Chapter 11

The fact that water on Earth can readily be found in all three states (solid, liquid, and gas) is in part a consequence of the fact that the triple point of water \(\left(T=0.01^{\circ} \mathrm{C}, P=0.006 \mathrm{~atm}\right)\) falls within a range of temperatures and pressures found on Earth. Saturn's largest moon Titan has a considerable amount of methane in its atmosphere. The conditions on the surface of Titan are estimated to be \(P=1.6\) atm and \(T=-178^{\circ} \mathrm{C}\). As seen from the phase diagram of methane (Figure 11.30 ), these conditions are not far from the triple point of methane, raising the tantalizing possibility that solid, liquid, and gaseous methane can be found on Titan. (a) What state would you expect to find methane in on the surface of Titan? (b) On moving upward through the atmosphere the pressure will decrease. If we assume that the temperature does not change, what phase change would you expect to see as we move away from the surface?

At \(25^{\circ} \mathrm{C}\) gallium is a solid with a density of \(5.91 \mathrm{~g} / \mathrm{cm}^{3}\). Its melting point, \(29.8{ }^{\circ} \mathrm{C},\) is low enough that you can melt it by holding it in your hand. The density of liquid gallium just above the melting point is \(6.1 \mathrm{~g} / \mathrm{cm}^{3} .\) Based on this information, what unusual feature would you expect to find in the phase diagram of gallium?

In terms of the arrangement and freedom of motion of the molecules, how are the nematic liquid crystalline phase and an ordinary liquid phase similar? How are they different?

For a given substance, the liquid crystalline phase tends to be more viscous than the liquid phase. Why?

Describe how a cholesteric liquid crystal phase differs from a nematic phase.

It often happens that a substance possessing a smectic liquid crystalline phase just above the melting point passes into a nematic liquid crystalline phase at a higher temperature. Account for this type of behavior.

The smectic liquid crystalline phase can be said to be more highly ordered than the nematic phase. In what sense is this true?

As the intermolecular attractive forces between molecules increase in magnitude, do you expect each of the following to increase or decrease in magnitude? (a) vapor pressure, (b) heat of vaporization, (c) boiling point, (d) freezing point, (e) viscosity, (f) surface tension, (g) critical temperature.

Suppose you have two colorless molecular liquids, one boiling at \(-84^{\circ} \mathrm{C}\), the other at \(34{ }^{\circ} \mathrm{C},\) and both at atmospheric pressure. Which of the following statements is correct? For each statement that is not correct, modify the statement so that it is correct. (a) The higher-boiling liquid has greater total intermolecular forces than the lower- boiling liquid. (b) The lower-boiling liquid must consist of nonpolar molecules. (c) The lower-boiling liquid has a lower molecular weight than the higher-boiling liquid. (d) The two liquids have identical vapor pressures at their normal boiling points. (e) \(\mathrm{At}-84{ }^{\circ} \mathrm{C}\) both liquids have vapor pressures of \(760 \mathrm{~mm} \mathrm{Hg}\).

In dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}(\mu=1.60 \mathrm{D})\), the dispersion force contribution to the intermolecular attractive forces is about five times larger than the dipole-dipole contribution. Compared to \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\), would you expect the relative importance of the dipole-dipole contribution to increase or decrease (a) in dibromomethane \((\mu=1.43 \mathrm{D}),(\mathbf{b})\) in difluoromethane \((\mu=1.93 \mathrm{D}) ?\) Explain.

When an atom or group of atoms is substituted for an \(\mathrm{H}\) atom in benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),\) the boiling point changes. Explain the order of the following boiling points: \(\mathrm{C}_{6} \mathrm{H}_{6}\left(80{ }^{\circ} \mathrm{C}\right), \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\) \(\left(132^{\circ} \mathrm{C}\right), \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}\left(156^{\circ} \mathrm{C}\right), \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\left(182^{\circ} \mathrm{C}\right)\)

Ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) is the major component of antifreeze. It is a slightly viscous liquid, not very volatile at room temperature, with a boiling point of \(198^{\circ} \mathrm{C}\). Pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right),\) which has about the same molecular weight, is a nonviscous liquid that is highly volatile at room temperature and whose boiling point is \(36.1^{\circ} \mathrm{C}\). Explain the differences in the physical properties of the two substances.

(a) When you exercise vigorously, you sweat. How does this help your body cool? (b) A flask of water is connected to a vacuum pump. A few moments after the pump is turned on, the water begins to boil. After a few minutes, the water begins to freeze. Explain why these processes occur.

The following table gives the vapor pressure of hexafluorobenzene \(\left(\mathrm{C}_{6} \mathrm{~F}_{6}\right)\) as a function of temperature: $$ \begin{array}{lc} \text { Temperature (K) } & \text { Vapor Pressure (torr) } \\ \hline 280.0 & 32.42 \\ 300.0 & 92.47 \\ 320.0 & 225.1 \\ 330.0 & 334.4 \\ 340.0 & 482.9 \end{array} $$ (a) By plotting these data in a suitable fashion, determine whether the Clausius-Clapeyron equation (Equation 11.1 ) is obeyed. If it is obeyed, use your plot to determine \(\Delta H_{\text {vap }}\) for \(\mathrm{C}_{6} \mathrm{~F}_{6}\) (b) Use these data to determine the boiling point of the compound.

Suppose the vapor pressure of a substance is measured at two different temperatures. (a) By using the Clausius-Clapeyron equation (Equation 11.1) derive the following relationship between the vapor pressures, \(P_{1}\) and \(P_{2}\), and the absolute temperatures at which they were measured, \(T_{1}\) and \(T_{2}\) : $$ \ln \frac{P_{1}}{P_{2}}=-\frac{\Delta H_{\text {vap }}}{R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right) $$ (b) Gasoline is a mixture of hydrocarbons, a major component of which is octane, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\). Octane has a vapor pressure of 13.95 torr at \(25^{\circ} \mathrm{C}\) and a vapor pressure of 144.78 torr at \(75^{\circ} \mathrm{C}\). Use these data and the equation in part (a) to calculate the heat of vaporization of octane. (c) By using the equation in part (a) and the data given in part (b), calculate the normal boiling point of octane. Compare your answer to the one you obtained from Exercise 11.80 . (d) Calculate the vapor pressure of octane at \(-30^{\circ} \mathrm{C}\).

The following data present the temperatures at which certain vapor pressures are achieved for dichloromethane \(\left(\mathrm{CH}_{2} \mathrm{Cl}_{2}\right)\) and methyl iodide \(\left(\mathrm{CH}_{3} \mathrm{I}\right)\) : $$ \begin{array}{lllll} \text { Vapor Pressure } & & & & \\ \text { (torr): } & 10.0 & 40.0 & 100.0 & 400.0 \\ \hline T \text { for } \mathrm{CH}_{2} \mathrm{Cl}_{2}\left({ }^{\circ} \mathrm{C}\right): & -43.3 & -22.3 & -6.3 & 24.1 \\ T \text { for } \mathrm{CH}_{3} \mathrm{I}\left({ }^{\circ} \mathrm{C}\right): & -45.8 & -24.2 & -7.0 & 25.3 \end{array} $$ (a) Which of the two substances is expected to have the greater dipole-dipole forces? Which is expected to have the greater dispersion forces? Based on your answers, explain why it is difficult to predict which compound would be more volatile. (b) Which compound would you expect to have the higher boiling point? Check your answer in a reference book such as the CRC Handbook of Chemistry and Physics. (c) The order of volatility of these two substances changes as the temperature is increased. What quantity must be different for the two substances in order for this phenomenon to occur? (d) Substantiate your answer for part (c) by drawing an appropriate graph.

A watch with a liquid crystal display (LCD) does not function properly when it is exposed to low temperatures during a trip to Antarctica. Explain why the LCD might not function well at low temperature.

Acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO},\) is widely used as an industrial solvent. (a) Draw the Lewis structure for the acetone molecule and predict the geometry around each carbon atom. (b) Is the acetone molecule polar or nonpolar? (c) What kinds of intermolecular attractive forces exist between acetone molecules? (d) 1-Propanol, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH},\) has a molecular weight that is very similar to that of acetone, yet acetone boils at \(56.5^{\circ} \mathrm{C}\) and 1-propanol boils at \(97.2^{\circ} \mathrm{C}\). Explain the difference.

The table shown here lists the molar heats of vaporization for several organic compounds. Use specific examples from this list to illustrate how the heat of vaporization varies with (a) molar mass, (b) molecular shape, (c) molecular polarity, (d) hydrogen-bonding interactions. Explain these comparisons in terms of the nature of the intermolecular forces at work. (You may find it helpful to draw out the structural formula for each compound.) $$ \begin{array}{ll} \text { Compound } & \begin{array}{l} \text { Heat of Vaporization } \\ \mathbf{( k J / m o l )} \end{array} \\ \hline \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3} & 19.0 \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3} & 27.6 \\ \mathrm{CH}_{3} \mathrm{CHBrCH}_{3} & 31.8 \\ \mathrm{CH}_{3} \mathrm{COCH}_{3} & 32.0 \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br} & 33.6 \\ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & 47.3 \end{array} $$

Liquid butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\), is stored in cylinders to be used as a fuel. The normal boiling point of butane is listed as \(-0.5^{\circ} \mathrm{C}\). (a) Suppose the tank is standing in the sun and reaches a temperature of \(35^{\circ} \mathrm{C}\). Would you expect the pressure in the tank to be greater or less than atmospheric pressure? How does the pressure within the tank depend on how much liquid butane is in it? (b) Suppose the valve to the tank is opened and a few liters of butane are allowed to escape rapidly. What do you expect would happen to the temperature of the remaining liquid butane in the tank? Explain. (c) How much heat must be added to vaporize \(250 \mathrm{~g}\) of butane if its heat of vaporization is \(21.3 \mathrm{~kJ} / \mathrm{mol} ?\) What volume does this much butane occupy at 755 torr and \(35^{\circ} \mathrm{C} ?\)

The vapor pressure of a volatile liquid can be determined by slowly bubbling a known volume of gas through it at a known temperature and pressure. In an experiment, \(5.00 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas is passed through \(7.2146 \mathrm{~g}\) of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), at \(26.0{ }^{\circ} \mathrm{C}\). The liquid remaining after the experiment weighs \(5.1493 \mathrm{~g}\). Assuming that the gas becomes saturated with benzene vapor and that the total gas volume and temperature remain constant, what is the vapor pressure of the benzene in torr?

The relative humidity of air equals the ratio of the partial pressure of water in the air to the equilibrium vapor pressure of water at the same temperature times \(100 \% .\) If the relative humidity of the air is \(58 \%\) and its temperature is \(68^{\circ} \mathrm{F}\), how many molecules of water are present in a room measuring \(12 \mathrm{ft} \times 10 \mathrm{ft} \times 8 \mathrm{ft} ?\)