Chapter 5

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. \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})+2 \mathrm{NaBr}(\mathrm{aq}) \rightarrow \mathrm{PbBr}_{2}(\mathrm{s})+2 \mathrm{NaNO}_{3}(\mathrm{aq})\) $$ \Delta_{\mathrm{r}} H^{\circ}=? $$ 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 \(1.5 \mathrm{M} \mathrm{NaBr}(\mathrm{aq})\) 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 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 CAN'T 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 the enthalpy of combustion of ethanol, in \(\mathrm{kJ} / \mathrm{mol}\).

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

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 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 \(44.0 \mathrm{kJ} /\) 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.)

When 0.850 g of Mg was burned in oxygen in a constant volume calorimeter, \(25.4 \mathrm{kJ}\) of energy as heat was evolved. The calorimeter was in an insulated container with \(750 . \mathrm{g}\) of water at an initial temperature of \(18 . \overline{6}^{\circ} \mathrm{C}\). 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 \(\mathrm{k} \mathrm{J} / \mathrm{mol}\) \(\mathrm{Mg})\) (b) What will be the final temperature of the water and the bomb calorimeter in this experiment?

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 \(10.0 \mathrm{g}\), \(\left.C_{\mathrm{Cu}}=0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\right)\) 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.

In lab, you plan to carry out a calorimetry experiment to determine \(\Delta_{\mathrm{r}} H\) 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 \(\Delta_{\mathrm{r}} H\). (The value calculated for \(\Delta_{\mathrm{r}} H\) for this reaction is a negative value so choose your answer from the following: \(\Delta_{r} H\) will be too low [that is, a larger negative value], \(\Delta_{\mathrm{r}} H\) will be unaffected, \(\Delta_{\mathrm{r}} H\) 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 \(\mathrm{CO}_{2}(\mathrm{g})\) (at \(-78^{\circ} \mathrm{C}\) and 1 atm pressure). The expanding gas can do work on the surroundings. Calculate the amount of work done on the surroundings using the equation \(w=-P \times \Delta V\) (Note: \(L \times\) atm is a unit of energy; 1 L atm \(=101.3 \mathrm{J}\).)

In the reaction of two moles of gaseous hydrogen and one mole of gaseous oxygen to form two moles of gaseous water vapor, two moles of products are formed from 3 moles of reactants. If this reaction is done at \(\left.1.0 \text { atm pressure (and at } 0^{\circ} \mathrm{C}\right),\) the volume is reduced by \(22.4 \mathrm{L}\) (a) In this reaction, how much work is done on the system \(\left(\mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{H}_{2} \mathrm{O}\right)\) by the surroundings? (b) The enthalpy change for this reaction is \(-483.6 \mathrm{kJ}\) Use this value, along with the answer to (a), to calculate \(\Delta_{r} U\), the change in internal energy in the system.