Chapter 9

The mineral spodumene \(\left(\operatorname{LiAlSi}_{2} \mathrm{O}_{6}\right)\) exists in two crystalline forms called \(\alpha\) and \(\beta .\) Use Hess's law and the following information to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the conversion of \(\alpha\) -spodumene into \(\beta\) -spodumene: $$\begin{array}{r}\mathrm{Li}_{2} \mathrm{O}(s)+2 \mathrm{Al}(s)+4 \mathrm{SiO}_{2}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow 2 \alpha-\mathrm{LiAlSi}_{2} \mathrm{O}_{6}(s) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-1870.6 \mathrm{kJ} \end{array}$$ $$\begin{array}{r}\mathrm{Li}_{2} \mathrm{O}(s)+2 \mathrm{Al}(s)+4 \mathrm{SiO}_{2}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \rightarrow 2 \beta-\mathrm{LiAlSi}_{2} \mathrm{O}_{6}(s) \\\\\Delta H_{\mathrm{rxn}}^{\circ}=-1814.6 \mathrm{kJ} \end{array}$$

Given the following thermochemical data: $$\begin{array}{ll}\frac{1}{2} \mathrm{N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \frac{1}{2} \mathrm{NO}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=+90.3 \mathrm{kJ} \\\ \mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{NOCl}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=-38.6 \mathrm{kJ} \end{array}$$ what is the value of \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the decomposition of NOCl? $$2 \mathrm{NOCl}(g) \rightarrow \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\mathrm{Cl}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=?$$

Synthetic natural gas (SNG), sometimes called substitute natural gas, is a methane-containing mixture produced from the gasification of coal or oil shale directly at the site of the mine or oil field. One reaction for the production of SNG is: $$4 \mathrm{CO}(g)+8 \mathrm{H}_{2}(g) \rightarrow 3 \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$$ Use the following thermochemical equations to determine \(\Delta H^{\circ}\) for the reaction as written. $$\begin{aligned}\mathrm{C}(\text { graphite })+2 \mathrm{H}_{2}(g) & \rightarrow \mathrm{CH}_{4}(g) & \Delta H^{\circ} &=-74.8 \mathrm{kJ} \\\\\mathrm{C}(\text { graphite })+\frac{1}{2} \mathrm{O}_{2}(g) & \rightarrow \mathrm{CO}(g) & \Delta H^{\circ} &=-110.5 \mathrm{kJ}\end{aligned}$$ $$\begin{array}{ll}\mathrm{CO}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) & \Delta H^{\circ}=-283.0 \mathrm{kJ} \\\\\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ}=-285.8 \mathrm{kJ}\end{array}$$

Why is the standard heat of formation of \(\mathrm{CO}(g)\) difficult to measure experimentally?

Explain how the use of \(\Delta H_{f}^{\circ}\) to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) is an example of Hess's law.

Oxygen and ozone are both forms of elemental oxygen. Are the standard heats of formation of oxygen and ozone the same? Why or why not?

Why are the standard heats of formation of elements in their standard states assigned a value of zero?

Why must the stoichiometry of a reaction be known in order to estimate the enthalpy change from bond energies?

Why must the structures of the reactants and products be known in order to estimate the enthalpy change of a reaction from bond energies?

When calculating the enthalpy change for a chemical reaction using bond energies, why is it important that the reactants and products all be gases?

If the energy needed to break two moles of \(\mathrm{C}=\mathrm{O}\) bonds is greater than the sum of the energies needed to break the \(\mathrm{O}=\mathrm{O}\) bonds in one mole of \(\mathrm{O}_{2}\) and vaporize one mole of carbon, why does the combustion of pure carbon release heat?

Use standard heats of formation from Appendix 4 to calculate the standard heat of reaction for the following methane-generating reaction of methanogenic bacteria: $$4 \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CH}_{4}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell)$$

Use standard enthalpies of formation from Appendix 4 to calculate the standard enthalpy of reaction for the following methane-generating reaction of methanogenic bacteria, given \(\Delta H_{f}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{NH}_{2}(g)=-22.97 \mathrm{kJ} / \mathrm{mol}:\) $$4 \mathrm{CH}_{3} \mathrm{NH}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 3 \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g)+4 \mathrm{NH}_{3}(g)$$

Explosives called amatols are mixtures of ammonium nitrate and trinitrotoluene (TNT) introduced during World War I when TNT was in short supply. The mixtures can provide \(30 \%\) more explosive power than TNT alone. Above \(300^{\circ} \mathrm{C},\) ammonium nitrate decomposes to \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{H}_{2} \mathrm{O} .\) Write a balanced chemical reaction describing the decomposition of ammonium nitrate, and calculate its \(\Delta H_{\mathrm{rxn}}^{\circ}\) using the appropriate \(\Delta H_{\mathrm{f}}^{\circ}\) values from Appendix 4.

Use average bond energies to estimate the difference in \(\Delta H_{\mathrm{rxn}}^{\circ}\) values between the incomplete combustion of one mole of ethane to carbon monoxide and water vapor and the complete combustion of ethane to carbon dioxide and water vapor.

Use average bond energies to estimate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the following reaction: $$4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$

How do ion-dipole interactions influence whether an ionic compound's heat of solution is exothermic or endothermic?

Sodium hydroxide is more soluble in hot water than in cold water, but dissolving sodium hydroxide in water is an exothermic process. How can this be the case?

What is meant by fuel value?

Without doing any calculations, predict which compound in each pair releases more energy during combustion: a. 1 mole of \(\mathrm{CH}_{4}\) or 1 mole of \(\mathrm{H}_{2}\) b. \(1 \mathrm{g}\) of \(\mathrm{CH}_{4}\) or \(1 \mathrm{g}\) of \(\mathrm{H}_{2}\)

Is fuel value or fuel density a more useful measure of energy content of liquid fuels? Explain your answer.

Use a Born-Haber cycle to calculate the lattice energy of potassium chloride (KCl) from the following data: $$\begin{aligned} &\text { Ionization energy of } \mathrm{K}(g)=419 \mathrm{kJ} / \mathrm{mol}\\\ &\text { Electron affinity of } \mathrm{Cl}(g)=-349 \mathrm{kJ} / \mathrm{mol}\\\ &\text { Energy to sublime } \mathrm{K}(s)=89 \mathrm{kJ} / \mathrm{mol}\\\ &\text { Bond energy of } \mathrm{Cl}_{2}(g)=243 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$ Standard heat of formation of \(\mathrm{KCl}=-436.5 \mathrm{kJ} / \mathrm{mol}\)

Calculate the lattice energy of sodium oxide \(\left(\mathrm{Na}_{2} \mathrm{O}\right)\) from the following data: Ionization energy of \(\mathrm{Na}(g)=495 \mathrm{kJ} / \mathrm{mol}\) Electron affinity of \(\mathrm{O}(g)\) for 2 electrons \(=603 \mathrm{kJ} / \mathrm{mol}\) Energy to sublime \(\mathrm{Na}(s)=109 \mathrm{kJ} / \mathrm{mol}\) Bond energy of \(\mathrm{O}_{2}(g)=498 \mathrm{kJ} / \mathrm{mol}\) \(\Delta H_{\mathrm{rxn}}\) for \(2 \mathrm{Na}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{Na}_{2} \mathrm{O}(s)=-416 \mathrm{kJ} / \mathrm{mol}\)

Lightweight camping stoves typically use white gas, a mixture of \(\mathrm{C}_{5}\) and \(\mathrm{C}_{6}\) hydrocarbons. a. Calculate the fuel value of \(\mathrm{C}_{5} \mathrm{H}_{12},\) given that \(\Delta H_{\text {comb }}^{\circ}=\) \(-3535 \mathrm{kJ} / \mathrm{mol}\) b. How much heat is released during the combustion of \(1.00 \mathrm{kg}\) of \(\mathrm{C}_{5} \mathrm{H}_{12} ?\) c. How many grams of \(\mathrm{C}_{5} \mathrm{H}_{12}\) must be burned to heat \(1.00 \mathrm{kg}\) of water from \(20.0^{\circ} \mathrm{C}\) to \(90.0^{\circ} \mathrm{C} ?\) Assume that all the heat released during combustion is used to heat the water.

The heavier (more dense) hydrocarbons in camp stove fuel are hexanes \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\). a. Calculate the fuel value of \(\mathrm{C}_{6} \mathrm{H}_{14},\) given that \(\Delta H_{\text {comb }}^{\circ}=\) \(-4163 \mathrm{kJ} / \mathrm{mol}\). b. How much heat is released during the combustion of \(1.00 \mathrm{kg}\) of \(\mathrm{C}_{6} \mathrm{H}_{14} ?\) c. How many grams of \(\mathrm{C}_{6} \mathrm{H}_{14}\) are needed to heat \(1.00 \mathrm{kg}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(85.0^{\circ} \mathrm{C} ?\) Assume that all of the heat released during combustion is used to heat the water. d. Assume white gas is \(25 \% \mathrm{C}_{5}\) hydrocarbons (see Problem 9.109) and \(75 \%\) C \(_{6}\) hydrocarbons; how many grams of white gas are needed to heat \(1.00 \mathrm{kg}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(85.0^{\circ} \mathrm{C} ?\)

The industrial production of hydrogen chloride gas is most frequently carried out by direct synthesis from hydrogen and chlorine: $$\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)$$ Smaller quantities of HCl \((g)\) may be produced on the laboratory scale by the reaction of sodium chloride and sulfuric acid: $$2 \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(\ell) \rightarrow 2 \mathrm{HCl}(g)+\mathrm{Na}_{2} \mathrm{SO}_{4}(s)$$ Apply concepts discussed in this chapter and data from the appendix to determine if either heating or cooling is required when these reactions are carried out.

A typical double-patty hamburger from a fast-food establishment contains about 563 Calories. (Remember that the dietary "Calorie" is actually a kilocalorie.) Walking at a brisk pace burns about 4.70 Calories per minute. How many minutes would you need to walk to "burn off" the Calories in one double burger?

A 100.0 mL sample of \(1.0 \mathrm{MNaOH}\) is mixed with \(50.0 \mathrm{mL}\) of \(1.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) in a large Styrofoam coffee cup; a thermometer is mounted in the lid of the cup to measure the temperature of the contents. The temperature of each solution before mixing is \(22.3^{\circ} \mathrm{C} .\) After mixing, their temperature reaches \(31.4^{\circ} \mathrm{C} .\) Assume that (1) the density of the mixed solutions is \(1.00 \mathrm{g} / \mathrm{mL},(2)\) the specific heat of the mixed solutions is \(4.18 \mathrm{J} /\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right),\) and (3) no heat is lost to the surroundings. a. Write a balanced chemical equation for the reaction that takes place in the cup. b. Is any \(\mathrm{NaOH}\) or \(\mathrm{H}_{2} \mathrm{SO}_{4}\) left in the cup when the reaction is over? c. Calculate the enthalpy change per mole of \(\mathrm{H}_{2} \mathrm{O}\) produced in the reaction.

An insulated container holds \(50.0 \mathrm{g}\) of water at \(25.0^{\circ} \mathrm{C} .\) A \(7.25 \mathrm{g}\) sample of copper that had been heated to \(100.1^{\circ} \mathrm{C}\) is dropped into the water. What is the final shared temperature of the copper and the water?

Magnetite \(\left(\mathrm{Fe}_{3} \mathrm{O}_{4}\right)\) is magnetic, whereas iron(II) oxide is not. a. Write and balance the chemical equation for the formation of magnetite from iron(II) oxide and oxygen. b. Given that \(318 \mathrm{kJ}\) of heat is released for each mole of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) formed, what is the enthalpy change of the balanced reaction of formation of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) from iron(II) oxide and oxygen?

Endothermic compounds have positive standard heats of formation. An example is acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\left(\Delta \mathrm{H}_{\mathrm{f}}^{\circ}=\right.\) \(226.7 \mathrm{kJ} / \mathrm{mol}) .\) Combustion of acetylene in pure oxygen produces a flame hot enough to cut and weld steel. a. What is the standard heat of combustion of acetylene? b. What is the fuel value of acetylene, assuming the products are \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) vapor?

Balance the following chemical equation, name the reactants and products, and calculate the enthalpy change under standard conditions. $$\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H_{\mathrm{rxn}}^{\circ}= ?$$

Use appropriate bond energies from Table A4.1 of Appendix 4 to predict whether the reaction in which ethylene forms polyethylene plastic is exothermic, endothermic, or involves no change in enthalpy. The reaction can be written: $$n \mathrm{CH}_{2}=\mathrm{CH}_{2} \rightarrow\left[-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\right]_{n}$$ where the structure in the brackets is the repeating unit of polyethylene and the value of \(n\) is typically in the thousands.

In a high-temperature gas-phase reaction, methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) reacts with \(\mathrm{N}_{2}\) to produce \(\mathrm{HCN}\) and \(\mathrm{NH}_{3}\). The reaction is endothermic, requiring \(164 \mathrm{kJ}\) of thermal energy per mole of methanol under standard conditions. a. Write a balanced chemical equation for this reaction. b. Is energy a reactant or a product? c. What is the change in enthalpy under standard conditions if \(60.0 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) reacts with excess \(\mathrm{N}_{2}(g),\) forming \(\mathrm{HCN}(g),\) and \(\mathrm{NH}_{3}(g) ?\)

Calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the reaction $$2 \mathrm{Ni}(s)+\frac{1}{4} \mathrm{S}_{8}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NiSO}_{3}(s) \quad \Delta H_{\mathrm{rxn}}^{\circ}=?$$ from the following data: (1) \(\mathrm{NiSO}_{3}(s) \rightarrow \mathrm{NiO}(s)+\mathrm{SO}_{2}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=156 \mathrm{kJ}\) (2) \(\frac{1}{8} S_{8}(s)+O_{2}(g) \rightarrow \operatorname{SO}_{2}(g) \quad \quad \Delta H_{\operatorname{rxn}}^{\circ}=-297 \mathrm{kJ}\) (3) \(\mathrm{Ni}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{NiO}_{2}(s) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-241 \mathrm{kJ}\)

Use the information in thermochemical equations (1) through ( 3 ) to calculate the value of \(\Delta H_{\mathrm{rxn}}^{\circ}\) for the reaction in equation (4). (1) \(\mathrm{Pb}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{PbO}(s) \quad \quad \Delta H_{\mathrm{rxn}}^{\circ}=-219 \mathrm{kJ}\) (2) \(\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) \Delta H_{\text {rxn }}^{\circ}=-394 \mathrm{kJ}\) (3) \(\mathrm{PbCO}_{3}(s) \rightarrow \mathrm{PbO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H_{\text {rxn }}^{\circ}=86 \mathrm{kJ}\) (4) \(2 \mathrm{Pb}(s)+2 \mathrm{C}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{PbCO}_{3}(s) \quad \Delta H_{\mathrm{rxn}}^{\circ}=?\)

At high temperatures, such as those in the combustion chambers of automobile engines, nitrogen and oxygen form nitrogen monoxide: $$\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g) \quad \Delta H_{\mathrm{comb}}^{\circ}=+180 \mathrm{kJ}$$ Any NO released into the environment may be oxidized to \(\mathrm{NO}_{2}:\) $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g) \quad \Delta H_{\mathrm{comb}}^{\circ}=-112 \mathrm{kJ}$$ Is the overall reaction, $$\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$$ exothermic or endothermic? What is \(\Delta H_{\text {comb }}^{\circ}\) for this reaction?