Chapter 11

Do you expect the viscosity of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3},\) to be larger or smaller than that of 1 -propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\) ? Explain. [Section 11.3\(]\)

If \(42.0 \mathrm{~kJ}\) of heat is added to a 32.0 -g sample of liquid methane under 1 atm of pressure at a temperature of \(-170{ }^{\circ} \mathrm{C},\) what are the final state and temperature of the methane once the system equilibrates? Assume no heat is lost to the surroundings. The normal boiling point of methane is \(-161.5^{\circ} \mathrm{C}\). The specific heats of liquid and gaseous methane are 3.48 and \(2.22 \mathrm{~J} / \mathrm{g}-\mathrm{K},\) respectively. [Section 11.4\(]\)

Using this graph of \(\mathrm{CS}_{2}\) data, determine (a) the approximate vapor pressure of \(\mathrm{CS}_{2}\) at \(30^{\circ} \mathrm{C}\), (b) the temperature at which the vapor pressure equals 300 torr, (c) the normal boiling point of \(\mathrm{CS}_{2}\). [Section 11.5]

The phase diagram of a hypothetical substance is (a) Estimate the normal boiling point and freezing point of the substance. (b) What is the physical state of the substance under the following conditions: (i) \(T=150 \mathrm{~K}, P=0.2 \mathrm{~atm}\) (ii) \(T=100 \mathrm{~K}, P=0.8 \mathrm{~atm},(\mathrm{iii}) T=300 \mathrm{~K}, P=1.0 \mathrm{~atm} ?\) (c) What is the triple point of the substance? [Section 11.6\(]\)

List the three states of matter in order of (a) increasing molecular disorder and (b) increasing intermolecular attractions. (c) Which state of matter is most easily compressed?

(a) How does the average kinetic energy of molecules compare with the average energy of attraction between molecules in solids, liquids, and gases? (b) Why does increasing the temperature cause a solid substance to change in succession from a solid to a liquid to a gas? (c) What happens to a gas if you put it under extremely high pressure?

Arrange substances \(\mathrm{CCl}_{4},\) Si, and Ar in order of increasing boiling point.

At standard temperature and pressure the molar volume of \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) gases are \(22.06 \mathrm{~L}\) and \(22.40 \mathrm{~L},\) respectively (a) Given the different molecular weights, dipole moments, and molecular shapes, why are their molar volumes nearly the same? (b) \(\mathrm{On}\) cooling to \(160 \mathrm{~K}\), both substances form crystalline solids. Do you expect the molar volumes to decrease or increase on cooling to \(160 \mathrm{~K} ?\) (c) The densities of crystalline \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) at \(160 \mathrm{~K}\) are \(2.02 \mathrm{~g} / \mathrm{cm}^{3}\) and \(0.84 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. Calculate their molar volumes. (d) Are the molar volumes in the solid state as similar as they are in the gaseous state? Explain. (e) Would you expect the molar volumes in the liquid state to be closer to those in the solid or gaseous state?

Benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH},\) melts at \(122{ }^{\circ} \mathrm{C}\). The density in the liquid state at \(130^{\circ} \mathrm{C}\) is \(1.08 \mathrm{~g} / \mathrm{cm}^{3}\). The density of solid benzoic acid at \(15^{\circ} \mathrm{C}\) is \(1.266 \mathrm{~g} / \mathrm{cm}^{3}\). (a) In which of these two states is the average distance between molecules greater? (b) Explain the difference in densities at the two temperatures in terms of the relative kinetic energies of the molecules.

Which type of intermolecular attractive force operates between (a) all molecules, (b) polar molecules, (c) the hydrogen atom of a polar bond and a nearby small electronegative atom?

Based on what you have learned about intermolecular forces, would you say that matter is fundamentally attracted or repulsed by other matter?

Describe the intermolecular forces that must be overcome to convert these substances from a liquid to a gas: (a) \(\mathrm{SO}_{2}\), (b) \(\mathrm{CH}_{3} \mathrm{COOH},\) (c) \(\mathrm{H}_{2} \mathrm{~S}\).

Which type of intermolecular force accounts for each of these differences: (a) \(\mathrm{CH}_{3} \mathrm{OH}\) boils at \(65^{\circ} \mathrm{C} ; \mathrm{CH}_{3} \mathrm{SH}\) boils at \(6^{\circ} \mathrm{C}\). (b) Xe is liquid at atmospheric pressure and \(120 \mathrm{~K}\), whereas \(\mathrm{Ar}\) is a gas under the same conditions. (c) \(\mathrm{Kr}\), atomic weight 84 , boils at \(120.9 \mathrm{~K},\) whereas \(\mathrm{Cl}_{2},\) molecular weight about \(71,\) boils at \(238 \mathrm{~K}\). (d) Acetone boils at \(56^{\circ} \mathrm{C}\), whereas 2 -methylpropane boils at \(-12^{\circ} \mathrm{C}\)

(a) What is meant by the term polarizability? (b) Which of the following atoms would you expect to be most polarizable: \(\mathrm{N}\), \(\mathrm{P},\) As, \(\mathrm{Sb}\) ? Explain. (c) Put the following molecules in order of increasing polarizability: \(\mathrm{GeCl}_{4}\), \(\mathrm{CH}_{4}\), \(\mathrm{SiCl}_{4}, \mathrm{SiH}_{4}\), and \(\mathrm{GeBr}_{4}\). (d) Predict the order of boiling points of the substances in part (c).

True or false: (a) For molecules with similar molecular weights, the dispersion forces become stronger as the molecules become more polarizable. (b) For the noble gases the dispersion forces decrease while the boiling points increase as you go down the column in the periodic table. (c) In terms of the total attractive forces for a given substance dipole- dipole interactions, when present, are always larger than dispersion forces. (d) All other factors being the same, dispersion forces between linear molecules are greater than dispersion forces between molecules whose shapes are nearly spherical.

Which member in each pair has the larger dispersion forces: (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{H}_{2} \mathrm{~S},(\mathbf{b}) \mathrm{CO}_{2}\) or \(\mathrm{CO}, \mathrm{C}\) (c) \(\mathrm{SiH}_{4}\) or \(\mathrm{GeH}_{4} ?\)

Which member in each pair has the stronger intermolecular dispersion forces: (a) \(\mathrm{Br}_{2}\) or \(\mathrm{O}_{2}\), (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{SH}\) or \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{SH},(\mathrm{c}) \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}\) or \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCl} ?\)

Butane and 2 -methylpropane, whose space-filling models are shown at the top of the next column, are both nonpolar and have the same molecular formula, \(\mathrm{C}_{4} \mathrm{H}_{10}\), yet butane has the higher boiling point \(\left(-0.5^{\circ} \mathrm{C}\right.\) compared to \(\left.-11.7^{\circ} \mathrm{C}\right)\). Explain.

Propyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) and isopropyl alcohol \(\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHOH}\right],\) whose space- filling models are shown, have boiling points of \(97.2^{\circ} \mathrm{C}\) and \(82.5^{\circ} \mathrm{C}\), respectively. Explain why the boiling point of propyl alcohol is higher, even though both have the molecular formula \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}\).

(a) What atoms must a molecule contain to participate in hydrogen bonding with other molecules of the same kind? (b) Which of the following molecules can form hydrogen bonds with other molecules of the same kind: \(\mathrm{CH}_{3} \mathrm{~F}, \mathrm{CH}_{3} \mathrm{NH}_{2}\), \(\mathrm{CH}_{3} \mathrm{OH}, \mathrm{CH}_{3} \mathrm{Br} ?\)

Rationalize the difference in boiling points in each pair: (a) \(\mathrm{HF}\left(20^{\circ} \mathrm{C}\right)\) and \(\mathrm{HCl}\left(-85^{\circ} \mathrm{C}\right),(\mathbf{b}) \mathrm{CHCl}_{3}\left(61{ }^{\circ} \mathrm{C}\right)\) and \(\mathrm{CHBr}_{3}\) \(\left(150^{\circ} \mathrm{C}\right),(\mathrm{c}) \mathrm{Br}_{2}\left(59^{\circ} \mathrm{C}\right)\) and \(\mathrm{ICl}\left(97^{\circ} \mathrm{C}\right)\)

Ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right),\) the major substance in antifreeze, has a normal boiling point of \(198^{\circ} \mathrm{C} .\) By comparison, ethyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right)\) boils at \(78^{\circ} \mathrm{C}\) at atmospheric pressure. Ethylene glycol dimethyl ether \(\left(\mathrm{CH}_{3} \mathrm{OCH}_{2} \mathrm{CH}_{2} \mathrm{OCH}_{3}\right)\) has a normal boiling point of \(83^{\circ} \mathrm{C}\), and ethyl methyl ether \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{3}\right)\) has a normal boiling point of \(11^{\circ} \mathrm{C}\). (a) \(\mathrm{Ex}-\) plain why replacement of a hydrogen on the oxygen by a \(\mathrm{CH}_{3}\) group generally results in a lower boiling point. (b) What are the major factors responsible for the difference in boiling points of the two ethers?

Identify the type or types of intermolecular forces present in each substance and then select the substance in each pair that has the higher boiling point: (a) propane \(\mathrm{C}_{3} \mathrm{H}_{8}\) or \(n\) -butane \(\mathrm{C}_{4} \mathrm{H}_{10},\) (b) diethyl ether \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OCH}_{2} \mathrm{CH}_{3}\) or 1 -butanol \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH},\) (c) sulfur dioxide \(\mathrm{SO}_{2}\) or sulfur trioxide (d) phosgene \(\mathrm{Cl}_{2} \mathrm{CO}\) or formaldehyde \(\mathrm{H}_{2} \mathrm{CO}\). \(\mathrm{SO}_{3},\)

Look up and compare the normal boiling points and normal melting points of \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{H}_{2} \mathrm{~S}\). Based on these physical properties, which substance has stronger intermolecular forces? What kinds of intermolecular forces exist for each molecule?

The following quote about ammonia \(\left(\mathrm{NH}_{3}\right)\) is from a textbook of inorganic chemistry: "It is estimated that \(26 \%\) of the hydrogen bonding in \(\mathrm{NH}_{3}\) breaks down on melting, \(7 \%\) on warming from the melting to the boiling point, and the final \(67 \%\) on transfer to the gas phase at the boiling point." From the standpoint of the kinetic energy of the molecules, explain (a) why there is a decrease of hydrogen-bonding energy on melting and (b) why most of the loss in hydrogen bonding occurs in the transition from the liquid to the vapor state.

A number of salts containing the tetrahedral polyatomic anion, \(\mathrm{BF}_{4}^{-},\) are ionic liquids, whereas salts containing the somewhat larger tetrahedral ion \(\mathrm{SO}_{4}^{2-}\) do not form ionic liquids. Explain this observation.

The generic structural formula for a 1 -alkyl-3-methylimidazolium cation is where \(\mathrm{R}\) is a \(-\mathrm{CH}_{2}\left(\mathrm{CH}_{2}\right)_{n} \mathrm{CH}_{3}\) alkyl group. The melting points of the salts that form between the 1 -alkyl-3-methylimidazolium cation and the \(\mathrm{PF}_{6}^{-}\) anion are as follows: \(\mathrm{R}=\mathrm{CH}_{2} \mathrm{CH}_{3}\left(\mathrm{~m} . \mathrm{p} .=60^{\circ} \mathrm{C}\right), \mathrm{R}=\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\left(\mathrm{m.p.}=40^{\circ} \mathrm{C}\right)\) \(\mathrm{R}=\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\left(\mathrm{~m} . \mathrm{p} .=10^{\circ} \mathrm{C}\right)\) and \(\mathrm{R}=\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\left(\mathrm{~m} . \mathrm{p} .=-61^{\circ} \mathrm{C}\right) . \mathrm{Why}\) does the melting point decrease as the length of alkyl group increases?

(a) Explain why surface tension and viscosity decrease with increasing temperature. (b) Why do substances with high surface tensions also tend to have high viscosities?

(a) Distinguish between adhesive forces and cohesive forces. (b) What adhesive and cohesive forces are involved when a paper towel absorbs water? (c) Explain the cause for the U-shaped meniscus formed when water is in a glass tube.

Explain the following observations: (a) The surface tension of \(\mathrm{CHBr}_{3}\) is greater than that of \(\mathrm{CHCl}_{3} .\) (b) As temperature increases, oil flows faster through a narrow tube. (c) Raindrops that collect on a waxed automobile hood take on a nearly spherical shape. (d) Oil droplets that collect on a waxed automobile hood take on a flat shape.

Hydrazine \(\left(\mathrm{H}_{2} \mathrm{NNH}_{2}\right),\) hydrogen peroxide \((\mathrm{HOOH}),\) and water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) all have exceptionally high surface tensions compared with other substances of comparable molecular weights. (a) Draw the Lewis structures for these three compounds. (b) What structural property do these substances have in common, and how might that account for the high surface tensions?

The boiling points, surface tensions, and viscosities of water and several alchohols are as follows: $$ \begin{array}{lrcc} & \begin{array}{l} \text { Boiling } \\ \text { Point }\left({ }^{\circ} \mathbf{C}\right) \end{array} & \begin{array}{l} \text { Surface } \\ \text { Tension }\left(\mathbf{J} / \mathbf{m}^{2}\right) \end{array} & \begin{array}{l} \text { Viscosity } \\ (\mathbf{k g} / \mathbf{m}-\mathbf{s}) \end{array} \\ \hline \text { Water, } \mathrm{H}_{2} \mathrm{O} & 100 & 7.3 \times 10^{-2} & 0.9 \times 10^{-3} \\ \text {Ethanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} & 78 & 2.3 \times 10^{-2} & 1.1 \times 10^{-3} \\ \text {Propanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & 97 & 2.4 \times 10^{-2} & 2.2 \times 10^{-3} \\ n \text { -Butanol, } \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} & 117 & 2.6 \times 10^{-2} & 2.6 \times 10^{-3} \\\ \text {Ethylene glycol, } \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH} & 197 & 4.8 \times 10^{-2} & 26 \times 10^{-3} \end{array} $$ (a) For ethanol, propanol, and \(n\) -butanol the boiling points, surface tensions, and viscosities all increase. What is the reason for this increase? (b) How do you explain the fact that propanol and ethylene glycol have similar molecular weights \((60\) versus \(62 \mathrm{amu}),\) yet the viscosity of ethylene glycol is more than 10 times larger than propanol? (c) How do you explain the fact that water has the highest surface tension but the lowest viscosity?

Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic: (a) When ice is heated, it turns to water. (b) Wet clothes dry on a warm summer day. (c) Frost appears on a window on a cold winter day. (d) Droplets of water appear on a cold glass of beer.

Name the phase transition in each of the following situations and indicate whether it is exothermic or endothermic: (a) Bromine vapor turns to bromine liquid as it is cooled. (b) Crystals of iodine disappear from an evaporating dish as they stand in a fume hood. (c) Rubbing alcohol in an open container slowly disappears. (d) Molten lava from a volcano turns into solid rock.

Explain why any substance's heat of fusion is generally lower than its heat of vaporization.

Ethyl chloride \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(12^{\circ} \mathrm{C}\). When liquid \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) under pressure is sprayed on a room-temperature \(\left(25^{\circ} \mathrm{C}\right)\) surface in air, the surface is cooled considerably. (a) What does this observation tell us about the specific heat of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(g)\) as compared with \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(l) ?\) (b) Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface?

For many years drinking water has been cooled in hot climates by evaporating it from the surfaces of canvas bags or porous clay pots. How many grams of water can be cooled from \(35^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\) by the evaporation of \(60 \mathrm{~g}\) of water? (The heat of vaporization of water in this temperature range is \(2.4 \mathrm{~kJ} / \mathrm{g}\). The specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g}-\mathrm{K} .)\)

Compounds like \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) are known as chlorofluorocarbons, or CFCs. These compounds were once widely used as refrigerants but are now being replaced by compounds that are believed to be less harmful to the environment. The heat of vaporization of \(\mathrm{CCl}_{2} \mathrm{~F}_{2}\) is \(289 \mathrm{~J} / \mathrm{g}\). What mass of this substance must evaporate to freeze \(200 \mathrm{~g}\) of water initially at \(15^{\circ} \mathrm{C} ?\) (The heat of fusion of water is \(334 \mathrm{~J} / \mathrm{g} ;\) the specific heat of water is \(4.18 \mathrm{~J} / \mathrm{g}-\mathrm{K} .)\)

Ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) melts at \(-114{ }^{\circ} \mathrm{C}\) and boils at \(78{ }^{\circ} \mathrm{C}\). The enthalpy of fusion of ethanol is \(5.02 \mathrm{~kJ} / \mathrm{mol},\) and its enthalpy of vaporization is \(38.56 \mathrm{~kJ} / \mathrm{mol}\). The specific heats of solid and liquid ethanol are \(0.97 \mathrm{~J} / \mathrm{g}-\mathrm{K}\) and \(2.3 \mathrm{~J} / \mathrm{g}-\mathrm{K},\) respectively. (a) How much heat is required to convert \(42.0 \mathrm{~g}\) of ethanol at \(35^{\circ} \mathrm{C}\) to the vapor phase at \(78{ }^{\circ} \mathrm{C} ?\) (b) How much heat is required to convert the same amount of ethanol at \(-155^{\circ} \mathrm{C}\) to the vapor phase at \(78^{\circ} \mathrm{C}\) ?

The fluorocarbon compound \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}\) has a normal boiling point of \(47.6^{\circ} \mathrm{C}\). The specific heats of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}(l)\) and \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}(g)\) are \(0.91 \mathrm{~J} / \mathrm{g}-\mathrm{K}\) and \(0.67 \mathrm{~J} / \mathrm{g}-\mathrm{K},\) respectively. The heat of vaporization for the compound is \(27.49 \mathrm{~kJ} / \mathrm{mol} .\) Calculate the heat required to convert \(35.0 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{Cl}_{3} \mathrm{~F}_{3}\) from a liquid at \(10.00^{\circ} \mathrm{C}\) to a gas at \(105.00^{\circ} \mathrm{C}\).

The critical temperatures \((\mathrm{K})\) and pressures \((\mathrm{atm})\) of a series of halogenated methanes are as follows: $$ \begin{array}{lcccc} \text { Compound } & \mathbf{C C l}_{3} \mathbf{F} & \mathbf{C C l}_{2} \mathbf{F}_{2} & \mathbf{C C I F}_{3} & \mathbf{C F}_{4} \\ \hline \text { Critical temperature } & 471 & 385 & 302 & 227 \\ \text { Critical pressure } & 43.5 & 40.6 & 38.2 & 37.0 \end{array} $$ (a) List the intermolecular forces that occur for each compound. (b) Predict the order of increasing intermolecular attraction, from least to most, for this series of compounds. (c) Predict the critical temperature and pressure for \(\mathrm{CCl}_{4}\) based on the trends in this table. Look up the experimentally determined critical temperatures and pressures for \(\mathrm{CCl}_{4}\), using a source such as the CRC Handbook of Chemistry and Physics, and suggest a reason for any discrepancies.

Explain how each of the following affects the vapor pressure of a liquid: (a) volume of the liquid, (b) surface area, (c) intermolecular attractive forces, (d) temperature, (e) density of the liquid.

(a) Place the following substances in order of increasing volatility: \(\mathrm{CH}_{4}, \mathrm{CBr}_{4}, \mathrm{CH}_{2} \mathrm{Cl}_{2}, \mathrm{CH}_{3} \mathrm{Cl}, \mathrm{CHBr}_{3},\) and \(\mathrm{CH}_{2} \mathrm{Br}_{2} .\) Explain. (b) How do the boiling points vary through this series?

True or false: (a) \(\mathrm{CBr}_{4}\) is more volatile than \(\mathrm{CCl}_{4}\). (b) \(\mathrm{CBr}_{4}\) has a higher boiling point than \(\mathrm{CCl}_{4}\). (c) \(\mathrm{CBr}_{4}\) has weaker intermolecular forces than \(\mathrm{CCl}_{4}\). (d) \(\mathrm{CBr}_{4}\) has a higher vapor pressure at the same temperature than \(\mathrm{CCl}_{4}\)

(a) Two pans of water are on different burners of a stove. One pan of water is boiling vigorously, while the other is boiling gently. What can be said about the temperature of the water in the two pans? (b) A large container of water and a small one are at the same temperature. What can be said about the relative vapor pressures of the water in the containers?

Explain the following observations: (a) Water evaporates more quickly on a hot, dry day than on a hot, humid day. (b) It takes longer to cook an egg in boiling water at high altitudes than it does at lower altitudes.

Appendix B lists the vapor pressure of water at various external pressures. (a) Plot the data in Appendix B, vapor pressure (torr) versus temperature \(\left({ }^{\circ} \mathrm{C}\right) .\) From your plot, estimate the vapor pressure of water at body temperature, \(37^{\circ} \mathrm{C}\). (b) Explain the significance of the data point at 760.0 torr, \(100^{\circ} \mathrm{C}\) (c) A city at an altitude of \(5000 \mathrm{ft}\) above sea level has a barometric pressure of 633 torr. To what temperature would you have to heat water to boil it in this city? (d) A city at an altitude of \(500 \mathrm{ft}\) below sea level would have a barometric pressure of 774 torr. To what temperature would you have to heat water to boil it in this city? (e) For the two cities in parts \((\mathrm{c})\) and \((\mathrm{d}),\) compare the average kinetic energies of the water molecules at their boiling points. Are the kinetic energies the same or different? Explain.

(a) What is the significance of the critical point in a phase diagram? (b) Why does the line that separates the gas and liquid phases end at the critical point?

(a) What is the significance of the triple point in a phase dia gram? (b) Could you measure the triple point of water b measuring the temperature in a vessel in which water vapo liquid water, and ice are in equilibrium under one atmospher of air? Explain.

Referring to Figure 11.28 , describe all the phase changes that would occur in each of the following cases: (a) Water vapor originally at 0.005 atm and \(-0.5^{\circ} \mathrm{C}\) is slowly compressed at constant temperature until the final pressure is 20 atm. (b) Water originally at \(100.0^{\circ} \mathrm{C}\) and \(0.50 \mathrm{~atm}\) is cooled at constant pressure until the temperature is \(-10^{\circ} \mathrm{C}\).