Chapter 11

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, \((\mathrm{g})\) critical temperature.

The table below lists the density of substance \(\mathrm{X}\) at various temperatures and at \(101.3 \mathrm{kPa}\). The normal melting point of substance \(X\) is \(80 \mathrm{~K}\). \begin{tabular}{cc} \hline Temperature \((\mathrm{K})\) & Density \((\mathrm{mol} / \mathrm{L})\) \\ \hline 90 & 35.2 \\ 100 & 33.8 \\ 110 & 32.1 \\ 120 & 0.136 \\ 140 & 0.110 \\ 160 & 0.0893 \\ 180 & 0.0796 \\ \hline \end{tabular} (a) Over what temperature range is substance \(X\) a solid? (b) Over what temperature range is \(\mathrm{X}\) a liquid? \((\mathbf{c})\) Over what temperature range in the table is \(\mathrm{X}\) a gas? (d) Estimate the normal boiling point of \(X .\) (e) Given that \(X\) is a nonpolar molecule, suggest the kind of intermolecular forces in \(\mathrm{X}\).

Suppose you have two colorless molecular liquids \(A\) and \(B\) whose boiling points are \(78^{\circ} \mathrm{C}\) and \(112^{\circ} \mathrm{C}\) respectively and both are 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) Both A and B are liquids with identical vapor pressure at room temperature of \(25^{\circ} \mathrm{C} .(\mathbf{b})\) Liquid \(\mathrm{A}\) must consist of nonpolar molecules with lower molecular weight than B. \((\mathbf{c})\) Both liquids \(A\) and \(B\) have higher total intermolecular forces than water. (d) Liquid \(A\) is more volatile than liquid B because it has a lower boiling point. (e) At \(112^{\circ} \mathrm{C}\) both liquids have a vapor pressure of 1 atm.

The table below shows some physical properties of compounds containing O-H groups. \begin{tabular}{lccc} \hline Liquid & Molecular Weight & Experimental Dipole Moment & Boiling Point \\\ \hline \(\mathrm{CH}_{3} \mathrm{OH}\) & 32.04 & 1.7 & \(64.7^{\circ} \mathrm{C}\) \\\ \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) & 74.12 & 1.66 & \(117.7^{\circ} \mathrm{C}\) \\ \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) & 62.07 & 1.5 & \(197.3^{\circ} \mathrm{C}\) \\ \hline \end{tabular} Which of the following statements best explains these data? (a) The larger the dipole moment, the stronger the intermolecular forces, and therefore the boiling point is lowest for the molecule with the largest dipole moment. (b) The dispersion forces increase from \(\mathrm{CH}_{3} \mathrm{OH} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) and \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\); since the boiling point also increases in this order, the dispersion forces must be the major contributing factor for the boiling point trend; \((\mathbf{c}) \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) has two groups capable of hydrogen bonding per molecule, whereas \(\mathrm{CH}_{3} \mathrm{OH}\) and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) have only one; therefore, \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) has the highest boiling point.

The DNA double helix (Figure 24.30 ) at the atomic level looks like a twisted ladder, where the "rungs" of the ladder consist of molecules that are hydrogen-bonded together. Sugar and phosphate groups make up the sides of the ladder. Shown are the structures of the adenine-thymine (AT) "base pair" and the guanine-cytosine (GC) base pair: You can see that AT base pairs are held together by two hydrogen bonds and the GC base pairs are held together by three hydrogen bonds. Which base pair is more stableto heating? Why?

Ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) and pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\) are both liquids at room temperature and room pressure, and have about the same molecular weight. (a) One of these liquids is much more viscous than the other. Which one do you predict is more viscous? (b) One of these liquids has a much lower normal boiling point \(\left(36.1^{\circ} \mathrm{C}\right)\) compared to the other one \(\left(198^{\circ} \mathrm{C}\right) .\) Which liquid has the lower normal boiling point? (c) One of these liquids is the major component in antifreeze in automobile engines. Which liquid would you expect to be used as antifreeze? (d) One of these liquids is used as a "blowing agent" in the manufacture of polystyrene foam because it is so volatile. Which liquid would you expect to be used as a blowing agent?

Use the normal boiling points propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) \quad-42.1^{\circ} \mathrm{C}\) \(\begin{array}{lc}\text { propane }\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) & -42.1^{\circ} \mathrm{C} \\ \text { butane }\left(\mathrm{C}_{4} \mathrm{H}_{10}\right) & -0.5^{\circ} \mathrm{C} \\ \text { pentane }\left(\mathrm{C}_{5} \mathrm{H}_{12}\right) & 36.1^{\circ} \mathrm{C} \\\ \text { hexane }\left(\mathrm{C}_{6} \mathrm{H}_{14}\right) & 68.7^{\circ} \mathrm{C}\end{array}\) heptane \(\left(\mathrm{C}_{7} \mathrm{H}_{16}\right) \quad 98.4{ }^{\circ} \mathrm{C}\) to estimate the normal boiling point of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\). Explain the trend in the boiling points.

One of the attractive features of ionic liquids is their low vapor pressure, which in turn tends to make them nonflammable. Why do you think ionic liquids have lower vapor pressures than most room-temperature molecular liquids?

(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.

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 component of which is octane \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\right)\). Octane has a vapor pressure of \(1.86 \mathrm{kPa}\) at \(25^{\circ} \mathrm{C}\) and a vapor pressure of \(19.3 \mathrm{kPa}\) at \(75^{\circ} \mathrm{C}\). Use these data and the equation in part (a) to calculate the heat of vaporization of octane. \((\mathbf{c})\) 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 11.81 . (d) Calculate the vapor pressure of octane at \(-30^{\circ} \mathrm{C}\).

Solid \(\mathrm{CO}_{2}\) is called dry ice. It sublimes at an atmospheric pressure of \(-78.5^{\circ} \mathrm{C}\). The triple point of \(\mathrm{CO}_{2}\) is \(-56.6{ }^{\circ} \mathrm{C}\) at \(517.8 \mathrm{kPa} . \mathrm{CO}_{2}\) becomes a supercritical fluid at \(31^{\circ} \mathrm{C}\) and 7.487 MPa. Using these data, construct a phase diagram for \(\mathrm{CO}_{2}\). labeling all the regions of your diagram.

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.

Rubbing alcohol is the common name for 2 -propanol (isopropanol), \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\). (a) Draw the three-dimensional structure of the 2 -propanol molecule and predict the geometry around each carbon atom. (b) Is the 2-propanol molecule polar or nonpolar? (c) What kinds of intermolecular attractive forces exist between the 2 -propanol molecules? (d) The isomer 1 -propanol has the same molecular weight as 2 -propanol, yet 2 -propanol boils at \(82.6^{\circ} \mathrm{C}\) 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, \((\mathbf{c})\) 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{tabular}{lc} \hline Compound & Heat of Vaporization (kJ/mol) \\ \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 \\ \hline \end{tabular}

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) is pressurized into liquid and stored in cylinders to be used as a fuel. The normal boiling point of propane is listed as \(-42^{\circ} \mathrm{C}\). (a) When converting propane into liquid at room temperature of \(25^{\circ} \mathrm{C}\), 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 propane is in it? (b) Suppose the fuel tank leaks and a few liters of propane escape rapidly. What do you expect would happen to the temperature of the remaining liquid propane in the tank? Explain. (c) How much heat must be added to vaporize \(20 \mathrm{~g}\) of propane if its heat of vaporization is \(18.8 \mathrm{~kJ} / \mathrm{mol} ?\) What volume does this amount of propane occupy at \(100 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C} ?\)

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, \(8.00 \mathrm{~L}\) of argon gas is passed through \(11.7872 \mathrm{~g}\) of liquid hexane \(\mathrm{C}_{6} \mathrm{H}_{14}\) at \(30.0^{\circ} \mathrm{C}\). The mass of the remaining liquid after the experiment is \(4.875 \mathrm{~g}\). Assuming that the gas becomes saturated with hexane vapor and that the total gas volume and temperature remain constant, what is the vapor pressure of hexane in atm?