Chapter 5

Define these terms: system, surroundings, thermal energy, chemical energy, potential energy, kinetic energy, law of conservation of energy.

What is heat? How does heat differ from thermal energy? Under what condition is heat transferred from one system to another?

What are the units for energy commonly employed in chemistry?

A truck initially traveling at \(60 \mathrm{~km} / \mathrm{h}\) is brought to a complete stop at a traffic light. Does this change violate the law of conservation of energy? Explain.

These are various forms of energy: chemical, heat, light, mechanical, and electrical. Suggest several ways of converting one form of energy to another.

Define these terms: thermochemistry, exothermic process, endothermic process.

Stoichiometry is based on the law of conservation of mass. On what law is thermochemistry based?

Describe the interconversions of forms of energy occurring in these processes: (a) You throw a softball up into the air and catch it. (b) You switch on a flashlight. (c) You ride the ski lift to the top of the hill and then ski down. (d) You strike a match and let it burn completely.

Decomposition reactions are usually endothermic, whereas combination reactions are usually exothermic. Give a qualitative explanation for these trends.

On what law is the first law of thermodynamics based? Explain the sign conventions in the equation $$ \Delta U=q+w $$

Explain what is meant by a state function. Give two examples of quantities that are state functions and two that are not state functions.

The work done to compress a gas is \(47 \mathrm{~J}\). As a result, \(93 \mathrm{~J}\) of heat is given off to the surroundings. Calculate the change in internal energy of the gas.

In a gas expansion, \(87 \mathrm{~J}\) of heat is released to the surroundings and the energy of the system decreases by \(128 \mathrm{~J}\). Calculate the work done.

Calculate \(w,\) and determine whether work is done \(b y\) the system or on the system when \(415 \mathrm{~J}\) of heat is released and \(\Delta U=510 \mathrm{~J} .\)

Calculate \(q,\) and determine whether heat is absorbed or released when a system does work on the surroundings equal to \(64 \mathrm{~J}\) and \(\Delta U=213 \mathrm{~J}\).

Define these terms: enthalpy and enthalpy of reaction. Under what condition is the heat of a reaction equal to the enthalpy change of the same reaction?

In writing thermochemical equations, why is it important to indicate the physical state (i.e., gaseous, liquid, solid, or aqueous) of each substance?

Explain the meaning of this thermochemical equation:$$\begin{aligned}4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow & 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \\ \Delta H=-904 \mathrm{~kJ} / \mathrm{mol}\end{aligned}$$

Consider this reaction: $$\begin{array}{l}2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{CO}_{2}(g) \\ \Delta H=-1452.8 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ What is the value of \(\Delta H\) if (a) the equation is multiplied throughout by \(2 ;(b)\) the direction of the reaction is reversed so that the products become the reactants, and vice versa; (c) water vapor instead of liquid water is formed as the product?

A sample of nitrogen gas expands in volume from 1.6 to \(5.4 \mathrm{~L}\) at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of 0.80 atm, and (c) against a constant pressure of 3.7 atm. (See Equation 5.4. \((1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J})\).

A gas expands in volume from 26.7 to \(89.3 \mathrm{~mL}\) at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum, (b) against a constant pressure of \(1.5 \mathrm{~atm},\) and \((\mathrm{c})\) against a constant pressure of \(2.8 \mathrm{~atm} .(1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J})\).

A gas expands and does \(P V\) work on the surroundings equal to \(325 \mathrm{~J}\). At the same time, it absorbs \(127 \mathrm{~J}\) of heat from the surroundings. Calculate the change in energy of the gas.

The first step in the industrial recovery of zinc from the zinc sulfide ore is roasting; that is, the conversion of \(\mathrm{ZnS}\) to \(\mathrm{ZnO}\) by heating:$$\begin{aligned}2 \mathrm{ZnS}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)+2 \mathrm{SO}_{2}(g) & \Delta H=-879 \mathrm{~kJ} / \mathrm{mol}\end{aligned}$$ Calculate the heat evolved (in kJ) per gram of \(\mathrm{ZnS}\) roasted.

Determine the amount of heat (in kJ) given off when \(1.26 \times 10^{4} \mathrm{~g}\) of \(\mathrm{NO}_{2}\) are produced according to the equation $$ \begin{array}{l} 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \\ \qquad \Delta H=-114.6 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Consider the reaction $$\begin{aligned}2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow & 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \\ \Delta H=&+483.6 \mathrm{~kJ} / \mathrm{mol}\end{aligned}$$ at a certain temperature. If the increase in volume is 32.7 \(\mathrm{L}\) against an external pressure of \(1.00 \mathrm{~atm},\) calculate \(\Delta U\) for this reaction. \((1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J})\)

Consider the reaction$$\begin{aligned}\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{HCl}(g) & \\\\\Delta H=-184.6 \mathrm{~kJ} / \mathrm{mol} \end{aligned}$$If 3 moles of \(\mathrm{H}_{2}\) react with 3 moles of \(\mathrm{Cl}_{2}\) to form \(\mathrm{HCl}\) calculate the work done (in joules) against a pressure of \(1.0 \mathrm{~atm} .\) What is \(\Delta U\) for this reaction? Assume the reaction goes to completion and that \(\Delta V=0\). \((1 \mathrm{~L} \cdot \mathrm{atm}=101.3 \mathrm{~J})\)

For most biological processes, the changes in internal energy are approximately equal to the changes in enthalpy. Explain.

What is the difference between specific heat and heat capacity? What are the units for these two quantities? Which is the intensive property and which is the extensive property?

Define calorimetry and describe two commonly used calorimeters. In a calorimetric measurement, why is it important that we know the heat capacity of the calorimeter? How is this value determined?

Calculate the amount of heat liberated (in kJ) from 366 \(\mathrm{g}\) of mercury when it cools from \(77.0^{\circ} \mathrm{C}\) to \(12.0^{\circ} \mathrm{C}\).

A sheet of gold weighing \(10.0 \mathrm{~g}\) and at a temperature of \(18.0^{\circ} \mathrm{C}\) is placed flat on a sheet of iron weighing \(20.0 \mathrm{~g}\) and at a temperature of \(55.6^{\circ} \mathrm{C}\). What is the final temperature of the combined metals? Assume that no heat is lost to the surroundings.

A \(0.1375-\mathrm{g}\) sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of \(3024 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The temperature increases by \(1.126^{\circ} \mathrm{C}\). Calculate the heat given off by the burning \(\mathrm{Mg},\) in \(\mathrm{kJ} / \mathrm{g}\) and in \(\mathrm{kJ} / \mathrm{mol} .\)

A quantity of \(2.00 \times 10^{2} \mathrm{~mL}\) of \(0.862 \mathrm{M} \mathrm{HCl}\) is mixed with \(2.00 \times 10^{2} \mathrm{~mL}\) of \(0.431 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the \(\mathrm{HCl}\) and \(\mathrm{Ba}(\mathrm{OH})_{2}\) solutions is the same at \(20.48^{\circ} \mathrm{C}\). For the process $$\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$$ the heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol}\). What is the final temperature of the mixed solution? Assume the specific heat of the solution is the same as that for pure water.

A \(50.75-\mathrm{g}\) sample of water at \(75.6^{\circ} \mathrm{C}\) is added to a sample of water at \(24.1^{\circ} \mathrm{C}\) in a constant-pressure calorimeter. If the final temperature of the combined water is \(39.4^{\circ} \mathrm{C}\) and the heat capacity of the calorimeter is \(26.3 \mathrm{~J} /{ }^{\circ} \mathrm{C},\) calculate the mass of the water originally in the calorimeter.

Consider two metals A and B, each having a mass of \(100 \mathrm{~g}\) and an initial temperature of \(20^{\circ} \mathrm{C}\). The specific heat of \(\mathrm{A}\) is larger than that of \(\mathrm{B}\). Under the same heating conditions, which metal would take longer to reach a temperature of \(21^{\circ} \mathrm{C} ?\)

Consider the following data:$$\begin{array}{lcc}\text { Metal } & \text { Al } & \text { Cu } \\\\\hline \text { Mass }(\mathrm{g}) & 10 & 30 \\\\\text { Specific heat }\left(\mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) & 0.900 & 0.385 \\\\\text { Temnerature }{\underline{\phantom{xx}}}^{\circ}{\underline{\phantom{xx}}}^{\circ} \mathrm{C} \text { ) } & 40 & 60\end{array}$$ When these two metals are placed in contact, which of the following will take place? (a) Heat will flow from \(\mathrm{Al}\) to Cu because \(\mathrm{Al}\) has a larger specific heat. (b) Heat will flow from \(\mathrm{Cu}\) to \(\mathrm{Al}\) because \(\mathrm{Cu}\) has a larger mass. (c) Heat will flow from \(\mathrm{Cu}\) to \(\mathrm{Al}\) because \(\mathrm{Cu}\) has a larger heat capacity (d) Heat will flow from Cu to Al because Cu is at a higher temperature. (e) No heat will flow in either direction.

State Hess's law. Explain, with one example, the usefulness of Hess's law in thermochemistry.

Describe how chemists use Hess's law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

Given the thermochemical data,$$\begin{array}{ll}\mathrm{A}+6 \mathrm{~B} \longrightarrow 4 \mathrm{C} & \Delta H_{1}=-1200 \mathrm{~kJ} / \mathrm{mol} \\\\\mathrm{C}+\mathrm{B} \longrightarrow \mathrm{D} & \Delta H_{1}=-150 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ Determine the enthalpy change for each of the following: a) \(\mathrm{D} \longrightarrow \mathrm{C}+\mathrm{B}\) d) \(2 \mathrm{D} \longrightarrow 2 \mathrm{C}+2 \mathrm{~B}\) b) \(2 \mathrm{C} \longrightarrow \frac{1}{2} \mathrm{~A}+3 \mathrm{~B}\) e) \(6 \mathrm{D}+\mathrm{A} \longrightarrow 10 \mathrm{C}\) c) \(3 \mathrm{D}+\frac{1}{2} \mathrm{~A} \stackrel{\longrightarrow}{\longrightarrow} \mathrm{C}\)

Given the thermochemical data, \(\mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C} \quad \Delta H_{1}=600 \mathrm{~kJ} / \mathrm{mol}\) \(\begin{array}{ll}2 \mathrm{C}+\mathrm{D} \longrightarrow 2 \mathrm{E} & \Delta H_{1}=210 \mathrm{~kJ} / \mathrm{mol}\end{array}\) Determine the enthalpy change for each of the following: a) \(4 \mathrm{E} \longrightarrow 4 \mathrm{C}+2 \mathrm{D}\) d) \(2 C+2 E \longrightarrow 2 A+2 B+D\) b) \(\mathrm{A}+\mathrm{B}+\mathrm{D} \longrightarrow 2 \mathrm{E}\) e) \(\mathrm{E} \longrightarrow \frac{1}{2} \mathrm{~A}+\frac{1}{2} \mathrm{~B}+\frac{1}{2} \mathrm{D}\) c) \(\mathrm{C} \longrightarrow \frac{1}{2} \mathrm{~A}+\frac{1}{2} \mathrm{~B}\)

From these data, $$\begin{array}{l}\mathrm{S} \text { (rhombic) }+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \\\\\qquad \begin{aligned}\Delta H_{\mathrm{rxn}}^{\circ} &=-296.4 \mathrm{~kJ} / \mathrm{mol}\end{aligned} \\\\\mathrm{S} \text { (monoclinic) }+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) \\\\\Delta H_{\mathrm{rxn}}^{\circ}=-296.7 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ calculate the enthalpy change for the transformation \(\mathrm{S}\) (rhombic) \(\longrightarrow \mathrm{S}\) (monoclinic) (Monoclinic and rhombic are different allotropic forms of elemental sulfur.)

From the following heats of combustion, \(\begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \Delta H_{\mathrm{rxn}}^{\circ}=-726.4 \mathrm{~kJ} / \mathrm{mol} \\\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) & \\ \Delta H_{\mathrm{rxn}}^{\circ}=-393.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H_{\mathrm{rxn}}^{\circ}=-285.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) calculate the enthalpy of formation of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) from its elements: $$ \mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l) $$

Calculate the standard enthalpy change for the reaction $$ 2 \mathrm{Al}(s)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \longrightarrow 2 \mathrm{Fe}(s)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ given that $$\begin{aligned} 2 \mathrm{Al}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s) & \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-1669.8 \mathrm{~kJ} / \mathrm{mol} \\ 2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) & \\ \Delta H_{\mathrm{rxn}}^{\circ}=-822.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned}$$

Determine the enthalpy change for the gaseous reaction of sulfur dioxide with ozone to form sulfur trioxide given the following thermochemical data: $$ \begin{aligned} 2 \mathrm{SO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{2}(g) & \Delta H^{\circ}=-602.8 \mathrm{~kJ} / \mathrm{mol} \\ 3 \mathrm{SO}(g)+2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{SO}_{3}(g) & \\\ \Delta H_{\mathrm{rxn}}^{\circ}=-1485.03 \mathrm{~kJ} / \mathrm{mol} \\ \frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{3}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=142.2 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$

How are the standard enthalpies of an element and of a compound determined?

What is meant by the standard enthalpy of a reaction?

Write the equation for calculating the enthalpy of a reaction. Define all the terms.

Which of the following standard enthalpy of formation values is not zero at \(25^{\circ} \mathrm{C}: \mathrm{Na}(\) monoclinic \(), \mathrm{Ne}(g)\) \(\mathrm{CH}_{4}(g), \mathrm{S}_{8}(\) monoclinic \(), \mathrm{Hg}(l), \mathrm{H}(g) ?\)

The \(\Delta H_{\mathrm{f}}^{\circ}\) values of the two allotropes of oxygen, \(\mathrm{O}_{2}\) and \(\mathrm{O}_{3}\), are 0 and \(142.2 \mathrm{~kJ} / \mathrm{mol}\), respectively, at \(25^{\circ} \mathrm{C}\). Which is the more stable form at this temperature?

The standard enthalpies of formation of ions in aqueous solutions are obtained by arbitrarily assigning a value of zero to \(\mathrm{H}^{+}\) ions; that is, \(\Delta H_{\mathrm{f}}^{\mathrm{o}}\left[\mathrm{H}^{+}(a q)\right]=0 .\) (a) For the following reaction \(\begin{aligned} \mathrm{HCl}(g) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{H}^{+}(a q)+\mathrm{Cl}^{-}(a q) & \Delta H^{\circ}=-74.9 \mathrm{~kJ} / \mathrm{mol} \end{aligned}\) calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for the \(\mathrm{Cl}^{-}\) ions. \((\mathrm{b})\) Given that \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{OH}^{-}\) ions is \(-229.6 \mathrm{~kJ} / \mathrm{mol},\) calculate the enthalpy of neutralization when 1 mole of a strong monoprotic acid (such as \(\mathrm{HCl}\) ) is titrated by \(1 \mathrm{~mole}\) of a strong base \((\) such as \(\mathrm{KOH})\) at \(25^{\circ} \mathrm{C}\).