Chapter 6

Which gives up more heat on cooling from \(50^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C}\) \(50.0 \mathrm{g}\) of water or \(100 .\) g of ethanol (specific heat capacity of ethanol \(=2.46 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}) ?\)

A 192 -g piece of copper is heated to \(100.0^{\circ} \mathrm{C}\) in a boiling water bath and then dropped into a beaker containing \(\left.751 \mathrm{g} \text { of water (density }=1.00 \mathrm{g} / \mathrm{cm}^{3}\right)\) at \(4.0^{\circ} \mathrm{C} .\) What is the final temperature of the copper and water after thermal equilibrium is reached? (The specific heat capacity of copper is \(0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K})\).

You determine that \(187 \mathrm{J}\) of heat is required to raise the temperature of \(93.45 \mathrm{g}\) of silver from \(18.5^{\circ} \mathrm{C}\) to \(27.0^{\circ} \mathrm{C}\) What is the specific heat capacity of silver?

Calculate the quantity of heat required to convert \(60.1 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) at \(0.0^{\circ} \mathrm{C}\) to \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(100.0^{\circ} \mathrm{C} .\) The heat of fusion of ice at \(0^{\circ} \mathrm{C}\) is \(333 \mathrm{J} / \mathrm{g}\); the heat of vaporization of liquid water at \(100^{\circ} \mathrm{C}\) is \(2260 \mathrm{J} / \mathrm{g}\).

You add \(100.0 \mathrm{g}\) of water at \(60.0^{\circ} \mathrm{C}\) to \(100.0 \mathrm{g}\) of ice at \(0.00^{\circ} \mathrm{C} .\) Some of the ice melts and cools the water to \(0.00^{\circ} \mathrm{C} .\) When the ice and water mixture has come to a uniform temperature of \(0^{\circ} \mathrm{C},\) how much ice has melted?

Three 45 -g ice cubes at \(0^{\circ} \mathrm{C}\) are dropped into \(5.00 \times\) \(10^{2} \mathrm{mL}\) of tea to make ice tea. The tea was initially at \(20.0^{\circ} \mathrm{C} ;\) when thermal equilibrium was reached, the final temperature was \(0^{\circ} \mathrm{C}\). How much of the ice melted and how much remained floating in the beverage? Assume the specific heat capacity of tea is the same as that of pure water.

Insoluble AgCl(s) precipitates when solutions of \(\mathrm{AgNO}_{3}(\mathrm{aq})\) and \(\mathrm{NaCl}(\mathrm{aq})\) are mixed. $$\mathrm{AgNO}_{3}(\mathrm{aq})+\mathrm{NaCl}(\mathrm{aq}) \longrightarrow \mathrm{AgCl}(\mathrm{s})+\mathrm{NaNO}_{3}(\mathrm{aq})$$ $$\Delta H_{\mathrm{rxn}}^{\circ}=?$$ To measure the heat evolved in this reaction, \(250 .\) mL of \(0.16 \mathrm{M} \mathrm{AgNO}_{3}(\mathrm{aq})\) and \(125 \mathrm{mL}\) of \(0.32 \mathrm{M} \mathrm{NaCl}(\mathrm{aq})\) are mixed in a coffee-cup calorimeter. The temperature of the mixture rises from \(21.15^{\circ} \mathrm{C}\) to \(22.90^{\circ} \mathrm{C}\). Calculate the enthalpy change for the precipitation of \(\mathrm{AgCl}(\mathrm{s})\), in kJ/mol. (Assume the density of the solution is \(1.0 \mathrm{g} / \mathrm{mL}\) and its specific heat capacity is \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) )

Insoluble \(\mathrm{PbBr}_{2}(\mathrm{s})\) precipitates when solutions of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) and \(\mathrm{NaBr}(\mathrm{aq})\) are mixed. $$\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{NaBr}(\mathrm{aq}) \longrightarrow \mathrm{PbBr}_{2}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})$$ $$\Delta H_{\mathrm{rsn}}^{\circ}=?$$ To measure the heat evolved, \(200 .\) mL of \(0.75 \mathrm{M}\) \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) and \(200 \mathrm{mL}\) of \(1.5 \mathrm{M} \mathrm{NaBr}(\mathrm{aq})\) are mixed in a coffee-cup calorimeter. The temperature of the mixture rises by \(2.44^{\circ} \mathrm{C} .\) Calculate the enthalpy change for the precipitation of \(\mathrm{PbBr}_{2}(\mathrm{s}),\) in \(\mathrm{k} \mathrm{J} / \mathrm{mol} .\) (Assume the density of the solution is \(1.0 \mathrm{g} / \mathrm{mL}\) and its specific heat capacity is \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .)\)

The heat evolved in the decomposition of \(7.647 \mathrm{g}\) of ammonium nitrate can be measured in a bomb calorimeter. The reaction that occurs is $$\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s}) \longrightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ The temperature of the calorimeter, which contains \(415 \mathrm{g}\) of water, increases from \(18.90^{\circ} \mathrm{C}\) to \(20.72^{\circ} \mathrm{C}\). The heat capacity of the bomb is \(155 \mathrm{J} / \mathrm{K}\). What quantity of heat is evolved in this reaction, in \(\mathrm{kJ} / \mathrm{mol}\) ?

A bomb calorimetric experiment was run to determine the heat of combustion of ethanol (a common fuel additive). The reaction is $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)$$ The bomb had a heat capacity of \(550 \mathrm{J} / \mathrm{K},\) and the calorimeter contained 650 g of water. Burning \(4.20 \mathrm{g}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)\) resulted in a rise in temperature from \(18.5^{\circ} \mathrm{C}\) to \(22.3^{\circ} \mathrm{C} .\) Calculate the heat of combustion of ethanol, in \(\mathrm{kJ} / \mathrm{mol}\).

Hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}(\ell),\) is an efficient oxygen scavenger. It is sometimes added to steam boilers to remove traces of oxygen that can cause corrosion in these systems. Combustion of hydrazine gives the following information: $$\begin{aligned}&\mathrm{N}_{2} \mathrm{H}_{4}(\ell)+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\\\&\Delta H_{\mathrm{rxn}}^{\circ}=-534.3 \mathrm{kJ}\end{aligned}$$ (a) Is the reaction product- or reactant-favored? (b) Use the value for \(\Delta H_{\mathrm{rxn}}^{\circ}\) with the enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) to calculate the molar enthalpy of formation of \(\mathrm{N}_{2} \mathrm{H}_{4}(\ell)\).

(a) Calculate the enthalpy change, \(\Delta H^{\circ},\) for the formation of 1.00 mol of strontium carbonate (the material that gives the red color in fireworks) from its elements. $$\operatorname{Sr}(\mathrm{s})+\mathrm{C}(\text { graphite })+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \operatorname{Sr} \mathrm{CO}_{3}(\mathrm{s})$$ The experimental information available is $$\begin{aligned}\mathrm{Sr}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow & \mathrm{SrO}(\mathrm{s}) & \Delta H_{f}^{\circ} &=-592 \mathrm{kJ} \\\\\mathrm{SrO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \longrightarrow & \mathrm{SrCO}_{3}(\mathrm{s}) & \Delta H_{\mathrm{rxn}}^{\circ} &=-234 \mathrm{kJ} \\\\\mathrm{C}(\mathrm{graphite})+\mathrm{O}_{2}(\mathrm{g}) & \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) & \Delta H_{f}^{0} &=-394 \mathrm{kJ}\end{aligned}$$ (b) Draw an energy level diagram relating the energy quantities in this problem.

Chloroform, \(\mathrm{CHCl}_{3},\) is formed from methane and chlorine in the following reaction. $$\mathrm{CH}_{4}(\mathrm{g})+3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{HCl}(\mathrm{g})+\mathrm{CHCl}_{3}(\mathrm{g})$$ Calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\), the enthalpy change for this reaction, using the enthalpy of formation of \(\mathrm{CHCl}_{3}(\mathrm{g}), \Delta \mathrm{H}_{f}^{\circ}=\) \(-103.1 \mathrm{kJ} / \mathrm{mol}),\) and the enthalpy changes for the following reactions: $$\begin{aligned}\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{CO}_{2}(\mathrm{g}) & \\\\\Delta H_{\mathrm{rxn}}^{\circ} &=-890.4 \mathrm{kJ}\end{aligned}$$ $$\begin{array}{ll}2 \mathrm{HCl}(\mathrm{g}) \longrightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) & \Delta H_{\mathrm{rxn}}^{\circ}=+184.6 \mathrm{kJ} \\\\\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) & \Delta H_{f}^{\circ}=-393.5 \mathrm{kJ} \\\\\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\ell) & \Delta H_{f}^{\circ}=-285.8 \mathrm{kJ}\end{array}$$

The first law of thermodynamics is often described as another way of stating the law of conservation of energy. Discuss whether this is an accurate portrayal.

Many people have tried to make a perpetual motion machine, but none have been successful although some have claimed success. Use the law of conservation of energy to explain why such a device is impossible.

Without doing calculations, decide whether each of the following is product- or reactant-favored. (a) the combustion of natural gas (b) the decomposition of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) to carbon and water

Suppose you are attending summer school and are living in a very old dormitory. The day is oppressively hot. There is no air-conditioner, and you can't open the windows of your room because they are stuck shut from layers of paint. There is a refrigerator in the room, however. In a stroke of genius you open the door of the refrigerator, and cool air cascades out. The relief does not last long, though. Soon the refrigerator motor and condenser begin to run, and not long thereafter the room is hotter than it was before. Why did the room warm up?

You want to heat the air in your house with natural gas \(\left.\left(\mathrm{CH}_{4}\right) . \text { Assume your house has } 275 \mathrm{m}^{2} \text { (about } 2800 \mathrm{ft}^{2}\right)\) of floor area and that the ceilings are 2.50 m from the floors. The air in the house has a molar heat capacity of \(29.1 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K} .\) (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 \(1.22 \mathrm{g} / \mathrm{L} .\) ) What mass of methane do you have to burn to heat the air from \(15.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C} ?\)

Suppose that an inch of rain falls over a square mile of ground. (A density of \(1.0 \mathrm{g} / \mathrm{cm}^{3}\) is assumed.) The heat of vaporization of water at \(25^{\circ} \mathrm{C}\) is \(44.0 \mathrm{kJ} / \mathrm{mol} .\) Calculate the quantity of heat transferred to the surroundings from the condensation of water vapor in forming this quantity of liquid water. (The huge number tells you how much energy is "stored" in water vapor and why we think of storms as such great forces of energy in nature. It is interesting to compare this result with the energy given off, \(4.2 \times 10^{6} \mathrm{kJ},\) when a ton of dynamite explodes.)