm{~kJ} $$ (a) What is the heat of formation of aluminum oxide? (b) What is \(\Delta H^{\circ}\) for the formation of \(12.50 \mathrm{~g}\) of aluminum oxide?

Given $$ 2 \mathrm{CuO}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{O}_{2}(g) \quad \Delta H^{\circ}=314.6 \mathrm{~kJ} $$ (a) Determine the heat of formation of \(\mathrm{CuO}\). (b) Calculate \(\Delta H^{\circ}\) for the formation of \(13.58 \mathrm{~g}\) of \(\mathrm{CuO}\).

Use the appropriate table to calculate \(\Delta H^{\circ}\) for (a) the reaction between copper(II) oxide and carbon monoxide to give copper metal and carbon dioxide. (b) the decomposition of one mole of methyl alcohol (CH \(_{3} \mathrm{OH}\) ) to methane and oxygen gases.

Butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), is widely used as a fuel for disposable lighters. When one mole of butane is burned in oxygen, carbon dioxide and steam are formed and \(2658.3 \mathrm{~kJ}\) of heat is evolved. (a) Write a thermochemical equation for the reaction. (b) Using Table \(8.3\), calculate the standard heat of formation of butane.

When one mole of calcium carbonate reacts with ammonia, solid calcium cyanamide, \(\mathrm{CaCN}_{2}\), and liquid water are formed. The reaction absorbs \(90.1 \mathrm{~kJ}\) of heat. (a) Write a balanced thermochemical equation for the reaction. (b) Using Table 8.3, calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for calcium cyanamide.

Chlorine trifluoride is a toxic, intensely reactive gas. It was used in World War II to make incendiary bombs. It reacts with ammonia and forms nitrogen, chlorine, and hydrogen fluoride gases. When two moles of chlorine trifluoride reacts, \(1196 \mathrm{~kJ}\) of heat is evolved. (a) Write a thermochemical equation for the reaction. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{ClF}_{3} ?\)

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is a powerful explosive used in rock blasting when roads are created. When ignited, it produces water, nitrogen, carbon dioxide, and oxygen. Detonation of one mole of nitroglycerine liberates \(5725 \mathrm{~kJ}\) of heat. (a) Write a balanced thermochemical equation for the reaction for the detonation of four moles of nitroglycerine. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l) ?\)

Glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s),\left(\Delta H_{\mathrm{f}}^{\circ}=-1275.2 \mathrm{~kJ} / \mathrm{mol}\right)\) is converted to ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), and carbon dioxide in the fermentation of grape juice. What quantity of heat is liberated when \(750.0 \mathrm{~mL}\) of wine containing \(12.0 \%\) ethyl alcohol by volume \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is produced by the fermentation of grape juice?

When ammonia reacts with dinitrogen oxide gas ( \(\Delta H_{\mathrm{f}}^{\circ}=82.05 \mathrm{~kJ} / \mathrm{mol}\) ), liquid water and nitrogen gas are formed. How much heat is liberated or absorbed by the reaction that produces \(345 \mathrm{~mL}\) of nitrogen gas at \(25^{\circ} \mathrm{C}\) and \(717 \mathrm{~mm} \mathrm{Hg}\) ?

Find (a) \(\Delta E\) when a gas absorbs \(18 \mathrm{~J}\) of heat and has \(13 \mathrm{~J}\) of work done on it. (b) \(q\) when 72 J of work is done on a system and its energy is increased by \(61 \mathrm{~J}\).

Calculate (a) \(g\) when a system does \(54 \mathrm{~J}\) of work and its energy decreases by \(72 \mathrm{~J}\). (b) \(\Delta E\) for a gas that releases \(38 \mathrm{~J}\) of heat and has \(102 \mathrm{~J}\) of work done on it.

Consider the following reaction in a vessel with a movable piston. $$ \mathrm{X}(g)+\mathrm{Y}(g) \longrightarrow \mathrm{Z}(l) $$ As the reaction occurs, the system loses \(1185 \mathrm{~J}\) of heat. The piston moves down and the surroundings do \(623 \mathrm{~J}\) of work on the system. What is \(\Delta E ?\)

For the vaporization of one mole of water at \(100^{\circ} \mathrm{C}\) determine (a) \(\Delta H\) (Table 8.3) (b) \(\Delta P V\) (in kilojoules) (c) \(\Delta E\)

Natural gas companies in the United States use the "therm" as a unit of energy. One therm is \(1 \times 10^{5} \mathrm{BTU}\). (a) How many joules are in one therm? \(\left(1 \mathrm{~J}=9.48 \times 10^{-4} \mathrm{BTU}\right)\) (b) When propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is burned in oxygen, \(\mathrm{CO}_{2}\) and steam are produced. How many therms of energy are given off by \(1.00 \mathrm{~mol}\) of propane gas?

A 12 -oz can of most colas has about 120 nutritional calories (1 nutritional calorie \(=1\) kilocalorie). Approximately how many minutes of walking are required to burn up as energy the calories taken in after drinking a can of cola? (Walking uses up about \(250 \mathrm{kcal} / \mathrm{h}\).)

Given the following reactions, $$ \begin{aligned} \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-534.2 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-241.8 \mathrm{~kJ} \end{aligned} $$ calculate the heat of formation of hydrazine.

Consider the reaction of methane with oxygen. Suppose that the reaction is carried out in a furnace used to heat a house. If \(q=-890 \mathrm{~kJ}\) and \(w=+5 \mathrm{~kJ}\), what is \(\Delta E ? \Delta H\) at \(25^{\circ} \mathrm{C} ?\)

Microwave ovens convert radiation to energy. A microwave oven uses radiation with a wavelength of \(12.5 \mathrm{~cm}\). Assuming that all the energy from the radiation is converted to heat without loss, how many moles of photons are required to raise the temperature of a cup of water \((350.0 \mathrm{~g}\), specific heat \(=4.18 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) ) from \(23.0^{\circ} \mathrm{C}\) to \(99.0^{\circ} \mathrm{C} ?\)

Some solar-heated homes use large beds of rocks to store heat. (a) How much heat is absorbed by \(100.0 \mathrm{~kg}\) of rocks if their temperature increases by \(12^{\circ} \mathrm{C} ?\) (Assume that \(c=0.82 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).) (b) Assume that the rock pile has total surface area \(2 \mathrm{~m}^{2}\). At maximum intensity near the earth's surface, solar power is about 170 watts \(/ \mathrm{m}^{2}\). (1 watt = \(1 \mathrm{~J} / \mathrm{s}\).) How many minutes will it take for solar power to produce the \(12^{\circ} \mathrm{C}\) increase in part (a)?

Draw a cylinder with a movable piston containing six molecules of a liquid. A pressure of 1 atm is exerted on the piston. Next draw the same cylinder after the liquid has been vaporized. A pressure of one atmosphere is still exerted on the piston. Is work done on the system or by the system?

Which statement(s) is/are true about bond enthalpy? (a) Energy is required to break a bond. (b) \(\Delta H\) for the formation of a bond is always a negative number. (c) Bond enthalpy is defined only for bonds broken or formed in the gaseous state. (d) Because the presence of \(\pi\) bonds does not influence the geometry of a molecule, the presence of \(\pi\) bonds does not affect the value of the bond enthalpy between two atoms either. (e) The bond enthalpy for a double bond between atoms \(A\) and \(B\) is twice that for a single bond between atoms \(\mathrm{A}\) and \(\mathrm{B}\).