Chapter 5

The flavor of anise is due to anethole, a compound with the molecular formula \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O} .\) The \(\Delta H_{\text {comb }}\) value for anethole is \(-5541 \mathrm{kJ} / \mathrm{mol} .\) Assume \(0.950 \mathrm{g}\) of anethole is combusted in a calorimeter whose heat capacity ( \(C_{\text {calorimeter }}\) ) is \(7.854 \mathrm{kJ} /^{\circ} \mathrm{C}\) at \(20.611^{\circ} \mathrm{C} .\) What is the final temperature of the calorimeter?

Adding \(2.00 \mathrm{g}\) of \(\mathrm{Mg}\) metal to \(95.0 \mathrm{mL}\) of \(1.00 \mathrm{MHCl}\) in a coffee-cup calorimeter leads to a temperature increase of \(9.2^{\circ} \mathrm{C}\) a. Write a balanced net ionic equation for the reaction. b. If the molar heat capacity of \(1.00 M \mathrm{HCl}\) is the same as that for water \(\left[c_{\mathrm{P}}=75.3 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right],\) what is \(\Delta H_{\mathrm{rxn}} ?\)

What is the \(\Delta H_{\text {rxn }}\) for the precipitation of AgCl if adding \(125 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{AgNO}_{3}\) to \(125 \mathrm{mL}\) of \(1.00 \mathrm{M} \mathrm{NaCl}\) at \(18.6^{\circ} \mathrm{C}\) causes the temperature to increase to \(26.4^{\circ} \mathrm{C} ?\) (Assume \(\left.c_{\mathrm{P}, \text { soln }}=c_{\text {P,water }}\right)\).

How much glucose must be metabolized to completely evaporate \(1.00 \mathrm{g}\) of water at \(37^{\circ} \mathrm{C},\) given \(\Delta H_{\text {comb, }, \text { glucose }}=\) \(-2803 \mathrm{kJ} / \mathrm{mol} ?\)

If all the energy obtained from burning 275 g of propane \(\left(\Delta H_{\mathrm{comb}, \mathrm{C}, \mathrm{H}_{3}}=-2220 \mathrm{kJ} / \mathrm{mol}\right)\) is used to heat water, how many liters of water can be heated from \(20.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\)

How is Hess's law consistent with the law of conservation of energy?

Why is it important for Hess's law that enthalpy is a state function?

How can the first two of the following reactions be combined to obtain the third reaction? a. \(\mathrm{CO}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g)\)

Cleansing the Atmosphere The atmosphere contains the highly reactive molecule OH, which acts to remove selected pollutants. Use the values for \(\Delta H_{\mathrm{rxn}}\) given below to find the \(\Delta H_{\mathrm{rxn}}\) for the formation of \(\mathrm{OH}\) and \(\mathrm{H}\) from water. $$\begin{array}{rll} \frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{OH}(g) & \Delta H_{\mathrm{rm}}=42.1 \mathrm{kJ} \\ \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{H}(g) & \Delta H_{\mathrm{rm}}=435.9 \mathrm{kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H_{\mathrm{rrm}}=-241.8 \mathrm{kJ} \\ \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}(g)+\mathrm{OH}(g) & \Delta H_{\mathrm{rm}}=? \end{array}$$

The destruction of the ozone layer by chlorofluorocarbons (CFCs) can be described by the following reactions: $$\begin{aligned} \mathrm{ClO}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{Cl}(g)+2 \mathrm{O}_{2}(g) & & \Delta H_{\mathrm{rxn}}=-29.90 \mathrm{kJ} \\ 2 \mathrm{O}_{3}(g) \rightarrow 3 \mathrm{O}_{2}(g) & & \Delta H_{\mathrm{rxn}}=24.18 \mathrm{kJ} \end{aligned}$$ Determine the value of the heat of reaction for the following: $$\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \rightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \quad \Delta H_{\mathrm{rxn}}=?$$

What is \(\Delta H_{\text {rxn }}\) for the reaction between \(\mathrm{H}_{2} \mathrm{S}\) and \(\mathrm{O}_{2}\) that yields \(\mathrm{SO}_{2}\) and water, \(2 \mathrm{H}_{2} \mathrm{S}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}=?\) given \(\Delta H_{\mathrm{rxn}}\) for the following reactions? $$\begin{aligned} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) & & \Delta H_{\mathrm{rxn}}=-241.8 \mathrm{kJ} \\ \mathrm{SO}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{S}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) & & \Delta H_{\mathrm{rxn}}=34.8 \mathrm{kJ} \end{aligned}$$

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

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

Oxygen and ozone are both forms of elemental oxygen. Are the standard enthalpies of formation of oxygen and ozone the same? Explain.

Explain why the heats of formation of elements in their standard states are zero.

For which of the following reactions does \(\Delta H_{\mathrm{rxn}}^{\circ}\) represent an enthalpy of formation? a. \(C(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)\) b. \(\mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightarrow 2 \mathrm{CO}(g)\) c. \(\mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)\) d. \(2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \rightarrow \mathrm{CH}_{4}(g)\)

For which of the following reactions does \(\Delta H_{\mathrm{rxn}}^{\circ}\) also represent an enthalpy of formation? a. \(2 \mathrm{N}_{2}(g)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)+2 \mathrm{NO}(g)\) b. \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}(g)\) c. \(2 \mathrm{NO}_{2}(g) \rightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) d. \(\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\)

Use the following standard heats of formation to calculate the molar enthalpy of vaporization of liquid hydrogen peroxide: \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}(\ell)\) is \(-188 \mathrm{kJ} / / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{H}_{2} \mathrm{O}_{2}(g)\) is \(-136 \mathrm{kJ} / \mathrm{mol}\)

Use the following standard heats of formation to calculate the molar enthalpy of vaporization of acetic acid: \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{COOH}(\ell)\) is \(-484.5 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ}\) of \(\mathrm{CH}_{3} \mathrm{COOH}(g)\) is \(-432.8 \mathrm{~kJ} / \mathrm{mol}\).

Ammonium nitrate decomposes to \(\mathrm{N}_{2} \mathrm{O}\) and water vapor at temperatures between \(250^{\circ} \mathrm{C}\) and \(300^{\circ} \mathrm{C} .\) Write a balanced chemical reaction describing the decomposition of ammonium nitrate, and calculate the enthalpy of reaction by using the appropriate enthalpies of formation from Appendix 4.

Explosives called amatols are mixtures of ammonium nitrate and 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 determine the standard enthalpy of reaction by using the appropriate standard enthalpies of formation from Appendix 4.

How can the standard enthalpy of formation of \(\mathrm{CO}(g)\) be calculated from the standard enthalpy of formation \(\Delta H_{f}^{\circ}\) of \(\mathrm{CO}_{2}(g)\) and the standard enthalpy of combustion \(\Delta H_{\mathrm{comb}}^{\circ}\) of \(\mathrm{CO}(g) ?\)

Calculate the standard enthalpy of formation of \(\mathrm{SO}_{2}(g)\) from the standard enthalpy changes of the following reactions: $$\begin{aligned} 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g) & & \Delta H_{\mathrm{rxn}}^{\circ}=-196 \mathrm{kJ} \\ \frac{1}{4} \mathrm{S}_{8}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g) & & \Delta H_{\operatorname{man}}^{\circ}=-790 \mathrm{kJ} \\\ \frac{1}{8} \mathrm{S}_{8}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{SO}_{2}(g) & \Delta H_{5}^{\circ} &=? \end{aligned}$$

Use the following data to calculate the enthalpy of formation of \(\mathrm{NO}_{2} \mathrm{Cl}\) from \(\mathrm{N}_{2}, \mathrm{O}_{2},\) and \(\mathrm{Cl}_{2}\) $$\begin{aligned} \mathrm{NO}_{2} \mathrm{Cl}(g) \rightarrow \mathrm{NO}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=+20.6 \mathrm{kJ} \\ \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g) & \Delta H_{f}^{\circ}=+33.2 \mathrm{kJ} \\ \frac{1}{2} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{NO}_{2} \mathrm{Cl}(g) & \Delta H_{f}^{\circ}=? \end{aligned}$$

Baking soda decomposes on heating as follows, creating the holes in baked bread: $$2 \mathrm{NaHCO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)$$ Calculate the standard enthalpy of formation of \(\mathrm{NaHCO}_{3}(s)\) from the following information: $$\begin{aligned} \Delta H_{\mathrm{rxn}}^{\circ} &=-129.3 \mathrm{kJ} & \Delta H_{\mathrm{f}}\left[\mathrm{Na}_{2} \mathrm{CO}_{3}(s)\right] &=-1131 \mathrm{kJ} / \mathrm{mol} \\ \Delta H_{\mathrm{f}}\left[\mathrm{CO}_{2}(g)\right] &=-394 \mathrm{kJ} / \mathrm{mol} & \Delta H_{5}^{\mathrm{C}}\left[\mathrm{H}_{2} \mathrm{O}(\ell)\right] &=-286 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$

What is meant by fuel value?

What are the units of fuel values?

How are fuel values calculated from molar enthalpies of combustion?

Is the fuel value of liquid propane the same as that of propane gas?

An increasing number of vehicles in the United States can run on either gasoline \(\left[\mathrm{C}_{9} \mathrm{H}_{20}(\ell), \Delta H_{\text {comb., } \text { assoline }}=-6160 \mathrm{kJ} / \mathrm{mol}\right]\) or ethanol \(\left[\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\ell), \Delta H_{\text {comb,ethanol}}=-1367 \mathrm{kJ} / \mathrm{mol}\right] .\) Which fuel has the greater fuel value?

Food contains three main categories of compounds: carbohydrate, protein, and fat. Arctic explorers often eat a high-fat diet because fats have a high food value. The average food values for carbohydrate, protein, and fat are \(4 \mathrm{Cal} / \mathrm{g}, 4 \mathrm{Cal} / \mathrm{g},\) and \(9 \mathrm{Cal} / \mathrm{g},\) respectively. Consider a typical fat to have the chemical formula \(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2},\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) to be a representative carbohydrate, and the amino acid alanine \(\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{NO}_{2}\right)\) a building block of proteins. Express the food values given above as \(\Delta H_{\text {comb }}\) in \(\mathrm{k} \mathrm{J} / \mathrm{mol}\).

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 \(\Delta H_{\mathrm{comb}}^{\circ}=-3535 \mathrm{kJ} / \mathrm{mol}\) b. How much energy 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 energy released during combustion is used to heat the water.

The heavier hydrocarbons in white gas are hexanes \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) a. Calculate the fuel value of \(C_{6} H_{14},\) given that \(\Delta H_{\mathrm{comb}}^{\circ}=-4163 \mathrm{kJ} / \mathrm{mol}\) b. How much energy 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 the energy released during combustion is used to heat the water. d. Assume white gas is \(25 \%\) C \(_{5}\) hydrocarbons and \(75 \% \mathrm{C}_{6}\) 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 standard enthalpies of combustion of ethyne \(\left[\mathrm{C}_{2} \mathrm{H}_{2}(g)\right], \mathrm{C}(s),\) and \(\mathrm{H}_{2}(g)\) are \(-1299.6,-393.5,\) and \(-285.9 \mathrm{kJ} / \mathrm{mol},\) respectively. Use this information to calculate the standard enthalpy of formation of ethyne.

Carbon tetrachloride (CCl_) was at one time used as a fire-extinguishing agent. It has a molar heat capacity cp of \(131.3 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) .\) How much energy is required to raise the temperature of \(275 \mathrm{g}\) of \(\mathrm{CCl}_{4}\) from room temperature \(\left(22^{\circ} \mathrm{C}\right)\) to its boiling point \(\left(77^{\circ} \mathrm{C}\right) ?\)

Ethylene glycol (HOCH,CH,OH) is mixed with the water in radiators to cool car engines. How much heat will \(725 \mathrm{g}\) of pure ethylene glycol remove from an engine as it is warmed from \(0^{\circ} \mathrm{C}\) to its boiling point of \(196^{\circ} \mathrm{C} ?\) The \(c_{\mathrm{P}}\) of ethylene glycol is \(149.5 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\)

The standard enthalpy of formation of \(\mathrm{NH}_{3}\) is \(-46.1 \mathrm{kJ} / \mathrm{mol}\). What is \(\Delta H_{\text {rxn }}^{\circ}\) for the following reactions? a. \(\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)\) b. \(\mathrm{NH}_{3}(g) \rightarrow \frac{1}{2} \mathrm{N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g)\)

Hung Out to Dry Laundry left outside to dry on a clothesline in the winter slowly dries by "ice vaporization" (sublimation). The increase in internal energy of water vapor produced by sublimation is less than the amount of heat absorbed. Explain.

Chlorofluorocarbons (CFCs) such as \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) are refrigerants whose use has been phased out because of their destructive effect on Earth's ozone layer. The standard enthalpy of vaporization of \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) is \(17.4 \mathrm{kJ} / \mathrm{mol}\) compared with \(\Delta H_{\mathrm{vap}}^{\circ}=40.67 \mathrm{kJ} / \mathrm{mol}\) for liquid water. How many grams of liquid \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) are needed to cool \(200.0 \mathrm{g}\) of water from \(50.0^{\circ} \mathrm{C}\) to \(40.0^{\circ} \mathrm{C} ?\) The specific heat of water is \(\left.4.184 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\right)\)

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

An insulated container is used to hold \(50.0 \mathrm{g}\) of water at \(25.0^{\circ} \mathrm{C} .\) A \(7.25 \mathrm{g}\) sample of copper is placed in a dry test tube and heated for 30 minutes in a boiling water bath at \(100.1^{\circ} \mathrm{C} .\) The heated test tube is carefully removed from the water bath with laboratory tongs and inclined so that the copper slides into the water in the insulated container. Given that the specific heat of solid copper is \(0.385 \mathrm{J} /\) \(\left(\mathrm{g} \cdot^{\circ} \mathrm{C}\right),\) calculate the maximum temperature of the water in the insulated container after the copper metal is added.

The mineral 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?

Which of the following substances has a standard enthalpy of formation equal to zero? (a) Pb at \(1000^{\circ} \mathrm{C} ;\) (b) \(\mathrm{C}_{3} \mathrm{H}_{8}(g)\) at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure; (c) solid glucose at room temperature; (d) \(\mathrm{N}_{2}(g)\) at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure.

The standard enthalpy of formation of liquid water is \(-285.8 \mathrm{kJ} / \mathrm{mol}\) a. What is the significance of the negative sign associated with this value? b. Why is the magnitude of this value so much larger than the enthalpy of vaporization of water \(\left(\Delta H_{\mathrm{vap}}^{\circ}=40.67 \mathrm{kJ} /\right.\) mol \() ?\) c. Calculate the amount of heat produced in making \(50.0 \mathrm{mL}\) of water from its elements under standard conditions.

Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\left(\Delta H_{\mathrm{f}}^{\circ}=226.7 \mathrm{kJ} / \mathrm{mol}\right),\) and benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\left(\Delta H_{\mathrm{f}}^{\circ}=49.0 \mathrm{kJ} / \mathrm{mol}\right),\) are sometimes referred to as endothermic compounds. a. Why are \(\mathrm{C}_{2} \mathrm{H}_{2}\) and \(\mathrm{C}_{6} \mathrm{H}_{6}\) called endothermic compounds? b. Calculate the standard molar enthalpy of combustion of acetylene and benzene.

Balance the following chemical equation, name the reactants and products, and calculate the standard enthalpy change by using the data in Appendix 4 $$\mathrm{FeO}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)$$

The standard enthalpies of formation of benzene \(C_{6} \mathrm{H}_{6}(\ell)\) \(\mathrm{CO}_{2}(g),\) and \(\mathrm{H}_{2} \mathrm{O}(\ell)\) are \(49.0,-394,\) and \(-286 \mathrm{kJ} / \mathrm{mol}\) respectively. Use this information to calculate the standard enthalpy of combustion of \(\mathrm{C}_{6} \mathrm{H}_{6}(\ell)\)

The specific heat of solid copper is \(0.385 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}\) ). What thermal energy change occurs when a \(35.3 \mathrm{g}\) sample of copper is cooled from \(35.0^{\circ} \mathrm{C}\) to \(15.0^{\circ} \mathrm{C} ?\) Be sure to give your answer the proper sign. This amount of energy is used to melt solid ice at \(0.0^{\circ} \mathrm{C} .\) The molar enthalpy of fusion of ice is \(6.01 \mathrm{kJ} / \mathrm{mol} .\) How many moles of ice are melted?

Use Hess's law and the following data to calculate the standard enthalpy of formation of ethanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\ell)\) $$\begin{array}{ll} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(g) \rightarrow & \\ 2 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(\ell) & \Delta H_{\mathrm{ren}}^{\circ}=-1368.2 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) & \Delta H_{f}^{\circ}=-393.5 \mathrm{kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell) & \Delta H_{f}^{\circ}=-285.9 \mathrm{kJ} / \mathrm{mol} \end{array}$$

Use Hess's law and the following data to calculate the standard enthalpy of formation of \(\mathrm{CH}_{4}(g)\). $$\begin{aligned} &\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) \quad \Delta H_{f}^{\circ}=-393.5 \mathrm{kJ} / \mathrm{mol}\\\ &\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell) \quad \Delta H_{\mathrm{f}}^{\circ}=-285.9 \mathrm{kJ} / \mathrm{mol}\\\ &\begin{aligned} \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow & \\ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) & \Delta H_{\mathrm{rxn}}^{\circ}=-890.4 \mathrm{kJ} / \mathrm{mol} \end{aligned} \end{aligned}$$