Chapter 4

For each situation, define a system and its surroundings, and give the direction of heat transfer: (a) Propane is burning in a Bunsen burner in the laboratory. (b) After you have a swim, water droplets on your skin evaporate. (c) Water, originally at \(25^{\circ} \mathrm{C}\), is placed in the freezing compartment of a refrigerator. (d) Two chemicals are mixed in a flask on a laboratory bench. A reaction occurs and heat is evolved.

What is the value of the standard formation enthalpy for any element under standard conditions?

Criticize each of these statements: (a) Formation enthalpy refers to a reaction in which \(1 \mathrm{~mol}\) of one or more reactants produces some quantity of product. (b) The standard formation enthalpy of \(\mathrm{O}_{2}\) as a gas at \(25^{\circ} \mathrm{C}\) and a pressure of 1 atm is \(15.0 \mathrm{~kJ} / \mathrm{mol}\).

What is required for heat transfer of energy from one sample of matter to another to occur?

Name two exothermic processes and two endothermic processes that you encountered recently and that were not associated with your chemistry course.

Explain what is meant by (a) energy density of a fuel and (b) caloric value of a food. Why is each of these terms important?

Explain in your own words why it is useful in thermodynamics to distinguish a system from its surroundings.

(a) A 2 -inch piece of two-layer chocolate cake with frosting provides \(1670 \mathrm{~kJ}\) of energy. Calculate this in Cal. (b) If you were on a diet that calls for eating no more than 1200 Cal per day, calculate how many joules you could consume per day.

Sulfur dioxide, \(\mathrm{SO}_{2}\), is found in wines and in polluted air. If a \(32.1-\mathrm{g}\) sample of sulfur is burned in the air to get \(64.1 \mathrm{~g} \mathrm{SO}_{2}, 297 \mathrm{~kJ}\) of energy is released. Express this energy in (a) joules, (b) calories, and (c) kilocalories.

Melting lead requires 5.50 cal/g. Calculate how many joules are required to melt \(1.00 \mathrm{lb}\) (454 g) lead.

On a sunny day, solar energy reaches Earth at a rate of 4.0 J min \(^{-1} \mathrm{~cm}^{-2}\). Suppose a house has a square, flat roof of dimensions \(12 \mathrm{~m}\) by \(12 \mathrm{~m}\). Calculate how much solar energy reaches this roof in \(1.0 \mathrm{~h}\). (Note: This is why roofs painted with light- reflecting paint keep buildings cooler than black, unpainted roofs. The painted roofs reflect most of this energy rather than absorb it.)

The energy unit used by electrical utilities in their monthly bills is the kilowatt hour \((\mathrm{kWh} ; 1\) kilowatt used for 1 hour). Calculate how many joules there are in a kilowatt hour. If electricity costs \(\$ .09\) per kilowatt hour, calculate how much it costs per megajoule.

A \(100-\mathrm{W}\) light bulb is left on for \(14 \mathrm{~h} .\) Calculate how many joules are used. With electricity at \(\$ 0.09\) per \(\mathrm{kWh}\), calculate how much it costs to leave the light on for \(14 \mathrm{~h}\).

Describe how energy is changed from one form to another in these processes: (a) At a July 4 th celebration, a match is lit and ignites the fuse of a rocket firecracker, which fires off and explodes at an altitude of \(1000 \mathrm{ft}\). (b) A gallon of gasoline is pumped from an underground storage tank into the fuel tank of your car, and you use it up by driving \(25 \mathrm{mi}\).

16\. Analyze transfer of energy from one form to another in each situation. (a) In a Space Shuttle, hydrogen and oxygen combine to form water, boosting the shuttle into orbit above Earth. (b) You eat a package of Fritos, go to class and listen to a lecture, walk back to your dorm, and climb the stairs to the fourth floor.

Analyze this situation in terms of potential and kinetic energy of water molecules: Water flows over a waterfall; the temperature of water at the bottom is higher than at the top.

Suppose that you are studying kinetic energy of helium molecules: A helium weather balloon rises to an altitude of \(40,000 \mathrm{ft} ;\) the temperature of the gas drops to \(-70{ }^{\circ} \mathrm{F}\). (a) Make an appropriate choice of system and surroundings and describe it unambiguously. (b) Explain why you chose the system and surroundings you did. (c) Identify transfers of energy and material into and out of the system that would be important for you to monitor in your study.

Solid ammonium chloride is added to water in a beaker and dissolves. The beaker becomes cold to the touch. (a) Make an appropriate choice of system and surroundings and describe it unambiguously. (b) Explain why you chose the system and surroundings you did. (c) Identify transfers of energy and material into and out of the system that would be important for you to monitor in your study. (d) Is the process of dissolving \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\) in water exothermic or endothermic? Explain your answer.

A bar of Monel (an alloy of nickel, copper, iron, and manganese) is heated until it melts, poured into a mold, and solidifies. (a) Make an appropriate choice of system and surroundings and describe it unambiguously. (b) Explain why you chose the system and surroundings you did. (c) Identify transfers of energy and material into and out of the system that would be important for you to monitor in your study.

You hold a gram of copper in one hand and a gram of aluminum in the other. Each metal was originally at \(0{ }^{\circ} \mathrm{C}\). (Both metals are in the shape of a little ball that fits into your hand.) If energy is transferred to both at the same rate, which will warm to your body temperature first? Explain your answer.

The specific heat capacity of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is 1.74 J \(\mathrm{g}^{-1} \mathrm{~K}^{-1}\). Calculate its molar heat capacity.

The specific heat capacity of carbon tetrachloride, \(\mathrm{CCl}_{4}\), is \(0.861 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\). Calculate its molar heat capacity.

A \(237-\mathrm{g}\) piece of molybdenum, initially at \(100.0^{\circ} \mathrm{C}\), is dropped into \(244 \mathrm{~g}\) water at \(10.0^{\circ} \mathrm{C}\). When the system comes to thermal equilibrium, the temperature is \(14.9^{\circ} \mathrm{C}\). Calculate the specific heat capacity of molybdenum.

A piece of iron ( \(400 . \mathrm{g}\) ) is heated in a flame and then plunged into a beaker containing \(1.00 \mathrm{~kg}\) water. The original temperature of the water was \(20.0^{\circ} \mathrm{C}\), but it is \(32.8^{\circ} \mathrm{C}\) after the iron bar is put in and thermal equilibrium is reached. Calculate the original temperature of the hot iron bar.

A chemical reaction occurs, and \(20.7 \mathrm{~J}\) is transferred from the chemical system to its surroundings. (Assume that no work is done.) (a) What is the algebraic sign of \(\Delta T_{\text {surroundings }} ?\) (b) What is the algebraic sign of \(\Delta_{r} E_{\text {system }}\) ?

A phase transition occurs in a sample of an alloy, and 437 kJ transfers from the surroundings to the alloy. (Assume that no work is done.) (a) What is the algebraic sign of \(\Delta T_{\text {alloy }}\) ? (b) What is the algebraic sign of \(\Delta_{\mathrm{r}} E_{\text {alloy }} ?\)

The heat of fusion of mercury is \(2.72 \mathrm{cal} / \mathrm{g} .\) Calculate the quantity of energy transferred when 4.37 mol Hg freezes at a temperature of \(-39^{\circ} \mathrm{C}\).

Chloromethane, \(\mathrm{CH}_{3} \mathrm{Cl}\), arises from microbial fermentation and is found throughout the environment. It is also produced industrially and is used in the manufacture of various chemicals and has been used as a topical anesthetic. Calculate how much energy is required to convert \(92.5 \mathrm{~g}\) liquid to a vapor at its boiling point, \(-24.09^{\circ} \mathrm{C}\). (The heat of vaporization of \(\mathrm{CH}_{3} \mathrm{Cl}\) is \(21.40 \mathrm{~kJ} / \mathrm{mol}\).)

The freezing point of mercury is \(-38.8{ }^{\circ} \mathrm{C}\). Calculate what quantity of energy, in joules, is released to the surroundings if \(1.00 \mathrm{~mL}\) mercury is cooled from \(23.0^{\circ} \mathrm{C}\) to \(-38.8^{\circ} \mathrm{C}\) and then frozen to a solid. (The density of liquid mercury is \(13.6 \mathrm{~g} / \mathrm{cm}^{3}\). Its specific heat capacity is \(0.140 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\) and its heat of fusion is \(11.4 \mathrm{~J} \mathrm{~g}^{-1}\).)

Calculate the quantity of heating required to convert the water in four ice cubes \((60.1 \mathrm{~g}\) each \()\) from \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) at \(0{ }^{\circ} \mathrm{C}\) to \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(100 .{ }^{\circ} \mathrm{C}\). The enthalpy of fusion of ice is \(333 \mathrm{~J} / \mathrm{g}\) and the enthalpy of vaporization of liquid water is \(2260 \mathrm{~J} / \mathrm{g}\).

What is the sign of \(w\) for these processes if they occur at constant pressure? Consider only \(P \Delta V\) work from gases. (a) \(\mathrm{Fe}_{2} \mathrm{~S}_{3}(\mathrm{~s})+6 \mathrm{HNO}_{3}(\mathrm{aq}) \longrightarrow 2 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(\mathrm{aq})+3 \mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})\) (b) \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 3 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\ell)\)

Assume that these reactions occur under constant atmospheric pressure. What is the sign of \(w\) for each? (a) \(\mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{CaC}_{2}(\mathrm{~s})+\mathrm{CO}(\mathrm{g})\) (b) \(2 \mathrm{C}_{6} \mathrm{H}_{6}(\ell)+15 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 12 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell)\)

Calculate how much energy must be transferred to vaporize \(125 \mathrm{~g}\) benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) at its boiling point, \(80.1{ }^{\circ} \mathrm{C}\). (The enthalpy of vaporization of benzene is \(30.8 \mathrm{~kJ} / \mathrm{mol}\).)

The enthalpy of fusion (melting) of water is \(6.0 \mathrm{~kJ} / \mathrm{mol}\). Calculate the quantity of energy that must be transferred to melt \(25.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\) at \(0{ }^{\circ} \mathrm{C}\).

Energy is stored in the body in adenosine triphosphate, ATP, which is formed by the reaction between adenosine diphosphate, ADP, and dihydrogen phosphate ions. \(\mathrm{ADP}^{3-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{PO}_{4}^{2-}(\mathrm{aq}) \longrightarrow \mathrm{ATP}^{4-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)\) $$ \Delta_{\mathrm{r}} H^{\circ}=20.5 \mathrm{~kJ} / \mathrm{mol} $$ Is the reaction endothermic or exothermic?

Calcium carbide, \(\mathrm{CaC}_{2}\), is manufactured by reducing lime with carbon at high temperature. (The carbide is used in turn to make acetylene, an industrially important organic chemical.) $$ \begin{aligned} \mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{CaC}_{2}(\mathrm{~s})+\mathrm{CO}(\mathrm{g}) \\ \Delta_{\mathrm{r}} H^{\circ}=464.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Is the reaction endothermic or exothermic?

When calcium oxide, \(\mathrm{CaO}(\mathrm{s})\), dissolves in water the water becomes hot. Write a chemical equation for this process and indicate whether it is exothermic or endothermic.

When table salt is dissolved in water, the temperature drops slightly. Write a chemical equation for this process and indicate if it is exothermic or endothermic.

Given the thermochemical expression \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell)\) $$ \Delta_{\mathrm{r}} H^{\circ}=6.0 \mathrm{~kJ} / \mathrm{mol} $$ calculate what quantity of energy is transferred to the surroundings when (a) 34.2 mol liquid water freezes. (b) \(100.0 \mathrm{~g}\) liquid water freezes.

Given the thermochemical expression $$ \begin{aligned} \mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{CaC}_{2}(\mathrm{~s})+\mathrm{CO}(\mathrm{g}) \\ \Delta_{\mathrm{r}} H^{\circ} &=464.8 \mathrm{~kJ} / \mathrm{mol} (a) \(2 \mathrm{~mol} \mathrm{O}_{2}\) reacts (b) \(0.115 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{3}\) forms (c) \(4.73 \mathrm{~g}\) NO reacts \end{aligned} $$ calculate the quantity of energy transferred when (a) \(34.8 \mathrm{~mol} \mathrm{CO}(\mathrm{g})\) is formed by this reaction. (b) A metric ton ( \(1000 \mathrm{~kg}\) ) of \(\mathrm{CaC}_{2}(\mathrm{~s})\) is manufactured. (c) \(0.432 \mathrm{~mol}\) carbon reacts with \(\mathrm{CaO}(\mathrm{s})\).

Determine the amount of reaction (in moles) that takes place for each process $$ 2 \mathrm{NO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{3}(\mathrm{~g}) $$ (a) \(2 \mathrm{~mol} \mathrm{O}_{2}\) reacts (b) \(0.115 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{3}\) forms (c) \(4.73 \mathrm{~g}\) NO reacts

Determine the amount of reaction (in moles) that takes place for each process $$ \frac{1}{2} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s}) \longrightarrow \mathrm{FeO}(\mathrm{s})+\frac{1}{4} \mathrm{O}_{2}(\mathrm{~g}) $$ (a) \(2 \mathrm{~mol} \mathrm{O}_{2}\) forms (b) \(0.824 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) reacts (c) \(1.34 \mathrm{~g} \mathrm{FeO}\) forms

Isooctane \((2,2,4\) -trimethylpentane), one of the many hydrocarbons that make up gasoline, burns in air to give water and carbon dioxide. $$ \begin{array}{r} 2 \mathrm{C}_{8} \mathrm{H}_{18}(\ell)+25 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{~g})+18 \mathrm{H}_{2} \mathrm{O}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ}=-10,922 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate the enthalpy change if you burn \(1.00 \mathrm{~L}\) isooctane (density \(=0.69 \mathrm{~g} / \mathrm{mL}\) ).

When \(\mathrm{KClO}_{3}(\mathrm{~s})\), potassium chlorate, is heated, it melts and decomposes to form oxygen gas. [Molten \(\mathrm{KClO}_{3}\) was shown reacting with a Fritos chip earlier in this chapter ( \(\in\) Sec. \(4-\mid a\) ). \(]\) The thermochemical expression for decomposition of potassium chlorate is $$ 2 \mathrm{KClO}_{3}(\mathrm{~s}) \longrightarrow 2 \mathrm{KCl}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{t}} H^{\circ}=-89.4 \mathrm{~kJ} / \mathrm{mol} $$ Calculate \(q\) at constant pressure for (a) Formation of \(97.8 \mathrm{~g} \mathrm{KCl}(\mathrm{s})\). (b) Production of \(24.8 \mathrm{~mol} \mathrm{O}_{2}(\mathrm{~g})\). (c) Decomposition of \(35.2 \mathrm{~g} \mathrm{KClO}_{3}(\mathrm{~s})\)

"Gasohol," a mixture of gasoline and ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) is used as automobile fuel. The alcohol releases energy in a combustion reaction with \(\mathrm{O}_{2}\). $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ If \(0.115 \mathrm{~g}\) ethanol evolves \(3.62 \mathrm{~kJ}\) when burned at constant pressure, calculate the combustion enthalpy for ethanol.

56White phosphorus, \(\mathrm{P}_{4}\), ignites in air to produce \(\mathrm{P}_{4} \mathrm{O}_{10}\). $$ \mathrm{P}_{4}(\mathrm{~s})+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(\mathrm{~s}) $$ When \(3.56 \mathrm{~g} \mathrm{P}_{4}\) is burned, \(85.8 \mathrm{~kJ}\) of thermal energy is evolved at constant pressure. Calculate the combustion enthalpy of \(\mathrm{P}_{4}\).

Acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\) is made industrially by the reaction of methanol and carbon monoxide. \(\mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(\ell)\) $$ \Delta_{\mathrm{r}} H^{\circ}=-135.3 \mathrm{~kJ} / \mathrm{mol} $$ If you produce \(1.00 \mathrm{~L}\) acetic acid \((d=1.044 \mathrm{~g} / \mathrm{mL})\) by this reaction, calculate how much energy is transferred out of the system.

$$ \begin{aligned} &\text { Use these bond enthalpy values to answer Question } { . }\\\ &\begin{array}{lclc} \hline \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k}\rfloor / \mathrm{mol}) \end{array} & \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k} / / \mathrm{mol}) \end{array} \\ \hline \mathrm{H}-\mathrm{F} & 566 & \mathrm{~F}-\mathrm{F} & 158 \\ \mathrm{H}-\mathrm{Cl} & 431 & \mathrm{Cl}-\mathrm{Cl} & 242 \\ \mathrm{H}-\mathrm{Br} & 366 & \mathrm{Br}-\mathrm{Br} & 193 \\ \mathrm{H}-\mathrm{I} & 299 & \mathrm{I}-\mathrm{I} & 151 \\ \mathrm{H}-\mathrm{H} & 436 & & \\ \hline \end{array} \end{aligned} $$ Which molecule, HF, HCl, HBr, or HI, has the strongest chemical bond?

$$ \begin{aligned} &\text { Use these bond enthalpy values to answer Question } { . }\\\ &\begin{array}{lclc} \hline \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k}\rfloor / \mathrm{mol}) \end{array} & \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k} / / \mathrm{mol}) \end{array} \\ \hline \mathrm{H}-\mathrm{F} & 566 & \mathrm{~F}-\mathrm{F} & 158 \\ \mathrm{H}-\mathrm{Cl} & 431 & \mathrm{Cl}-\mathrm{Cl} & 242 \\ \mathrm{H}-\mathrm{Br} & 366 & \mathrm{Br}-\mathrm{Br} & 193 \\ \mathrm{H}-\mathrm{I} & 299 & \mathrm{I}-\mathrm{I} & 151 \\ \mathrm{H}-\mathrm{H} & 436 & & \\ \hline \end{array} \end{aligned} $$ Which molecule, \(\mathrm{F}_{2}, \mathrm{Cl}_{2}, \mathrm{Br}_{2},\) or \(\mathrm{I}_{2}\), has the weakest chemical bond?

$$ \begin{aligned} &\text { Use these bond enthalpy values to answer Question } { . }\\\ &\begin{array}{lclc} \hline \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k}\rfloor / \mathrm{mol}) \end{array} & \text { Bond } & \begin{array}{c} \text { Bond Enthalpy } \\ (\mathrm{k} / / \mathrm{mol}) \end{array} \\ \hline \mathrm{H}-\mathrm{F} & 566 & \mathrm{~F}-\mathrm{F} & 158 \\ \mathrm{H}-\mathrm{Cl} & 431 & \mathrm{Cl}-\mathrm{Cl} & 242 \\ \mathrm{H}-\mathrm{Br} & 366 & \mathrm{Br}-\mathrm{Br} & 193 \\ \mathrm{H}-\mathrm{I} & 299 & \mathrm{I}-\mathrm{I} & 151 \\ \mathrm{H}-\mathrm{H} & 436 & & \\ \hline \end{array} \end{aligned} $$ For the reactions of molecular hydrogen with fluorine and with chlorine: (a) Calculate the enthalpy change for breaking all the bonds in the reactants. (b) Calculate the enthalpy change for forming all the bonds in the products. (c) From the results in parts (a) and (b), calculate the enthalpy change for the reaction. (d) Which reaction is most exothermic?