Chapter 5

Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure: (a) Liquid water at \(100^{\circ} \mathrm{C}\) is converted to steam at \(100^{\circ} \mathrm{C}\) (b) Dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) sublimes to give \(\mathrm{CO}_{2}(\mathrm{g})\)

Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure: (a) Ozone, \(\mathrm{O}_{3}\), decomposes to form \(\mathrm{O}_{2}\) (b) Methane burns: \(\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)\)

You determine that 187 J of energy as 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 energy 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 enthalpy of fusion of ice at \(0^{\circ} \mathrm{C}\) is \(333 \mathrm{J} / \mathrm{g}\) i the enthalpy of vaporization of liquid water at \(100^{\circ} \mathrm{C}\) is \(2256 \mathrm{J} / \mathrm{g}.\)

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 reaches thermal equilibrium at \(0^{\circ} \mathrm{C},\) how much ice has melted?

A Three \(45-g\) ice cubes at \(0^{\circ} \mathrm{C}\) are dropped into \(5.00 \times 10^{2} \mathrm{mL}\) of tea to make iced 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.

A The standard molar enthalpy of formation of diborane, \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g}),\) cannot be determined directly because the compound cannot be prepared by the reaction of boron and hydrogen. It can be calculated from other enthalpy changes, however. The following enthalpy changes can be measured. \(4 \mathrm{B}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{s})\) \(\Delta_{1} H^{\circ}=-2543.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{pxn}\) \(\mathrm{H}_{2}(\mathrm{g})+^{1 / 2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta_{r} H^{\prime \prime}=-241.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{B}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) \(\Delta_{\tau} H^{\circ}=-2032.9 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) (a) Show how these equations can be added together to give the equation for the formation of \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})\) from \(\mathrm{B}(\mathrm{s})\) and \(\mathrm{H}_{2}(\mathrm{g})\) in their standard states. Assign enthalpy changes to each reaction. (b) Calculate \(\Delta_{f} H^{\circ}\) for \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})\) (c) Draw an energy level diagram that shows how the various enthalpies in this problem are related. (d) Is the formation of \(\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})\) from its elements exo-or endothermic?

(a) Calculate the enthalpy change, \(\Delta_{r} H^{\circ},\) for the formation of 1.00 mol of strontium carbonate (the material that gives the red color in fireworks) from its elements. $$ \mathrm{Sr}(\mathrm{s})+\mathrm{C}(\mathrm{s})+3 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SrCO}_{3}(\mathrm{s}) $$ The experimental information available is \(\mathrm{Sr}(\mathrm{s})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SrO}(\mathrm{s}) \quad \Delta_{i} H^{\circ}=-592 \mathrm{kJ} / \mathrm{mol}-\mathrm{pxn}\) \(\mathrm{SrO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightarrow \mathrm{SrCO}_{3}(\mathrm{s})\) $$ \Delta_{\tau} H^{\circ}=-234 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} $$ C(graphite) \(+\mathbf{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})\) \(\Delta_{j} H^{\circ}=-394 \mathrm{kJ} / \mathrm{mol}-\mathrm{Dxn}\) (b) Draw an energy level diagram relating the energy quantities in this problem.

You drink \(350 \mathrm{mL}\) of diet soda that is at a temperature of \(5^{\circ} \mathrm{C}\) (a) How much energy will your body expend to raise the temperature of this liquid to body temperature \(\left(37^{\circ} \mathrm{C}\right) ?\) Assume that the density and specific heat capacity of diet soda are the same as for water. (b) Compare the value in part (a) with the caloric content of the beverage. (The label says that it has a caloric content of 1 Calorie.) What is the net energy change in your body resulting from drinking this beverage? (1 Calorie = \(1000 \mathrm{kcal}=4184 \mathrm{J} .)\) (c) Carry out a comparison similar to that in part (b) for a nondiet beverage whose label indicates a caloric content of 240 Calories.

According to the Nutrient Data Laboratory website (www, ars. usda.gov/ba/bhnrc/ndl), corn oil contains \(3766 \mathrm{kJ}\) of energy per \(100 .\) g serving. (a) What is the energy content of \(100 .\) g of corn oil in units of nutritional calories (Cal)? (b) How many tablespoons of corn oil have an energy content equivalent to 1500 nutritional calories? (1.0 Tbsp \(=14\) g of corn oil) (c) What mass of water can be heated from \(25.0^{\circ} \mathrm{C}\) to its boiling point of \(100.0^{\circ}\) C using the energy of combustion of 1.00 Tbsp of corn oil?

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 751 g of water (density = \(1.00 \mathrm{g} / \mathrm{cm}^{3}\) ) at \(4.0^{\circ} \mathrm{C}\). What was the final temperature of the copper and water after thermal equilibrium was reached? \(\left(C_{C u}=0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\right).\)

Insoluble AgCl(s) precipitates when solutions of \(\mathrm{AgNO}_{3}(\mathrm{aq})\) and \(\mathrm{NaCl}(\mathrm{aq})\) are mixed. \(\operatorname{AgNO}_{3}(\mathrm{aq})+\mathrm{NaCl}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s})+\mathrm{NaNO}_{3}(\mathrm{aq})\) $$ \Delta_{i} H^{0}=? $$ To measure the energy evolved in this reaction, 250\. mL. of 0.16 M AgNO \(_{3}\) (aq) and 125 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 \(\mathrm{kJ} / \mathrm{mol}\). (Assume the density of the solution is \(1.0 \mathrm{g} / \mathrm{mL}\) and its specific heat capacity is \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .)\)

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. $$\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{NaBr}(\mathrm{aq}) \rightarrow \mathrm{PbBr}_{2}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})$$ To measure the enthalpy change, \(200 .\) mL of \(0.75 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\) and \(200 . \mathrm{mL}\) of \(1.5 \mathrm{M}\) NaBr(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 \(\mathrm{kJ} / \mathrm{mol}\). (Assume the density of the solution is \(1.0 \mathrm{g} / \mathrm{mI}_{7}\) and its specific heat capacity is \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .)\)

The value of \(\Delta U\) for 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}) \rightarrow \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 is the value of \(\Delta U\) for this reaction, in \(\mathrm{kJ} / \mathrm{mol}\) ? (IMAGE CANNOT COPY)

A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ The bomb had a heat capacity of \(550 \mathrm{J} / \mathrm{K},\) and the calorimeter contained \(650 \mathrm{g}\) 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 \(\Delta U\) for the combustion of ethanol, in \(\mathrm{kJ} / \mathrm{mol}\).

The following questions may use concepts from this and previous chapters. Without doing calculations, decide whether each of the following is exo-or endothermic. (a) the combustion of natural gas (b) the decomposition of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) to carbon and water

Which of the following are state functions? (a) the volume of a balloon (b) the time it takes to drive from your home to your college or university (c) the temperature of the water in a coffee cup (d) the potential energy of a ball held in your hand

Prepare a graph of specific heat capacities for metals versus their atomic weights. Combine the data in Figure 5.4 and the values in the following table. What is the relationship between specific heat capacity and atomic weight? Use this relationship to predict the specific heat capacity of platinum. The specific heat capacity for platinum is given in the literature as \(0.133 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) How good is the agreement between the predicted and actual values? $$\begin{aligned} &\begin{array}{|l|c|} \hline & \text { Specific Heat Capacity } \\ \text { Metal } & (\mathrm{J} / \mathrm{g} \cdot \mathrm{K}) \\ \hline \text { Chromium } & 0.450 \\ \text { Lead } & 0.127 \\ \text { Silver } & 0.236 \\ \text { Tin } & 0.227 \\ \text { Titanium } & 0.522 \end{array}\\\ &1 \end{aligned}$$

A You are attending summer school and 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. 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 \(\left(\mathrm{CH}_{4}\right) .\) Assume your house has \(275 \mathrm{m}^{2}\) (about \(2800 \mathrm{ft}^{2}\) ) of floor area and that the ceilings are \(2.50 \mathrm{m}\) 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 \((2.54 \mathrm{cm})\) of rain falls over a square mile of ground \(\left(2.59 \times 10^{6} \mathrm{m}^{2}\right) .\) (Density of water is \(1.0 \mathrm{g} / \mathrm{cm}^{3} .\) ) The enthalpy of vaporization of water at \(25^{\circ} \mathrm{C}\) is \(44.0 \mathrm{kJ} / \mathrm{mol} .\) How much energy is transferred as heat 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.

Several standard enthalpies of formation (from Appendix L) are given below. Use these data to calculate (a) the standard enthalpy of vaporization of bromine. (b) the energy required for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \rightarrow\) \(2 \mathrm{Br}(g) .\) (This is the Br \(-\mathrm{Br}\) bond dissociation enthalpy.) $$\begin{aligned} &\text { Species } \quad \Delta_{f} H^{\circ}(\mathrm{kJ} / \mathrm{mol})\\\ &\begin{array}{lc} \hline B r(g) & 111.9 \\ B r_{2}(\ell) & 0 \\ B r_{2}(g) & 30.9 \end{array} \end{aligned}$$

When \(0.850 \mathrm{g}\) of \(\mathrm{Mg}\) was burned in oxygen in a constant- volume calorimeter, 25.4 kJ of energy as heat was evolved. The calorimeter was in an insulated container with \(750 .\) g of water at an initial temperature of \(18.6^{\circ} \mathrm{C}\). The heat capacity of the bomb in the calorimeter is \(820 . \mathrm{J} / \mathrm{K}.\) (a) Calculate \(\Delta U\) for the oxidation of \(\mathrm{Mg}\) (in kJ/mol Mg). (b) What will be the final temperature of the water and the bomb calorimeter in this experiment?

A A piece of gold \(\left(10.0 \mathrm{g}, C_{\mathrm{Au}}=0.129 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\right)\) is heated to \(100.0^{\circ} \mathrm{C} .\) A piece of copper (also \(10.0 \mathrm{g}\) \(\left.C_{\alpha_{i}}=0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\right)\) is chilled in an ice bath to \(0^{\circ} \mathrm{C} .\) Both pieces of metal are placed in a beaker containing \(150 . \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) at \(20^{\circ} \mathrm{C} .\) Will the temperature of the water be greater than or less than \(20^{\circ} \mathrm{C}\) when thermal equilibrium is reached? Calculate the final temperature.

A You have the six pieces of metal listed below, plus a beaker of water containing \(3.00 \times 10^{2} \mathrm{g}\) of water. The water temperature is \(21.00^{\circ} \mathrm{C}.\) $$\begin{array}{|l|c|c|} \hline \text { Metals } & \text { Specific Heat }(J / g K) & \text { Mass }(g) \\\ \hline 1 . A 1 & 0.9002 & 100.0 \\ 2 . A 1 & 0.9002 & 50.0 \\ 3 . A u & 0.1289 & 100.0 \\ 4 . A u & 0.1289 & 50.0 \\ 5 . Z n & 0.3860 & 100.0 \\ 6 . Z n & 0.3860 & 50.0 \\ \hline \end{array}$$ (a) In your first experiment you select one piece of metal and heat it to \(100^{\circ} \mathrm{C},\) and then select a second piece of metal and cool it to \(-10^{\circ} \mathrm{C}\) Both pieces of metal are then placed in the beaker of water and the temperatures equilibrated. You want to select two pieces of metal to use, such that the final temperature of the water is as high as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water? (b) The second experiment is done in the same way as the first. However, your goal now is to cause the temperature to change the least, that is, the final temperature should be as near to \(21.00^{\circ} \mathrm{C}\) as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water?

In the lab, you plan to carry out a calorimetry experiment to determine \(\Delta_{r} H\) for the exothermic reaction of \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) and \(\mathrm{HCl}(\mathrm{aq}) .\) Predict how each of the following will affect the calculated value of \(\Delta_{t} H .\) (The value calculated for \(\Delta_{i} H\) for this reaction is a negative value so choose your answer from the following: \(\Delta, H\) will be too low [that is, a larger negative valuel, \(\Delta_{r} H\) will be unaffected, \(\Delta_{r} H\) will be too high [that is, a smaller negative value].) (a) You spill a little bit of the \(\mathrm{Ca}(\mathrm{OH})_{2}\) on the benchtop before adding it to the calorimeter. (b) Because of a miscalculation, you add an excess of HCl to the measured amount of \(\mathrm{Ca}(\mathrm{OH})_{2}\) in the calorimeter. (c) \(\mathrm{Ca}(\mathrm{OH})_{2}\) readily absorbs water from the air. The \(\mathrm{Ca}(\mathrm{OH})_{2}\) sample you weighed had been exposed to the air prior to weighing and had absorbed some water. (d) After weighing out \(\mathrm{Ca}(\mathrm{OH})_{2},\) the sample sat in an open beaker and absorbed water. (e) You delay too long in recording the final temperature. (f) The insulation in your coffee-cup calorimeter was poor, so some energy as heat was lost to the surroundings during the experiment. (g) You have ignored the fact that energy as heat also raised the temperature of the stirrer and the thermometer in your system.

Sublimation of \(1.0 \mathrm{g}\) of dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) forms \(0.36 \mathrm{L}\) of \(\mathrm{CO}_{2}(\mathrm{g})\left(\mathrm{at}-78^{\circ} \mathrm{C} \text { and } 1.01 \times 10^{5} \mathrm{Pa}\right)\) The expanding gas can do work on the surroundings (Figure 5.8 ). Calculate the amount of work done on the surroundings.