Chapter 13

Classify the following properties as intensive or extensive: density; amount in moles; pressure; length; temperature. (Section \(13.1)\)

The heat capacity of air at room temperature \(\left(20^{\circ} \mathrm{C}\right)\) is approximately \(21 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\). (Section 13.1 ) (a) How much heat is required to raise the temporature of a \(5 m \times 5 m \times 3 m\) room by \(10^{\circ} \mathrm{C} ?\) (b) How long will it take a \(1 \mathrm{kW}\) heater to achieve this? (Assume that the volume of 1 mol of air is \(24 \mathrm{dm}^{3}\) at \(20^{\circ} \mathrm{C} .\)

A \(50.0 \mathrm{g}\) block of copper at \(90.0^{\circ} \mathrm{C}\) is placed in a beaker containing \(200.0 \mathrm{g}\) of water at \(20.0^{\circ} \mathrm{C}\). Calculate the final temperature of the copper and water. (The specific heat capacities of copper and water are \(0.38 \mathrm{JK}^{-1} \mathrm{g}^{-1}\) and \(4.18 \mathrm{JK}^{-1} \mathrm{g}^{-1},\) respoctively. (Section 13.1)

Calculate the onthalpy change when \(100 \mathrm{g}\) of water froezes at \(0^{\circ} \mathrm{C}\). (The standard enthalpy change of fusion of water is \(+6.01 \mathrm{kJmol}^{-1}\), ) (Section 13.2)

Calculate the energy needed to melt \(750 \mathrm{kg}\) of sodium metal at \(371 \mathrm{K}\). (The standard enthalpy change of fusion of sodium is \(+2.60 \mathrm{kJmol}^{-1} .\) ) (Section 13.2

The decomposition at constant volume of \(1 \mathrm{mol}\) of gaseous krypton difluoride \(\left(\mathrm{KrF}_{2}\right)\) to its elements at \(298 \mathrm{K}\) gives out \(59.4 \mathrm{kJ}\) of heat. Calculate the standard enthalpy change of formation, \(\Delta_{t} H_{298}^{\circ}\), of solid \(\mathrm{KrF}_{2}\). (The enthalpy change of sublimation of solid \(\mathrm{KrF}_{2}\) is \(+41 \mathrm{kJmol}^{-1}\). ) (Section \(13.3)\).

Calcite and aragonite are two forms of calcium carbonate. Calculate the enthalpy change for the transition from calcite to aragonite. (AH(calcite) \(=-1206.9 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(\Delta \mathrm{H}\) (aragonite) \(=\) \(-1207.1 \mathrm{kJ} \mathrm{mol}^{-1}\), j (Section 13.3)

Calculate the enthalpy change when gaseous benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) dissociates into gaseous atoms at \(298 \mathrm{K}\). Carry out the calculation by two different methods using the data in (a) and (b) below. Comment on the difference in the values you obtain by the two methods. (Section 13.3 ) (a) Assume benzene molecules contain three single and three double carbon- carbon bonds, and use mean bond enthalpy data. (Mean bond enthalpies/kJmol- \(^{-1}:\) C-C \(, 347\); \(\mathrm{C}=\mathrm{C}, 612 ; \mathrm{C}-\mathrm{H}, 412 .\) (b) The enthalpy change of combustion of liquid benzene at \(298 \mathrm{K}\) is \(-3267.4 \mathrm{kJmol}^{-1}\). The enthalpy change of vaporization of benzene at \(298 \mathrm{K}\) is \(+33.9 \mathrm{kJ} \mathrm{mol}^{-1}\) \\[ \begin{array}{l} \left(\mathrm{A}_{1} \mathrm{H}_{298}^{\circ} / \mathrm{kJmol}^{-1}: \mathrm{CO}_{2}(\mathrm{g}),-393.5 ; \mathrm{H}_{2} \mathrm{O}(0,-285.8 ; \mathrm{C}(\mathrm{g})\right. \\ 716.7 ; \mathrm{H}(\mathrm{g}), 218 .) \end{array} \\]

Calculate the energy transferred as work, \(w\), when a gas is comprossed from \(250 \mathrm{cm}^{3}\) to \(125 \mathrm{cm}^{3}\) by an external prossure of \(10 \mathrm{kPa}\). (Section 13.5 )

For a reaction at constant pressure, the enthalpy change is \(+30 \mathrm{kJ} .\) During the reaction, the system expands and does \(25 \mathrm{kJ}\) of work. What is the change in internal energy for the reaction? (Section 13.5 )

Calculate the energy transforred as work, \(w,\) for a system that releases \(450 \mathrm{J}\) of heat in a process for which the internal energy of the system decreases by 135 J. (Section 13.5 )

The molar heat capacity of water at constant pressure is \(75.3 \mathrm{JK}^{-1} \mathrm{mol}^{-1}\) at room temperature. Calculate the mass of methanol that must be burned to heat \(1 \mathrm{dm}^{3}\) of water from \(20^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\). (Assume the density of water is \(1.0 \mathrm{gcm}^{-3}\) ) (Section \(13.3)\)

A slice of banana weighing \(2.7 \mathrm{g}\) was burned in oxygen in a bomb calorimeter and produced a temperature rise of \(3.05 \mathrm{K}\) In the same calorimeter, the combustion of \(0.316 \mathrm{g}\) of benzoic acid produced a temperature rise of \(3.24 \mathrm{K}\). Ac U for benzoic acid is \(-3251 \mathrm{kJmol}^{-1}\). If the average mass of a banana is \(125 \mathrm{g}\), how much energy in (a) \(\mathrm{kJ}\) and (b) calories (kcal) can be obtained on average from a banana? (1 calorie \(=4.18 \mathrm{kJ}\) ) (Section 13.5 )

Car safoty airbags inflate when the car undergoes a sudden deceleration, setting oft a reaction which produces a large amount of gas. One of the reactions used is \(\mathrm{NaN}_{3}(\mathrm{s}) \rightarrow \mathrm{Na}(\mathrm{s})+1.5 \mathrm{N}_{2}(\mathrm{g}) \quad \Delta, \mathrm{H}^{0}_{29 \mathrm{e}}=-21.7 \mathrm{kJmol}^{-1}\) (Section \(13.3)\) (a) What is the value of \(\Delta_{1} H_{294}\) for \(\mathrm{NaN}_{3} ?\) (b) \(\quad\) An airbag system is inflated by 2.4 mol (around \(60 \mathrm{dm}^{3}\) ) of \(\mathrm{N}_{2}(\mathrm{q})\). Calculate the enthalpy change when this amount of nitrogen is produced at \(298 \mathrm{K}\) (c) Assuming this energy all goes into heating the \(\mathrm{N}_{2}(\mathrm{g}),\) what Will be the final ternperature of the gas? \(\left(C_{p} \text { for } N_{2}(g)=\right.\) \(\left.29.1 \mathrm{JK}^{-1} \mathrm{mol}^{-1} .\right)\)

A flame calorimeter is used to measure enthalpy changes in gaseous reactions. In order to calibrate a particular flame calorimeter, a quantity of methane was burned in oxygen to release \(12.54 \mathrm{kJ}\) of energy which resulted in a temperature rise of \(1.000 \mathrm{K}\) Using the same flame calorimeter, the combustion of \(0.02 \mathrm{mol}\) of butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), raised the temperature by \(5.017 \mathrm{K}\) while combustion of the same amount of methylpropane caused a temperature rise of \(4.575 \mathrm{K}\) Calculate the enthalpy change of isomerization for the two butane isomers. (Section 13.5 )

A chemist is trying to measure the enthalpy change for the hydration reaction: \\[ \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{s}) \rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \\] Calibration of a solution calorimeter shows that 357.9 J of heat raises the temperature by \(1.00 \mathrm{K}\). When \(2.500 \mathrm{g}\) of anhydrous sodium carbonate, \(\mathrm{Na}_{2} \mathrm{CO}_{3}\), was dissolved in \(100.00 \mathrm{cm}^{3}\) of water, the temperature increased by \(1.550 \mathrm{K}\). On dissolving \(3.500 \mathrm{g}\) of sodium carbonate decahydrate, \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) in \(100.00 \mathrm{cm}^{3}\) of water, the temperature decreased by \(2.310 \mathrm{K}\) Calculate enthalpy change of hydration of sodium carbonate. (Section 13.5 )

A student used a calorimeter containing \(100 \mathrm{g}\) of deionized water which required an energy change of \(818 \mathrm{J}\) to cause a temperature change of \(1 \mathrm{K}\) An unknown mass of sodium hydroxide, NaOH, was dissolved in the water and the temperature rose from \(25.00^{\circ} \mathrm{C}\) to \(31.00^{\circ} \mathrm{C}\). Given that the molar enthalpy of solution of NaOH is \(-44.51 \mathrm{kJ} \mathrm{mol}^{-1}\), what mass of sodium hydroxide was dissolved? (Section 13.6)