Chapter 6

Identify the following systems as open, closed, or isolated: (a) coffec in a very high quality thermos bottle; (b) coolant in a refrigerator coil; (c) a bomb calorimeter in which benzene is bumed.

Identify the following systems as open, closed, or isolated: (a) gasoline burning in an automobile enginc; (b) mercury in a thermometer; (c) a living plant.

A gas sample is heated in a cylinder, using \(375 \mathrm{~kJ}\) of heat. At the same time a piston compresses the gas, using \(645 \mathrm{~kJ}\) of work. What is the change in internal energy of the gas during this process?

A gas sample in a piston axsembly expands, doing \(235 \mathrm{~kJ}\) of work on its surroundings at the same time that \(695 \mathrm{~kJ}\) of heat is added to the gas. (a) What is the change in internal encrgy of the gas churing this process? (b) Will the pressure of the gas be higher or lower when these changes are completed?

(a) Calculate the work for a system that absorbs \(150 \mathrm{~kJ}\) of heat in a process for which the increase in internal energy is \(120 \mathrm{~kJ}\). (b) Is work done on or by the system during this process?

(a) Calculate the work for a system that releases \(346 \mathrm{~kJ}\) of heat in a process for which the decrease in internal energy is \(125 \mathrm{~kJ}\). (b) Is work done on or by the system during this process?

A gas in a cylinder was placed in a heater and gained \(7000 \mathrm{~kJ}\) of heat. If the cylinder increased in volume from \(700 \mathrm{~mL}\) to \(1450 \mathrm{~mL}\) against an atmospheric pressure of 750 Torr during this process, what is the change in internal energy of the gas in the cylinder?

In a combustion cylinder, the total internal energy change produced from the burning of a fuel is \(-2573 \mathrm{~kJ}\). The cooling system that surrounds the cylinder absorbs \(947 \mathrm{~kJ}\) as heat. How much work can be done by the fuel in the cylinder during this process?

For a certain reaction at constant pressure, \(\Delta H=-15 \mathrm{~kJ}\) and \(22 \mathrm{~kJ}\) of expansion work is done on the system. What is \(\Delta U\) for this process?

For a certain reaction at constant pressure, \(\Delta U=-95 \mathrm{~kJ}\) and \(56 \mathrm{~kJ}\) of expansion work is done by the system. What is \(\Delta H\) for this process?

(a) Near room temperature the specific heat capacity of ethanol is \(2.42 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1} \cdot \mathrm{g}^{-1}\). Calculate the heat that must be removed to reduce the temperature of \(150.0 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\) from \(50.0^{\circ} \mathrm{C}\) to \(16.6^{\circ} \mathrm{C}\). (b) What mass of copper can be heated from \(15^{\circ} \mathrm{C}\) to \(205^{\circ} \mathrm{C}\) when \(425 \mathrm{~kJ}\) of energy is available?

Near room temperature, the specific heat capacity of benzene is \(1.05 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1} \mathrm{~g}^{-1}\). Calculate the heat nceded to raise the temperature of \(50.0 \mathrm{~g}\) of benzene from \(25.3^{\circ} \mathrm{C}\) to \(37.2^{\circ} \mathrm{C}\). (b) A \(1.0-\mathrm{kg}\) block of aluminum is supplied with \(490 \mathrm{~kJ}\) of heat. What is the temperature change of the aluminum? The specific heat capacity of aluminum is \(0.90 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1} \cdot \mathrm{g}^{-1}\).

A piece of metal of mass \(20.0 \mathrm{~g}\) at \(100.0^{\circ} \mathrm{C}\) is placed in a calorimeter containing \(50.7 \mathrm{~g}\) of watcr at \(22.0^{\circ} \mathrm{C}\). The final temperature of the mixture is \(25.7^{\circ} \mathrm{C}\) What is the specific heat capacity of the mctal? Assume that all the energy lost by the metal is gained by the water.

A calorimeter was calibrated with an electric heater, which was used to supply \(22.5 \mathrm{~kJ}\) of energy to the calorimeter; the heat increased the temperature of the calorimeter and its water bath from \(22.45^{\circ} \mathrm{C}\) to \(23.97^{\circ} \mathrm{C}\). What is the heat capacity of the calorimeter?

Calculate the amount of heat needed to raise the temperature of \(0.325 \mathrm{~mol}\) of a monatomic idcal gas from a temperature of \(-25^{\circ} \mathrm{C}\) to \(+50^{\circ} \mathrm{C}\) at (a) constant volume and (b) constant pressure. (c) Why is more heat needed to raise the temperature at constant pressure than at constant volume?

A calorimeter has a measured heat capacity of \(6.27 \mathrm{~kJ} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1}\). The combustion of \(1.84 \mathrm{~g}\) of magnesium led to a temperature change from \(21.30^{\circ} \mathrm{C}\) to \(28.56^{\circ} \mathrm{C}\). Calculare the enthalpy change of the reaction \(2 \mathrm{Mg}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{MgO}(\mathrm{s})\).

Which gas do you expect to have the higher molar heat capacity, \(\mathrm{NO}\) or \(\mathrm{NO}_{2}\) ? Why?

(a) At its boiling point, the vaporization of \(0.235 \mathrm{~mol} \mathrm{CH}_{4}(1)\) requires \(1.93 \mathrm{~kJ}\) of heat. What is the enthalpy of vaporization of methane? (b) An electric heater was immersed in a flask of boiling crhanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), and \(22.45 \mathrm{~g}\) of ethanol was vaporized when \(21.2 \mathrm{~kJ}\) of energy was supplied. What is the enthalpy of vaporization of ethanol?

(a) At its boiling point, the vaporization of \(0.235 \mathrm{~mol} \mathrm{CH}_{4}(1)\) requires \(1.93 \mathrm{~kJ}\) of heat. What is the enthalpy of vaporization of methane? (b) An electric heater was immersed in a flask of boiling crhanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), and \(22.45 \mathrm{~g}\) of ethanol was vaporized when \(21.2 \mathrm{~kJ}\) of energy was supplied. What is the enthalpy of vaporization of ethanol?

The standard enthalpies of combustion of graphite and diamond are \(-393.51\) and \(-395.41 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\), respectively. Calculate the change in molar enthalpy for the graphite \(\rightarrow\) diamond transition.

Elemental sulfur occurs in several forms, with rhombic sulfur being the most stable under normal conditions and monoclinic sulfur slightly less stable. The standard cnthalpies of combustion of the two forms to sulfur dioxide are \(-296.83\) and \(-297.16 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\), respectively. Calculate the change in molar enthalpy for the rhombic \(\rightarrow\) monoclinic transition.

Two successive stages in the industrial manufacture of sulfuric acid are the combustion of sulfur and the oxidation of sulfur dioxide to sulfur trioxide. From the standard reaction enthalpies $$ \begin{gathered} \mathrm{S}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{~g}) \\ \Delta H^{\circ}=-296.83 \mathrm{~kJ} \\ 2 \mathrm{~S}(\mathrm{~s})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{3}(\mathrm{~g}) \\ \Delta H^{\circ}=-791.44 \mathrm{~kJ} \end{gathered} $$ Calculate the reaction enthalpy for the oxidation of sulfur dioxide to sulfur trioxide in the reaction \(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_{3}(\mathrm{~g})\).

In the manufacture of nitric acid by the oxidation of ammonia, the first product is nitric oxide, which is then cxidized to nitrogen dioxide. From the standard reaction enthalpies $$ \begin{gathered} \mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g}) \\ \Delta H^{\circ}=+180.5 \mathrm{~kJ} \\ \mathrm{~N}_{2}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) \\ \Delta H^{\circ}=+66.4 \mathrm{~kJ} \end{gathered} $$ calculate the standard reaction enthalpy for the oxidation of nitric oxide to nitrogen dioxide: $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{~g}) $$

Calculate the enthalpy of the reaction \(\mathrm{P}_{4}(\mathrm{~s})+10 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{PCl}_{5}(\mathrm{~s})\) from the reactions $$ \begin{gathered} \mathrm{P}_{4}(\mathrm{~s})+6 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PCl}_{3}(\mathrm{I}) \\ \Delta H^{\circ}=-1278.8 \mathrm{~kJ} \\ \mathrm{PCl}_{3}(\mathrm{l})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{~s}) \\ \Delta H^{m}=-124 \mathrm{~kJ} \end{gathered} $$

Determine the reaction enthalpy for the hydrogenation of ethyne to ethane, \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\) \(2 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g})\), from the following data: enthalpy of combustion of ethyne, \(-1300 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\); enthalpy of combustion of ethane, \(-1560 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\); enthalpy of combustion of hydrogen, \(-286 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\).

Calculate the reaction enthalpy for the formation of anhydrous aluminum chloride, \(2 \mathrm{Al}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{AlCl}_{3}(\mathrm{~s})\), from the following data: $$ \begin{array}{ll} 2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g}) \\ & \Delta H^{\circ}=-1049 \mathrm{~kJ} \\ \mathrm{HCl}(\mathrm{g}) \longrightarrow \mathrm{HCl}(\mathrm{aq}) & \Delta H^{\circ}=-74.8 \mathrm{~kJ} \\ \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(\mathrm{g}) & \Delta H^{\circ}=-185 \mathrm{~kJ} \\ \mathrm{AlCl}_{3}(\mathrm{~s}) \longrightarrow \mathrm{AlCl}_{3}(\mathrm{aq}) & \Delta H^{\circ}=-323 \mathrm{~kJ} \end{array} $$

Write the thermochemical equations that give the values of the standard enthalpies of formation for (a) \(\mathrm{KClO}_{3}\) (s), potassium chlorate; (b) \(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{COOH}\) (s), glycine(s); (c) \(\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})\), alumina.

Write the thermochemical equations that give the values of the standard enthalpies of formation for (a) \(\mathrm{CH}_{2} \mathrm{COOH}\) (I); (b) \(\mathrm{SO}_{2}\) (g); (c) \(\mathrm{CO}_{2}\) (g).

Use the enthalpies of formation in Appendix \(2 \mathrm{~A}\) to calculate the standard enthalpy of the following reactions: (a) the replacement of deuterium by ordinary hydrogen in heavy water: \(\mathrm{H}_{2}(\mathrm{~g})+\mathrm{D}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{D}_{2}(\mathrm{~g})\) (b) the removal of sulfur from the hydrogen sulfide and sulfur dioxide in natural gas: \(2 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})+\mathrm{SO}_{2}(\mathrm{~g}) \rightarrow 3 \mathrm{~S}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) (c) the oxidation of ammonia: \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Using standard enthalpies of formation from Appendix \(2 \mathrm{~A}\), calculate the standard reaction enthalpy for each of the following reactions: (a) the final stage in the production of nitric acid, when nitrogen dioxide dissolves in and reacts with water: \(3 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow 2 \mathrm{HNO}_{3}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})\) (b) the formation of boron trifluoride, which is widely used in the chemical industry: \(\mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{CaF}_{2}(\mathrm{~s}) \rightarrow 2 \mathrm{BF}_{3}(\mathrm{~g})+3 \mathrm{CaO}(\mathrm{s})\) (c) the formation of a sulfide by the action of hydrogen sulfide on an aqueous solution of a base: \(\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{K}_{2} \mathrm{~S}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})\)

The internal energy of a system increased by \(400 \mathrm{~J}\) when it absorbed \(600 \mathrm{~J}\) of heat. (a) Was work done by or on the system? (b) How much work was done?

(a) Describe three ways in which you could increase the internal energy of an open system. (b) Which of these methods could you use to increase the internal energy of a closed system? (c) Which, if any, of these methods could you use to increase the internal energy of an isolated system?

If a \(70-\mathrm{kg}\) male burns \(2000 \mathrm{~kJ}\) of energy while jogging for \(1.0 \mathrm{~h}\), what mass of fat would be consumed, given that the typical standard energy of combustion of fat is about \(38 \mathrm{~kJ} \cdot \mathrm{g}^{-1}\) ? How many hours would he need to jog if he wished to lose \(0.50 \mathrm{~kg}\) of fat?

Strong sunshine bombards the Earth with about \(1 \mathrm{~kJ} \cdot \mathrm{m}^{-2}\) in \(1 \mathrm{~s}\). Calculate the maximum mass of pure ethanol that can be vaporized in 10 min from a beaker left in strong sunshine, assuming the surface area of the ethanol to be \(50 \mathrm{~cm}^{2}\). Assume all the heat is used for vaporization, not to increase the temperature.

When \(25.0 \mathrm{~g}\) of a metal at a temperature of \(90.0^{\circ} \mathrm{C}\) is added to \(50.0 \mathrm{~g}\) of water at \(25.0^{\circ} \mathrm{C}\), the water temperature rises to \(29.8^{\circ} \mathrm{C}\). The specific heat capacity of water is \(4.184 \mathrm{~J}-\left({ }^{\circ} \mathrm{C}\right)^{-1} \mathrm{~g}^{-1}\). What is the specific heat capacity of the metal?

The heat capacity of a certain empty calorimeter is \(488.1 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1}\). When \(25.0 \mathrm{~mL}\) of \(0.700 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq})\) was mixed in that calorimeter with \(25.0 \mathrm{~mL}\) of \(0.700 \mathrm{M} \mathrm{HCl}\) (aq), both initially at \(20.00^{\circ} \mathrm{C}\), the temperature increased to \(21.34^{\circ} \mathrm{C}\). Calculate the enthalpy of neutralization in kilojoules per mole of HCI.

Calculate the lattice enthalpy of solid potassium bromide, \(\mathrm{KBr}(\mathrm{s}) \rightarrow \mathrm{K}^{+}(\mathrm{g})+\mathrm{Br}^{-}(\mathrm{g})\), from the following information: $$ \begin{aligned} &\Delta H_{i}{\underline{\phantom{xx}}}^{\circ}\left(\mathrm{KBr}, \text { s) }=-394 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\right. \\ &\Delta H_{i}{\underline{\phantom{xx}}}^{\circ}(\mathrm{K}, \mathrm{g})=+89.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1} \end{aligned} $$ First ionization energy of \(\mathrm{K}(\mathrm{g})=+425.0 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\) \(\Delta H_{\text {vap }}{\underline{\phantom{xx}}}^{\circ}\left(\mathrm{Br}_{2}, \mathrm{l}\right)=+30.9 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\) Br-Br bond dissociation cuthalpy \(=+192.9 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}\) Electron attachment to \(\mathrm{Br}(\mathrm{g})\) : $$ \mathrm{Br}(\mathrm{g})+\mathrm{e}^{-}(\mathrm{g}) \rightarrow \mathrm{Be}^{-}(\mathrm{g}), \quad \Delta H^{*}=-331.0 \mathrm{~kJ} $$