Chapter 7

Objects placed together eventually reach the same temperature. When you go into a room and touch a piece of metal in that room, it feels colder than a piece of plastic. Explain.

What is meant by the term lower in energy? Which is lower in energy, a mixture of hydrogen and oxygen gases or liquid water? How do you know? Which of the two is more stable? How do you know?

A fire is started in a fireplace by striking a match and lighting crumpled paper under some logs. Explain all the energy transfers in this scenario using the terms exothermic, endothermic, system, surroundings, potential energy, and kinetic energy in the discussion.

Liquid water turns to ice. Is this process endothermic or exothermic? Explain what is occurring using the terms system, surroundings, heat, potential energy, and kinetic energy in the discussion.

Consider the following statements: "Heat is a form of energy, and energy is conserved. The heat lost by a system must be equal to the amount of heat gained by the surroundings. Therefore, heat is conserved." Indicate everything you think is correct in these statements. Indicate everything you think is incorrect. Correct the incorrect statements and explain.

Explain why oceanfront areas generally have smaller temperature fluctuations than inland areas.

Hess's law is really just another statement of the first law of thermodynamics. Explain.

In the equation \(w=-P \Delta V,\) why is there a negative sign?

Consider an airplane trip from Chicago, Illinois, to Denver, Colorado. List some path-dependent functions and some state functions for the plane trip.

How is average bond strength related to relative potential energies of the reactants and the products?

Assuming gasoline is pure \(\mathrm{C}_{8} \mathrm{H}_{18}(l),\) predict the signs of \(q\) and \(w\) for the process of combusting gasoline into \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\).

What is the difference between \(\Delta H\) and \(\Delta E ?\)

The enthalpy change for the reaction $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ is \(-891 \mathrm{kJ}\) for the reaction \(a s\) written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

For the reaction \(\mathrm{HgO}(s) \rightarrow \mathrm{Hg}(l)+\frac{1}{2} \mathrm{O}_{2}(g), \Delta H=+90.7 \mathrm{kJ}\). a. What quantity of heat is required to produce 1 mole of mercury by this reaction? b. What quantity of heat is required to produce 1 mole of oxygen gas by this reaction? c. What quantity of heat would be released in the following reaction as written? $$2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{HgO}(s)$$

The enthalpy of combustion of \(\mathrm{CH}_{4}(g)\) when \(\mathrm{H}_{2} \mathrm{O}(l)\) is formed is \(-891 \mathrm{kJ} / \mathrm{mol}\) and the enthalpy of combustion of \(\mathrm{CH}_{4}(g)\) when \(\mathrm{H}_{2} \mathrm{O}(g)\) is formed is \(-803 \mathrm{kJ} / \mathrm{mol} .\) Use these data and Hess's law to determine the enthalpy of vaporization for water.

The enthalpy change for a reaction is a state function and it is an extensive property. Explain.

Standard enthalpies of formation are relative values. What are \(\Delta H_{\mathrm{f}}^{\circ}\) values relative to?

Why is it a good idea to rinse your thermos bottle with hot water before filling it with hot coffee?

Photosynthetic plants use the following reaction to produce glucose, cellulose, and so forth: $$6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \stackrel{\text { Sunlight }}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)$$ How might extensive destruction of forests exacerbate the greenhouse effect?

What is incomplete combustion of fossil fuels? Why can this be a problem?

Explain the advantages and disadvantages of hydrogen as an alternative fuel.

Which has the greater kinetic energy, an object with a mass of \(2.0 \mathrm{kg}\) and a velocity of \(1.0 \mathrm{m} / \mathrm{s}\) or an object with a mass of \(1.0 \mathrm{kg}\) and a velocity of \(2.0 \mathrm{m} / \mathrm{s} ?\)

A gas absorbs \(45 \mathrm{kJ}\) of heat and does \(29 \mathrm{kJ}\) of work. Calculate \(\Delta E\).

A system releases \(125 \mathrm{kJ}\) of heat while \(104 \mathrm{kJ}\) of work is done on it. Calculate \(\Delta E\).

Calculate \(\Delta E\) for each of the following. a. \(q=-47 \mathrm{kJ}, w=+88 \mathrm{kJ}\) b. \(q=+82 \mathrm{kJ}, w=-47 \mathrm{kJ}\) c. \(q=+47 \mathrm{kJ}, w=0\) d. In which of these cases do the surroundings do work on the system?

A system undergoes a process consisting of the following two steps: Step 1: The system absorbs \(72 \mathrm{J}\) of heat while \(35 \mathrm{J}\) of work is done on it. Step 2: The system absorbs \(35 \mathrm{J}\) of heat while performing \(72 \mathrm{J}\) of work. Calculate \(\Delta E\) for the overall process.

If the internal energy of a thermodynamic system is increased by \(300 .\) \(\mathrm{J}\) while \(75 \mathrm{J}\) of expansion work is done, how much heat was transferred and in which direction, to or from the system?

A sample of an ideal gas at \(15.0 \mathrm{atm}\) and \(10.0 \mathrm{L}\) is allowed to expand against a constant external pressure of \(2.00 \mathrm{atm}\) to a volume of \(75.0 \mathrm{L}\). Calculate the work in units of \(\mathrm{kJ}\) for the gas expansion.

A piston performs work of \(210 . \mathrm{L}\). \(\mathrm{atm}\) on the surroundings, while the cylinder in which it is placed expands from \(10. \mathrm{L}\) to \(25 \mathrm{L}\). At the same time, \(45 \mathrm{J}\) of heat is transferred from the surroundings to the system. Against what pressure was the piston working?

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is \(40 . \mathrm{cm}^{3} .\) If the combustion of this mixture releases \(950 .\) \(\mathrm{J}\) of energy, to what volume will the gases expand against a constant pressure of \(650 .\) torr if all the energy of combustion is converted into work to push back the piston?

As a system increases in volume, it absorbs \(52.5 \mathrm{J}\) of energy in the form of heat from the surroundings. The piston is working against a pressure of \(0.500 \mathrm{atm}\). The final volume of the system is \(58.0 \mathrm{L}\). What was the initial volume of the system if the internal energy of the system decreased by \(102.5 \mathrm{J} ?\)

A balloon filled with \(39.1 \mathrm{moles}\) of helium has a volume of \(876 \mathrm{L}\) at \(0.0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}\) pressure. The temperature of the balloon is increased to \(38.0^{\circ} \mathrm{C}\) as it expands to a volume of \(998 \mathrm{L}\), the pressure remaining constant. Calculate \(q, w,\) and \(\Delta E\) for the helium in the balloon. (The molar heat capacity for helium gas is \(20.8 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{mol}.\))

One mole of \(\mathrm{H}_{2} \mathrm{O}(g)\) at 1.00 atm and \(100 .^{\circ} \mathrm{C}\) occupies a volume of 30.6 L. When 1 mole of \(\mathrm{H}_{2} \mathrm{O}(g)\) is condensed to 1 mole of \(\mathrm{H}_{2} \mathrm{O}(l)\) at 1.00 atm and \(100 .^{\circ} \mathrm{C}, 40.66 \mathrm{kJ}\) of heat is released. If the density of \(\mathrm{H}_{2} \mathrm{O}(l)\) at this temperature and pressure is \(0.996 \mathrm{g} / \mathrm{cm}^{3},\) calculate \(\Delta E\) for the condensation of 1 mole of water at 1.00 atm and \(100 .^{\circ} \mathrm{C}\).

One of the components of polluted air is NO. It is formed in the high- temperature environment of internal combustion engines by the following reaction: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) \quad \Delta H=180 \mathrm{kJ}$$ Why are high temperatures needed to convert \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) to NO?

The reaction $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ is the last step in the commercial production of sulfuric acid. The enthalpy change for this reaction is \(-227 \mathrm{kJ}\). In designing a sulfuric acid plant, is it necessary to provide for heating or cooling of the reaction mixture? Explain.

Are the following processes exothermic or endothermic? a. When solid \(\mathrm{KBr}\) is dissolved in water, the solution gets colder. b. Natural gas \(\left(\mathrm{CH}_{4}\right)\) is burned in a furnace. c. When concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added to water, the solution gets very hot. d. Water is boiled in a teakettle.

Are the following processes exothermic or endothermic? a. the combustion of gasoline in a car engine b. water condensing on a cold pipe c. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) d. \(\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{F}(g)\)

The overall reaction in a commercial heat pack can be represented as $$4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{kJ}$$ a. How much heat is released when 4.00 moles of iron are reacted with excess \(\mathrm{O}_{2} ?\) b. How much heat is released when 1.00 mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{g}\) iron is reacted with excess \(\mathbf{O}_{2} ?\) d. How much heat is released when \(10.0 \mathrm{g}\) Fe and \(2.00 \mathrm{g} \mathrm{O}_{2}\) are reacted?

Consider the following reaction: $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{kJ}$$ a. How much heat is evolved for the production of 1.00 mole of \(\mathrm{H}_{2} \mathrm{O}(l) ?\) b. How much heat is evolved when 4.03 g hydrogen are reacted with excess oxygen? c. How much heat is evolved when \(186 \mathrm{g}\) oxygen are reacted with excess hydrogen?

Consider the following reaction: $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-891 \mathrm{kJ}$$ Calculate the enthalpy change for each of the following cases: a. \(1.00 \mathrm{g}\) methane is burned in excess oxygen. b. \(1.00 \times 10^{3} \mathrm{L}\) methane gas at \(740 .\) torr and \(25^{\circ} \mathrm{C}\) are burned in excess oxygen. The density of \(\mathrm{CH}_{4}(g)\) at these conditions is \(0.639 \mathrm{g} / \mathrm{L}\).

The specific heat capacity of silver is \(0.24 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\). a. Calculate the energy required to raise the temperature of \(150.0 \mathrm{g}\) Ag from \(273 \mathrm{K}\) to \(298 \mathrm{K}\). b. Calculate the energy required to raise the temperature of 1.0 mole of Ag by \(1.0^{\circ} \mathrm{C}\) (called the molar heat capacity of silver). c. It takes \(1.25 \mathrm{kJ}\) of energy to heat a sample of pure silver from \(12.0^{\circ} \mathrm{C}\) to \(15.2^{\circ} \mathrm{C}\). Calculate the mass of the sample silver.

It takes \(585 \mathrm{J}\) of energy to raise the temperature of \(125.6 \mathrm{g}\) mercury from \(20.0^{\circ} \mathrm{C}\) to \(53.5^{\circ} \mathrm{C}\). Calculate the specific heat capacity and the molar heat capacity of mercury.

A \(30.0 -\mathrm{g}\) sample of water at \(280 .\) K is mixed with \(50.0 \mathrm{g}\) water at \(330 . K\). Calculate the final temperature of the mixture assuming no heat loss to the surroundings.

A biology experiment requires the preparation of a water bath at \(37.0^{\circ} \mathrm{C}\) (body temperature). The temperature of the cold tap water is \(22.0^{\circ} \mathrm{C},\) and the temperature of the hot tap water is \(55.0^{\circ} \mathrm{C} .\) If a student starts with \(90.0 \mathrm{g}\) cold water, what mass of hot water must be added to reach \(37.0^{\circ} \mathrm{C} ?\)

A \(5.00-\mathrm{g}\) sample of aluminum pellets (specific heat capacity \(=\) \(0.89 \mathrm{J} / \mathrm{C} \cdot \mathrm{g}\) ) and a \(10.00-\mathrm{g}\) sample of iron pellets (specific heat capacity \(=0.45 \mathrm{J} / \mathrm{C} \cdot \mathrm{g}\) ) are heated to \(100.0^{\circ} \mathrm{C}\). The mixture of hot iron and aluminum is then dropped into 97.3 g water at \(22.0^{\circ} \mathrm{C} .\) Calculate the final temperature of the metal and water mixture, assuming no heat loss to the surroundings.

Hydrogen gives off \(120 .\) J/g of energy when burned in oxygen, and methane gives off \(50 .\) J/g under the same circumstances. If a mixture of 5.0 g hydrogen and \(10 .\) g methane is burned, and the heat released is transferred to \(50.0 \mathrm{g}\) water at \(25.0^{\circ} \mathrm{C},\) what final temperature will be reached by the water?

A \(150.0 -\mathrm{g}\) sample of a metal at \(75.0^{\circ} \mathrm{C}\) is added to \(150.0 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(15.0^{\circ} \mathrm{C}\). The temperature of the water rises to \(18.3^{\circ} \mathrm{C}\). Calculate the specific heat capacity of the metal, assuming that all the heat lost by the metal is gained by the water.

A \(110 .-\mathrm{g}\) sample of copper (specific heat capacity \(=\) the \(0.20 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\)) is heated to \(82.4^{\circ} \mathrm{C}\) and then placed in a container of water at \(22.3^{\circ} \mathrm{C} .\) The final temperature of the water and copper is \(24.9^{\circ} \mathrm{C} .\) What is the mass of the water in the container, assuming that all the heat lost by the copper is gained by the water?

In a coffee-cup calorimeter, \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) and \(50.0 \mathrm{mL}\) of \(0.100 \mathrm{M}\) HCl are mixed to yield the following reaction: $$\mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s)$$ The two solutions were initially at \(22.60^{\circ} \mathrm{C},\) and the final temperature is \(23.40^{\circ} \mathrm{C}\). Calculate the heat that accompanies this reaction in \(\mathrm{kJ} / \mathrm{mol}\) of \(\mathrm{AgCl}\) formed. Assume that the combined solution has a mass of \(100.0 \mathrm{g}\) and a specific heat capacity of \(4.18 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\).

In a coffee-cup calorimeter, \(100.0 \mathrm{mL}\) of \(1.0 M \mathrm{NaOH}\) and \(100.0 \mathrm{mL}\) of \(1.0 \mathrm{M}\) HCl are mixed. Both solutions were originally at \(24.6^{\circ} \mathrm{C}\). After the reaction, the final temperature is \(31.3^{\circ} \mathrm{C}\). Assuming that all the solutions have a density of \(1.0 \mathrm{g} / \mathrm{cm}^{3}\) and a specific heat capacity of \(4.18 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g},\) calcu- late the enthalpy change for the neutralization of HCl by NaOH. Assume that no heat is lost to the surroundings or to the calorimeter.