Chapter 4

A diamond can be considered a giant all-carbon supermolecule in which almost every carbon atom is bonded to four other carbons. When a diamond cutter cleaves (splits) a diamond, carbon-carbon bonds must be broken. Is the cleavage (splitting) of a diamond endothermic or exothermic? Explain.

When \(0.100 \mathrm{~g} \mathrm{CaO}(\mathrm{s})\) is added to \(125 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\) at \(23.6^{\circ} \mathrm{C}\) in a coffee cup calorimeter, this reaction occurs. \(\mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) \quad \Delta_{t} H^{\circ}=-81.9 \mathrm{~kJ} / \mathrm{mol}\) Calculate the final temperature of the solution.

A coffee cup calorimeter can be used to investigate the "cold pack reaction," the process that occurs when solid ammonium nitrate dissolves in water: $$ \mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{NH}_{4}^{+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) $$ Suppose \(25.0 \mathrm{~g}\) solid \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) at \(23.0{ }^{\circ} \mathrm{C}\) is added to 250\. \(\mathrm{mL} \mathrm{H}_{2} \mathrm{O}\) at the same temperature. After all of the solid dissolves, the temperature is measured to be \(15.6^{\circ} \mathrm{C}\). Calculate the reaction enthalpy for the cold pack reaction. (Assume that the specific heat capacity of the solution is the same as for water.) Is the reaction endothermic or exothermic?

When a \(13.0-\mathrm{g}\) sample of \(\mathrm{NaOH}(\mathrm{s})\) dissolves in \(400.0 \mathrm{~mL}\) water in a coffee cup calorimeter, the temperature of the water changes from \(22.6^{\circ} \mathrm{C}\) to \(30.7^{\circ} \mathrm{C}\). Assuming that the specific heat capacity of the solution is the same as for water, calculate (a) The heat transfer from system to surroundings. (b) \(\Delta_{\mathrm{r}} H\) for the reaction. $$ \mathrm{NaOH}(\mathrm{s}) \longrightarrow \mathrm{Na}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) $$

Suppose that you mix \(200.0 \mathrm{~mL}\) of \(0.200-\mathrm{M} \mathrm{RbOH}(\) aq \()\) with \(100 . \mathrm{mL}\) of \(0.400-\mathrm{M} \mathrm{HBr}(\mathrm{aq})\) in a coffee cup calorimeter. If the temperature of each of the two solutions was \(24.40^{\circ} \mathrm{C}\) before mixing, and the temperature rises to \(26.18^{\circ} \mathrm{C}\) (a) Calculate the heat transfer as a result of the reaction. (b) Write the thermochemical expression for the reaction.

A 0.692 -g sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is burned in a constant-volume calorimeter. The temperature rises from \(21.70{ }^{\circ} \mathrm{C}\) to \(25.22{ }^{\circ} \mathrm{C}\). The calorimeter contains \(575 \mathrm{~g}\) water, and the bomb has a heat capacity of \(650 \mathrm{~J} / \mathrm{K}\). Determine \(\Delta_{t} E\) per mole of glucose.

Benzoic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2},\) occurs naturally in many berries. Suppose you burn \(1.500 \mathrm{~g}\) of the compound in a combustion calorimeter and find that the temperature of the calorimeter increases from \(22.50^{\circ} \mathrm{C}\) to \(31.69^{\circ} \mathrm{C}\). The calorimeter contains \(775 \mathrm{~g}\) water, and the bomb has a heat capacity of \(893 \mathrm{~J}^{\circ} \mathrm{C}^{-1}\). Calculate \(\Delta_{\mathrm{r}} E\) per mole of benzoic acid.

Design an experiment to directly measure the reaction enthalpy for this reaction $$ 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ Describe the apparatus and how the experiment would be carried out.

These reaction enthalpies can be measured: \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)\) \(\Delta_{\mathrm{r}} H^{\circ}=-1411.1 \mathrm{~kJ} / \mathrm{mol}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)\) \(\Delta_{t} H^{\circ}=-1367.5 \mathrm{~kJ} / \mathrm{mol}\) Use these values and Hess's law to determine the reaction enthalpy for $$ \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell) $$

Three reactions very important to the semiconductor industry are (a) The reduction of silicon dioxide to crude silicon, \(\mathrm{SiO}_{2}(\mathrm{~s})+2 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{Si}(\mathrm{s})+2 \mathrm{CO}(\mathrm{g})\) $$ \Delta_{\mathrm{r}} H^{\circ}=689.9 \mathrm{~kJ} / \mathrm{mol} $$ (b) The formation of silicon tetrachloride from crude silicon, $$ \mathrm{Si}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SiCl}_{4}(\mathrm{~g}) \quad \Delta_{\mathrm{t}} H^{\circ}=-657.01 \mathrm{~kJ} / \mathrm{mol} $$ (c) The reduction of silicon tetrachloride to pure silicon with magnesium, $$ \begin{array}{r} \mathrm{SiCl}_{4}(\mathrm{~g})+2 \mathrm{Mg}(\mathrm{s}) \longrightarrow 2 \mathrm{MgCl}_{2}(\mathrm{~s})+\mathrm{Si}(\mathrm{s}) \\ \Delta_{\mathrm{r}} H^{\circ}=-625.6 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate the overall enthalpy change when \(1.00 \mathrm{~mol}\) sand, \(\mathrm{SiO}_{2}\), changes into very pure silicon by this series of reactions.

You wish to know the standard formation enthalpy of liquid \(\mathrm{PCl}_{3}\) $$ \mathrm{P}_{4}(\mathrm{~s})+6 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PCl}_{3}(\ell) $$ These reaction enthalpies have been determined experimentally: $$ \begin{array}{ll} \mathrm{P}_{4}(\mathrm{~s})+10 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{PCl}_{5}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-1774.0 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{PCl}_{3}(\ell)+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-123.8 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate the formation enthalpy for \(\mathrm{PCl}_{3}(\ell)\).

Calculate the standard reaction enthalpy, \(\Delta_{\mathrm{t}} H^{\circ}\), for formation of \(1 \mathrm{~mol}\) strontium carbonate (the material that gives the red color in fireworks) from its elements. $$ \mathrm{Sr}(\mathrm{s})+\mathrm{C}(\text { graphite })+\frac{3}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{Sr} \mathrm{CO}_{3}(\mathrm{~s}) $$ The information available is $$ \begin{array}{ll} \mathrm{Sr}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SrO}(\mathrm{s}) & \Delta_{\mathrm{r}} H^{\circ}=-592 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{SrO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SrCO}_{3}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-234 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g}) & \Delta_{\mathrm{r}} H^{\circ}=-394 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Calorimetric measurements show that the reaction of magnesium with chlorine releases \(26.4 \mathrm{~kJ}\) per gram of magnesium reacted. (a) Write a balanced chemical equation for the reaction. (b) Calculate the standard formation enthalpy of magnesium chloride.

We burn 3.47 g lithium in excess oxygen at constant atmospheric pressure to form \(\mathrm{Li}_{2} \mathrm{O} .\) Then, we bring the reaction mixture back to \(25^{\circ} \mathrm{C}\). In this process \(146 \mathrm{~kJ}\) of heat is given off. Calculate the standard formation enthalpy of \(\mathrm{Li}_{2} \mathrm{O}\)

When \(43.2 \mathrm{~g} \mathrm{Mg}\) reacts with sufficient sulfur, \(615 \mathrm{~kJ}\) is transferred to the surroundings. Calculate the standard formation enthalpy for \(\mathrm{MgS}\).

You want to heat the air in your house with natural gas, \(\mathrm{CH}_{4}\). Assume your house has \(275 \mathrm{~m}^{2}\) (about \(2800 \mathrm{ft}^{2}\) ) of floor area and that the ceilings are \(2.50 \mathrm{~m}\) (about \(8 \mathrm{ft}\) ) from the floors. The air in the house has a molar heat capacity of \(29.1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). (The number of moles of air in the house can be found by assuming that the average molar mass of air is \(28.9 \mathrm{~g} / \mathrm{mol}\) and that the density of air at these temperatures is \(1.22 \mathrm{~g} / \mathrm{L}\). ) Calculate what mass of methane you have to burn to heat the air from \(15.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C}\)

If you want to convert \(56.0 \mathrm{~g}\) ice (at \(\left.0^{\circ} \mathrm{C}\right)\) to water at \(75.0^{\circ} \mathrm{C},\) calculate how many grams of propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\), you would have to burn to supply the energy to melt the ice and then warm it to the final temperature (at 1 bar).

Calculate the quantity of energy, in joules, required to raise the temperature of \(454 \mathrm{~g}\) tin from room temperature, \(25.0^{\circ} \mathrm{C}\), to its melting point, \(231.9{ }^{\circ} \mathrm{C},\) and then melt the tin at that temperature. (The specific heat capacity of tin is \(0.227 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\), and the enthalpy of fusion of this metal is \(59.2 \mathrm{~J} / \mathrm{g} .\) )

A \(25.0-\mathrm{mL}\) sample of benzene at \(19.9{ }^{\circ} \mathrm{C}\) was cooled to its melting point, \(5.5^{\circ} \mathrm{C}\), and then frozen. Calculate how much heat transfer to the surroundings occurred in this process. (The density of benzene is \(0.880 \mathrm{~g} / \mathrm{mL} ;\) its specific heat capacity is \(1.74 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}\), and its enthalpy of fusion is \(127 \mathrm{~J} / \mathrm{g} .)\)

You add \(100.0 \mathrm{~g}\) water at \(60.0^{\circ} \mathrm{C}\) to \(100.0 \mathrm{~g}\) ice at \(0.00^{\circ} \mathrm{C}\). Some of the ice melts and cools the water to \(0.00^{\circ} \mathrm{C}\). Calculate what mass of ice has melted when the ice and water mixture reaches a uniform temperature $$ \text { of } 0^{\circ} \mathrm{C} $$

From these enthalpies of reaction, $$ \begin{array}{ll} \mathrm{CaCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g}) & \Delta_{\mathrm{r}} H^{\circ}=178.3 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{~s}) & \Delta_{\mathrm{r}} H^{\circ}=-65.2 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{~s}) \longrightarrow \mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})\) $$ \Delta_{\mathrm{r}} H^{\circ}=-16.7 \mathrm{~kJ} / \mathrm{mol} $$ calculate \(\Delta_{\mathrm{r}} H^{\circ}\) for \(\mathrm{Ca}^{2+}(\mathrm{aq})+2 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CaCO}_{3}(\mathrm{~s})+\mathrm{H}_{2} \mathrm{O}(\ell)\)

How fast (in meters per second) must an iron ball with a mass of \(56.6 \mathrm{~g}\) be traveling to have a kinetic energy of \(15.75 \mathrm{~J} ?\)

Based on your experience, when ice melts to liquid water, is the process exothermic or endothermic? When liquid water freezes to ice at \(0{ }^{\circ} \mathrm{C}\), is this exothermic or endothermic? (Assume that the ice/water is the system in each case.) Explain your answers.

You pick up a six-pack of soft drinks from the floor, but it slips from your hand and smashes onto your foot. Comment on the work and energy involved in this sequence. What forms of energy are involved at what stages of the process?

The specific heat capacity of copper is \(0.385 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\), whereas it is \(0.128 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) for gold. Assume you place \(100 . \mathrm{g}\) of each metal, originally at \(25^{\circ} \mathrm{C},\) in a boiling water bath at \(100^{\circ} \mathrm{C}\). If energy is transferred to each metal at the same rate, determine which piece of metal will reach \(100^{\circ} \mathrm{C}\) first.

The sketch shows two identical beakers with different volumes of water at the same temperature. Is the thermal energy content of beaker 1 greater than, less than, or equal to that of beaker \(2 ?\) Explain your reasoning.

In their home laboratory, two students do an experiment (a rather dangerous one-don't try it without proper safety precautions!) with drain cleaner (Drano, a solid) and toilet bowl cleaner (The Works, a liquid solution). The students measure 1 teaspoon (tsp) of Drano into each of four Styrofoam coffee cups and dissolve the solid in half a cup of water. Then they wash their hands and go have lunch. When they return, they measure the temperature of the solution in each of the four cups and find it to be \(22.3^{\circ} \mathrm{C}\). Next they measure into separate small empty cups \(1,2,3,\) and 4 tablespoons (Tbsp) of The Works. In each cup they add enough water to make the total volume 4 Tbsp. After a few minutes they measure the temperature of each cup and find it to be \(22.3^{\circ} \mathrm{C}\). Finally the two students take each cup of The Works, pour it into a cup of Drano solution, and measure the temperature over a period of a few minutes. Their results are reported in the table. $$ \begin{array}{ccc} \hline & \text { Volume of } & \text { Highest } \\ \text { Experiment } & \text { The Works (Tbsp) } & \text { Temperature ( } \left.{ }^{\circ} \mathrm{C}\right) \\ \hline 1 & 1 & 28.0 \\ 2 & 2 & 33.6 \\ 3 & 3 & 39.3 \\ 4 & 4 & 39.4 \\ \hline \end{array} $$ Discuss these results and interpret them in terms of the thermochemistry and stoichiometry of the reaction. Is the reaction exothermic or endothermic? Why is more energy transferred in some cases than others? For each experiment, which reactant, Drano or The Works, is limiting? Why are the final temperatures nearly the same in experiments 3 and \(4 ?\) What can you conclude about the stoichiometric ratio between the two reactants?

In some cities, taxicabs run on liquefied propane fuel instead of gasoline. This practice extends the lifetime of the vehicle and produces less pollution. Given that it costs about 2000 to modify the engine of a taxicab to run on propane and that the cost of gasoline and liquid propane are 3.50 per gallon and 2.50 per gallon, respectively, make reasonable assumptions and figure out how many miles a taxi would have to go so that the decreased fuel cost would balance the added cost of modifying the taxi's motor.