General Chemistry

Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly

Chapter 15

Liquids and Solids - all with Video Answers

Educators

Chapter Questions

Problem 1

Ammonia is used as a refrigerant in some industrial refrigeration units. The molar enthalpy of vaporization of liquid ammonia is $23.33 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$. Calculate the amount of heat absorbed in the vaporization of $5.00$ kilograms of $\mathrm{NH}_{3}(l)$

Nicole Smina

Nicole Smina

Numerade Educator

Problem 2

Given that $23.6$ kilojoules of heat are required to completely vaporize $60.0$ grams of benzene, $\mathrm{C}_{6} \mathrm{H}_{6}(l)$ at $80.1^{\circ} \mathrm{C}$, calculate the molar enthalpy of vaporization, $\Delta H_{\text {vap }}$, of benzene.

Nicole Smina

Numerade Educator

Problem 3

Calculate the energy as heat released when $20.1$ grams of liquid mercury at $25.0^{\circ} \mathrm{C}$ are converted to solid mercury at its melting point. The heat capacity of $\mathrm{Hg}(l)$ is $28.0 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$

Adriano Chikande

Adriano Chikande

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Problem 4

The chlorofluorocarbon refrigerant Freon-12, $\mathrm{CCl}_{2} \mathrm{~F}_{2}$, was banned in 1995 to help protect the ozone layer. Most new air conditioning units now use the refrigerant tetrafluoroethane, $\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}$. The enthalpy of vaporization of Freon-12 is $155 \mathrm{~J} \cdot \mathrm{g}^{-1}$ and that of tetrafluoroethane is $215.9 \mathrm{~J} \cdot \mathrm{g}^{-1}$. Estimate the number of grams of Freon-12 that must be vaporized to freeze a tray of 16 one-ounce $(1 \mathrm{oz}=28 \mathrm{~g})$ ice cubes with the water initially at $18^{\circ} \mathrm{C}$. How many grams of tetrafluoroethane are required to perform the same task?

Adriano Chikande

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Problem 5

The metal gallium melts when held in the hand; its melting point is $29.76^{\circ} \mathrm{C}$. How much energy as heat is removed from the hand when $5.00$ grams of gallium initially at $20.0^{\circ} \mathrm{C}$ melts? The value of $\Delta H_{\mathrm{fus}}$ is $5.576 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ and the specific heat of gallium is $0.374 \mathrm{~J} \cdot \mathrm{g}^{-1} \cdot \mathrm{K}^{-1}$. Take the final temperature to be
$29.76^{\circ} \mathrm{C} .$

Adriano Chikande

Adriano Chikande

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Problem 6

The enthalpy of vaporization of einsteinium was determined to be $128 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ using only a $100-\mu \mathrm{g}$ sample. How much heat is required to vaporize $100 \mu \mathrm{g}$ of einsteinium?

Nicole Smina

Numerade Educator

Problem 7

Calculate the amount of energy as heat absorbed by the sublimation of $100.0$ grams of dry ice (solid carbon dioxide). The value of $\Delta H_{\text {sub }}$ for $\mathrm{CO}_{2}$ is $25.2 \mathrm{k} J \cdot \mathrm{mol}^{-1}$

Nicole Smina

Numerade Educator

Problem 8

Calculate the number of moles of water at $0^{\circ} \mathrm{C}$ that can be frozen by one mole of dry ice (solid carbon dioxide). See Table $15.3$ for the necessary data. The value of $\Delta H_{\text {sub }}$ for $\mathrm{CO}_{2}$ is $25.2 \mathrm{k} J \cdot \mathrm{mol}^{-1}$.

Adriano Chikande

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Problem 9

Sketch a heating curve for $7.50$ grams of mercury from $200 \mathrm{~K}$ to $800 \mathrm{~K}$ using a heat input rate of $100 \mathrm{~J} \cdot \mathrm{min}^{-1} .$ Refer to Table $15.3$ for some of the necessary data for mercury. The molar heat capacities of solid, liquid, and gaseous mercury are $28.3 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$, $28.0 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$, and $20.8 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$, respectively.

Adriano Chikande

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Problem 10

What would take longer, heating $10.0$ grams of water at $50.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ or vaporizing the $10.0$ grams at $100.0^{\circ} \mathrm{C}$ if the rate of heating in both cases is $5 \mathrm{~J} \cdot \mathrm{s}^{-1} ?$

Adriano Chikande

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Problem 11

Heat was added to $25.0$ grams of solid sodium chloride, $\mathrm{NaCl}(s)$, at the rate of $3.00 \mathrm{~kJ} \cdot \mathrm{min}^{-1} .$ The temperature remained constant at $800.7^{\circ} \mathrm{C}$, the normal melting point of $\mathrm{NaCl}(s)$, for 241 seconds. Calculate the molar enthalpy of fusion of $\mathrm{NaCl}(s)$.

Adriano Chikande

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Problem 12

Heat was added to a 45.0-gram sample of liquid propane, $\mathrm{C}_{3} \mathrm{H}_{8}(l)$, at the rate of $500.0 \mathrm{~J} \cdot \mathrm{min}^{-1}$. The temperature remained constant at $-42.1^{\circ} \mathrm{C}$, the normal boiling point of propane, for $38.9$ minutes. Calculate the molar enthalpy of vaporization of propane.

Adriano Chikande

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Problem 13

Which of the following molecules have polar interactions?
$\mathrm{Cl}_{2}$
$\begin{array}{lll}\text { ClF } & \mathrm{NF}_{3} & \mathrm{~F}_{2}\end{array}$

Nicole Smina

Numerade Educator

Problem 14

Which of the following exhibit primarily only London forces?
$\begin{array}{llll}\mathrm{H}_{2} \mathrm{O} & \mathrm{He} & \mathrm{Cl}_{2} & \mathrm{HCl}\end{array}$

Nicole Smina

Numerade Educator

Problem 15

Which of the following molecules can form hydrogen bonds?
$\mathrm{H}_{2}$
$\begin{array}{lll}\mathrm{HF} & \mathrm{CH}_{4} & \mathrm{CH}_{3} \mathrm{OH}\end{array}$

Nicole Smina

Numerade Educator

Problem 16

Which of the following molecules do you predict to have unusually high boiling points due to hydrogen bonding?

Adriano Chikande

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Problem 17

Arrange the following compounds in order of increasing boiling point:
$\begin{array}{llll}\mathrm{KBr} & \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} & \mathrm{C}_{2} \mathrm{H}_{6} & \mathrm{Ne}\end{array}$

Nicole Smina

Numerade Educator

Problem 18

Arrange the following compounds in order of increasing boiling point:
$\begin{array}{lllll}\mathrm{Mg} \mathrm{O} & \mathrm{NH}_{3} & \mathrm{PH}_{3} & \mathrm{KCl}\end{array}$

Adriano Chikande

Adriano Chikande

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Problem 19

Arrange the following molecules in order of increasing molar enthalpy of vaporization:
$\begin{array}{llll}\mathrm{CH}_{4} & \mathrm{C}_{2} \mathrm{H}_{6} & \mathrm{CH}_{3} \mathrm{OH} & \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\end{array}$

Nicole Smina

Numerade Educator

Problem 20

Arrange the following molecules in order of increasing molar enthalpy of vaporization:
$\begin{array}{llll}\mathrm{CCl}_{4} & \mathrm{SiCl}_{4} & \mathrm{CH}_{4} & \mathrm{SiBr}_{4}\end{array}$

Nicole Smina

Numerade Educator

Problem 21

A $0.75$ -gram sample of ethanol is placed in a sealed 400-milliliter container. Is there any liquid present when the temperature is held at $60^{\circ} \mathrm{C}$ ?

Adriano Chikande

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Problem 22

Mexico City lies at an elevation of 2300 meters $\left(7400\right.$ feet). If water boils at $93^{\circ} \mathrm{C}$ in Mexico City, what is the atmospheric pressure there?

Adriano Chikande

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Problem 23

A sample of ethanol vapor in a vessel of constant volume exerts a pressure of 300 Torr at $75.0^{\circ} \mathrm{C}$. Use the ideal-gas law to plot pressure versus temperature of the vapor between $80.0^{\circ} \mathrm{C}$ and $40.0^{\circ} \mathrm{C}$. Assume no condensation. Compare your result with the vapor pressure curve for ethanol shown in Figure 15.23. Estimate the temperature at which condensation occurs upon cooling from $80.0^{\circ} \mathrm{C}$.

Adriano Chikande

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Problem 24

Atmospheric pressure decreases with altitude. Plot the following data (you may use either units of meters or feet):
$$
\begin{array}{ccc}
\hline \text { Altitude/m } & \text { Altitude/ft } & \begin{array}{l}
\text { Atmospheric } \\
\text { pressure/bar }
\end{array} \\
\hline 1500 & 5000 & 0.83 \\
3000 & 10000 & 0.70 \\
4500 & 15000 & 0.58 \\
6000 & 20000 & 0.47 \\
\hline
\end{array}
$$
Using your plot and the vapor pressure curve of water (Figure $15.23)$, estimate the boiling point of water at the following locations:
$$
\begin{array}{lcc}
\hline \text { Location } & \text { Altitude/m } & \text { Altitude/ft } \\
\hline \text { Denver } & 1610 & 5280 \\
\text { Mount Kilimanjaro } & 5895 & 19340 \\
\text { Mount Washington } & 1917 & 6290 \\
\text { the Matterhorn } & 4478 & 14690 \\
\hline
\end{array}
$$

Adriano Chikande

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Problem 25

The relative humidity in a greenhouse at $40^{\circ} \mathrm{C}$ is $92 \%$. Calculate the vapor pressure of water vapor in the greenhouse.

Adriano Chikande

Adriano Chikande

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Problem 26

The relative humidity in a greenhouse at $40^{\circ} \mathrm{C}$ is $92 \% .$ Calculate the vapor pressure of water vapor in the greenhouse.

Adriano Chikande

Adriano Chikande

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Problem 27

The surface tension of water is $72 \mathrm{~mJ} \cdot \mathrm{m}^{-2}$. What is the energy required to change a spherical drop of water with a diameter of $2 \mathrm{~mm}$ to two smaller spherical drops of equal size? The surface area of a sphere of radius $r$ is $4 \pi r^{2}$ and the volume is $4 \pi r^{3} / 3$.

Adriano Chikande

Adriano Chikande

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Problem 28

The surface tension of water is $72 \mathrm{~mJ} \cdot \mathrm{m}^{-2}$. Calculate the amount of energy required to disperse one spherical drop of radius $3.0 \mathrm{~mm}$ into spherical drops of radius $3.0 \times 10^{-3} \mathrm{~mm} .$ The surface area of a sphere of radius $r$ is $4 \pi r^{2}$ and the volume is $4 \pi r^{3} / 3$.

Adriano Chikande

Adriano Chikande

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Problem 29

The simple hydrocarbon $n$ -heptane has a structural formula of $\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{CH}_{3} .$ Would you expect water or cyclohexane to be a better solvent for heptane?

Nicole Smina

Numerade Educator

Problem 30

Although it is only slightly polar, ethanol, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)$, is completely miscible in water. $\mathrm{Ex}$
plain this apparent contradiction to the "like dissolves like" adage for determining solubility. (Hint: What special property do water and ethanol have in common?)

Nicole Smina

Numerade Educator

Problem 31

Determine whether water is a solid, liquid, or gas at the following pressure and temperature combinations (use Figure 15.24):
(a) $373 \mathrm{~K}, 0.70 \mathrm{~atm}$
(b) $-100^{\circ} \mathrm{C}, 0.006 \mathrm{~atm}$
(c) $400 \mathrm{~K}, 200 \mathrm{~atm}$
(d) $0^{\circ} \mathrm{C}, 300 \mathrm{~atm}$

Adriano Chikande

Adriano Chikande

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Problem 32

Referring to Figure $15.25$, state the phase of carbon dioxide under the following conditions:
(a) $127^{\circ} \mathrm{C}, 8 \mathrm{~atm}$
(b) $-60^{\circ} \mathrm{C}, 40 \mathrm{~atm}$
(c) $50^{\circ} \mathrm{C}, 1 \mathrm{~atm}$
(d) $-80^{\circ} \mathrm{C}, 5 \mathrm{~atm}$

Adriano Chikande

Adriano Chikande

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Problem 33

Sketch the phase diagram for oxygen using the following data:
$$
\begin{array}{lcc}
\hline & \text { Triple point } & \text { Critical point } \\
\hline \text { temperature/K } & 54.3 & 154.6 \\
\text { pressure/Torr } & 1.14 & 37826 \\
\hline
\end{array}
$$
The normal melting point and normal boiling point of oxygen are $-218.8^{\circ} \mathrm{C}$ and $-183.0^{\circ} \mathrm{C}$. Does oxygen melt under an applied pressure as water does?

Adriano Chikande

Adriano Chikande

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Problem 34

Sketch the phase diagram for nitrogen given the following data:
triple point, $63.15 \mathrm{~K}$ and 139 Torr
normal melting point, $63.15 \mathrm{~K}$
normal boiling point, $77.35 \mathrm{~K}$
critical point, $126.21 \mathrm{~K}$ and $33.9$ bar

Adriano Chikande

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Problem 35

Potassium exists as a body-centered cubic lattice. How many potassium atoms are there per unit cell?

Nicole Smina

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Problem 36

Crystalline potassium fluoride has the NaCltype structure shown in Figure $15.30 .$ How many potassium ions and fluoride ions are there per unit cell?

Adriano Chikande

Adriano Chikande

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Problem 37

The density of silver is $10.50 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ at $20^{\circ} \mathrm{C}$. Given that the unit cell of silver is face-centered cubic, calculate the length of an edge of a unit cell.

Adriano Chikande

Adriano Chikande

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Problem 38

The density of tantalum is $16.654 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ at $20^{\circ} \mathrm{C}$. Given that the unit cell of tantalum is body-centered cubic, calculate the length of an edge of a unit cell.

Adriano Chikande

Adriano Chikande

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Problem 39

Copper crystallizes in a face-centered cubic lattice with a density of $8.96 \mathrm{~g} \cdot \mathrm{cm}^{-3}$. Given that the length of an edge of a unit cell is $361.5 \mathrm{pm}$, calculate Avogadro's number.

Adriano Chikande

Adriano Chikande

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Problem 40

Chromium crystallizes in a body-centered cubic lattice with a density of $7.20 \mathrm{~g} \cdot \mathrm{cm}^{-3}$. Given that the length of an edge of a unit cell is $288.4 \mathrm{pm}$, calculate Avogadro's number.

Adriano Chikande

Adriano Chikande

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Problem 41

Crystalline potassium fluoride has the NaCltype structure shown in Figure $15.30 .$ Given that the density of $\mathrm{KF}(s)$ is $2.481 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ at $20^{\circ} \mathrm{C}$, calculate the unit cell length and the nearest-neighbor distance in $\mathrm{KF}(s)$. (The nearest-neighbor distance is the shortest distance between the centers of any two adjacent ions in the lattice.)

Adriano Chikande

Adriano Chikande

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Problem 42

Crystalline cesium bromide has the CsCl-type structure shown in Figure 15.30. Given that the density of $\operatorname{CsBr}(s)$ is $4.43 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ at $25^{\circ} \mathrm{C}$, calculate the
unit cell length and the nearest-neighbor distance (see the previous Problem) in $\operatorname{CsBr}(s)$.

Adriano Chikande

Adriano Chikande

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Problem 43

Given that the density of $\mathrm{KBr}(s)$ is $2.75 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ and that the length of an edge of a unit cell is $654 \mathrm{pm}$, determine how many formula units of $\mathrm{KBr}$ there are in a unit cell. Does the unit cell have a $\mathrm{NaCl}(s)$ or a CsCl $(s)$ structure? (See Figure 15.30.)

Adriano Chikande

Adriano Chikande

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Problem 44

Given that the density of $\mathrm{CaO}(s)$ is $3.34 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ and that the length of an edge of a unit cell is $481.08 \mathrm{pm}$, determine how many formula units of $\mathrm{CaO}$ there are in a unit cell. Does the unit cell have a $\mathrm{NaCl}(s)$ or a CsCl $(s)$ structure? (See Figure $15.30 .)$

Adriano Chikande

Adriano Chikande

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Problem 45

Why do packages of "minute rice" and instant noodles often contain instructions to "boil longer at altitude"?

Nicole Smina

Numerade Educator

Problem 46

Moisture often forms on the outside of a glass containing a mixture of ice and water. Use the principles developed in this chapter to explain this phenomenon.

Nicole Smina

Numerade Educator

Problem 47

As illustrated in Figure 15.11, it is possible to float a paper clip on the surface of water. However, if a small amount of detergent is added to the water the clip will no longer float. Why is this?

Adriano Chikande

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Problem 48

In describing vapor pressure we described the equilibrium between the gas and liquid phases as being dynamic. Why is the equilibrium dynamic? Can you give an example of another system that is in a state of "dynamic equilibrium"?

Adriano Chikande

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Problem 49

Is it possible to boil water at a temperature lower than $100^{\circ} \mathrm{C}$ in the laboratory? If so, explain how this might be achieved.

Adriano Chikande

Adriano Chikande

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Problem 50

(a) What is the difference between evaporation and boiling? (b) Can a solid evaporate?

Adriano Chikande

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Problem 51

Two students are arguing whether an equal mass of steam or hot water at $100^{\circ} \mathrm{C}$ would be more scalding if it came in contact with your skin. Is there a difference?

Adriano Chikande

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Problem 52

A pressure cooker is a sealed container that uses water to cook foods faster than by boiling on a stovetop. Why do foods cook faster in a pressure cooker?

Adriano Chikande

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Problem 53

The stained glass windows in many old churches are thicker at the bottom than the top. At one point scientists thought that this was evidence that the glass had "flowed" downward over the years. However, it has since been shown that this effect is due to the manufacturing process that was used and that glass does not flow appreciably. Why had scientists first thought it might be possible for glass to flow?

Adriano Chikande

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Problem 54

Suppose you are stranded in a mountain cabin by a snowstorm. You have plenty of wood, but only a limited supply of food and wish to conserve it as long as possible. You remember reading that you should melt snow to get water to drink and not eat the snow directly because the body expends energy to melt the snow. How many nutritional Calories are expended by your body in melting enough snow to make a liter of water (1 nutritional Calorie $=1 \mathrm{kcal}$ $=4184 J) ?$

Adriano Chikande

Adriano Chikande

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Problem 55

Prove that $4 r=l \sqrt{3}$ for a body-centered cubic unit cell, where $l$ is the length of an edge of the unit cell and $r$ is the radius of the atoms.

Adriano Chikande

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Problem 56

Trouton's rule states that the molar enthalpy of vaporization of a liquid that does not have strong molecular interactions such as hydrogen bonding or ion-ion attractions is given by
$$
\Delta H_{\text {vap }}=\left(85 \mathrm{~J} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1}\right) T_{\mathrm{b}}
$$
where $T_{\mathrm{b}}$ is the normal boiling point of the liquid in kelvins. Use Trouton's rule to estimate the value of $\Delta H_{\text {vap }}$ for each of the noble gases listed in Table 15.3.

Adriano Chikande

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Problem 57

Use Trouton's rule, given in the previous Problem, to estimate the value of $\Delta H_{\text {vap }}$ for each of the halogens listed in Table $15.3$.

Adriano Chikande

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Problem 58

Apply Trouton's rule, given in Problem $15-56$, to estimate the value of $\Delta H_{\text {vap }}$ for chloromethane, water, and hydrogen sulfide, listed in Table $15.3 .$ What is the percentage error in each case? Suggest a molecular explanation for any discrepancy with the values of $\Delta H_{\text {vap }}$.

Adriano Chikande

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Problem 59

What is the relationship between $\Delta H_{\text {fus }}, \Delta H_{\text {vap }}$, and $\Delta H_{\text {sub }}$ in the vicinity of the triple point?

Adriano Chikande

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Problem 60

Why is $\mathrm{H}_{2} \mathrm{~S}$ a gas at $-10^{\circ} \mathrm{C}$, whereas $\mathrm{H}_{2} \mathrm{O}$ is a solid at this temperature?

Adriano Chikande

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Problem 61

Sulfur melts at $119^{\circ} \mathrm{C}$ to a thin, pale-yellow liquid consisting of $\mathrm{S}_{8}$ rings:
As sulfur is heated to $150^{\circ} \mathrm{C}$ and higher, it becomes so viscous that it hardly pours. Explain these observations in terms of the breaking of the $\mathrm{S}_{8}$ rings.

Nicole Smina

Numerade Educator

Problem 62

Both silicon carbide, $\operatorname{SiC}(s)$, and boron nitride, $\mathrm{BN}(s)$, are about as hard as diamond. What does this suggest about their crystal structures?

Nicole Smina

Numerade Educator

Problem 63

In 2002 researchers at Lawrence Livermore National Laboratory demonstrated that the metal osmium, which does not form a covalent network, is less compressible than diamond, the former record holder. The researchers measured the compressibility under pressures up to 600000 bars using X-ray diffraction. Explain how X-ray diffraction may be used to determine the compressibility of a solid.

Adriano Chikande

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Problem 64

Athough the temperature may not exceed $0^{\circ} \mathrm{C}$, the amount of ice on a sidewalk decreases owing to sublimation. A source of heat for the sublimation is solar radiation. The average daily solar radiation in February for Boston is $8.1 \mathrm{MJ} \cdot \mathrm{m}^{-2} .$ Calculate how much ice will disappear from a $1.0-\mathrm{m}^{2}$ area in one day assuming that all the radiation is used to sublime the ice. Take the density of ice to be $0.917 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ and the molar enthalpy of sublimation to be $50.9 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ at $0^{\circ} \mathrm{C}$.

Adriano Chikande

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Problem 65

Commercial refrigeration units in the United States are rated in tons. During 24 hours of operation a one-ton unit is capable of removing an amount of heat equal to that released when $1.00$ ton of water at $0^{\circ} \mathrm{C}$ is converted to ice. Calculate the number of kilojoules of heat per hour that can be removed by a four-ton home air conditioner $(1$ ton $=2000$ pounds).

Adriano Chikande

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Problem 66

In the 1800 s, British surveyors were prevented from extending their survey of India into the Himalayas because entry into Tibet was banned. In 1865 , the Indian Nain Singh secretly entered Lhasa, the capital city of Tibet, and determined its correct location for map placement. Singh was not able to bring instruments for measuring altitude with him, but he did have a thermometer. He estimated that Lhasa was 3420 meters above sea level. (Its true elevation is 3540 meters or 11600 feet) Describe how he was able to estimate the altitude from a measurement of the boiling point of water.

Adriano Chikande

Adriano Chikande

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Problem 67

The vapor pressures (in Torr) of solid and liquid chlorine are given by
$$
\begin{aligned}
&\text { In } P_{\mathrm{s}}=24.320-\frac{3777 \mathrm{~K}}{T} \\
&\ln P_{1}=17.892-\frac{2669 \mathrm{~K}}{T}
\end{aligned}
$$
where $T$ is the absolute temperature. Calculate the temperature and pressure at the triple point of chlorine.

Adriano Chikande

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Problem 68

The relative humidity is $65 \%$ on a certain day on which the temperature is $30^{\circ} \mathrm{C}$. As the air cools during the night, what will be the dew point?

Adriano Chikande

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Problem 69

Sodium chloride has the crystal structure shown in Figure $15.30 .$ By X-ray diffraction, it is determined that the shortest distance between a sodium ion and a chloride ion is $282 \mathrm{pm}$. Using the fact that the density of sodium chloride is $2.163 \mathrm{~g} \cdot \mathrm{cm}^{-3}$, calculate Avogadro's number.

Adriano Chikande

Adriano Chikande

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Problem 70

Cesium chloride has the crystal structure shown in Figure $15.30$. The length of a side of a unit cell is determined by X-ray diffraction to be $412.1 \mathrm{pm}$. What is the density of cesium chloride?

Adriano Chikande

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Problem 71

The unit cell of lithium is body-centered cubic, and the length of an edge of a unit cell is $351 \mathrm{pm}$ at $20^{\circ} \mathrm{C}$. Calculate the density of lithium at $20^{\circ} \mathrm{C}$.

Adriano Chikande

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Problem 72

Calculate the concentration in moles per liter of water vapor in air saturated with water vapor at $25^{\circ} \mathrm{C} .$

Adriano Chikande

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Problem 73

Arrange the following substances in order of increasing polarity:
$$
\begin{array}{llll}
\mathrm{CCl}_{4} & \mathrm{CHCl}_{3} & \mathrm{CH}_{2} \mathrm{Cl}_{2} & \mathrm{CH}_{3} \mathrm{Cl}
\end{array}
$$

Adriano Chikande

Adriano Chikande

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Problem 74

The phase diagram for sulfur is shown below.
The regions labeled Rhombic and Monoclinic indicate two different crystalline forms of sulfur. How many triple points are there? Describe what happens if sulfur is heated from $40^{\circ} \mathrm{C}$ at one $\mathrm{atm}$ to $200^{\circ} \mathrm{C}$ at one atm. Below what pressure will sublimation occur?

Adriano Chikande

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Problem 75

Use hybrid orbitals to describe the bonding in diamond.

Adriano Chikande

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Problem 76

Use hybrid orbitals to describe the bonding within a layer and between the molecular layers in graphite.

Adriano Chikande

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Problem 77

(*) Two 20.0-gram ice cubes at $-21.0^{\circ} \mathrm{C}$ are placed into 250 milliliters of water at $25.0^{\circ} \mathrm{C}$. Calculate the final temperature of the water in the glass after all the ice melts. Assume no energy is transferred as heat to or from the surroundings. Take the density of water to be $1.00 \mathrm{~g} \cdot \mathrm{mL}^{-1}$ and the heat capacity of ice and water to be $37.7 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$ and $75.3 \mathrm{~J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$,
respectively.

Adriano Chikande

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Problem 78

The vapor pressures (in Torr) of solid and liquid uranium hexafluoride are given by
$$
\begin{aligned}
&\ln P_{\mathrm{s}}=24.513-\frac{5892.5 \mathrm{~K}}{T} \\
&\ln P_{1}=17.357-\frac{3479 \mathrm{~K}}{T}
\end{aligned}
$$
(liquid)
where $T$ is the absolute temperature. Calculate the temperature and pressure at the triple point of $\mathrm{UF}_{6}$.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 79

It has been suggested that the reason why ice skates slide on ice is that the pressure exerted by the skater melts a small area of water below the blade. Determine the pressure on ice created by a 75 -kilogram skater standing on a skate with a blade that measures $3 \mathrm{~mm}$ by $20 \mathrm{~cm}$ (recall that $\mathrm{P}=\mathrm{F} / \mathrm{A}$, and $\mathrm{F}$ $=\mathrm{mg}$ where $\left.\mathrm{g}=9.8 \mathrm{~m} \cdot \mathrm{s}^{-2}\right)$. The melting point of ice decreases by about $0.01^{\circ} \mathrm{C}$ per atm of applied pressure (Figure $15.24)$. Show that pressure alone cannot explain why a skater glides over ice at temperatures of 5 to $10^{\circ} \mathrm{C}$ below freezing. It turns out that the heat generated by friction is also insufficient to explain this phenomenon. Recent work by Gabor Somorjai at Lawrence Berkeley National Laboratory suggests that the surface of ice has a disordered, quasi-fluid layer that makes ice "slippery," even at temperatures below $144 \mathrm{~K}\left(-129^{\circ} \mathrm{C}\right)$

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 80

A $0.677$ -gram sample of zinc reacts completely with sulfuric acid according to
$$
\mathrm{Zn}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q)+\mathrm{H}_{2}(g)
$$
A volume of 263 milliliters of hydrogen gas is collected over water; the water level in the collecting vessel is the same as that surrounding the vessel. The atmospheric pressure is $756.0$ Torr and the temperature is $25^{\circ} \mathrm{C}$. Calculate the atomic mass of zinc.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 81

(*) Steel can be made by inserting atoms of carbon into the spaces between the atoms in metallic iron. Iron has a body-centered crystal structure with a density of $7.86 \mathrm{~g} \cdot \mathrm{cm}^{-3}$. Carbon has an atomic radius of $77 \mathrm{pm}$. Show that there is enough space between the iron atoms to hold a carbon atom.

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 82

The Clapeyron-Clausisus equation (which we will derive in Chapter 23) is
$$
\ln \left(\frac{P_{2}}{P_{1}}\right)=\frac{\Delta H_{\mathrm{vap}}}{R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right]
$$
This equation, which assumes that $\Delta H_{\text {vap }}$ does not vary with temperature, relates the change in vapor pressure and temperature to a substance's enthalpy of vaporization (or sublimation), where $R$ is the molar gas constant. Use this relationship and the fact that $\Delta H_{\text {vap }}$ of water at $25^{\circ} \mathrm{C}$ is $43.99 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ to calculate the vapor pressure of water at $5^{\circ} \mathrm{C}, 25^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C}$, and $95^{\circ} \mathrm{C}$. Compare your results to the values in Table 15.7. What might account for the slight discrepancy between the values in Table $15.7$ and your results?

Adriano Chikande

Adriano Chikande

Numerade Educator

Problem 83

(*) Use the Clapeyron-Clausisus equation (see the previous Problem) to determine the molar enthalpy of vaporization and the normal boiling point of chlorine given the equations in Problem $15-67 .$

Adriano Chikande

Adriano Chikande

Numerade Educator