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9: Natural States of the Elements

9: Natural States of the Elements

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444 Chapter 13 Gases

118. Convert the following pressures into pascals.

a.

b.

c.

d.



645 mm Hg

221 kPa

0.876 atm

32 torr



119. For each of the following sets of pressure/volume

data, calculate the missing quantity. Assume that the

temperature and the amount of gas remain constant.

a. V ϭ 123 L at 4.56 atm; V ϭ ? at 1002 mm Hg

b. V ϭ 634 mL at 25.2 mm Hg; V ϭ 166 mL at ? atm

c. V ϭ 443 L at 511 torr; V ϭ ? at 1.05 kPa

120. For each of the following sets of pressure/volume

data, calculate the missing quantity. Assume that the

temperature and the amount of gas remain constant.

a. V ϭ 255 mL at 1.00 mm Hg; V ϭ ? at 2.00 torr

b. V ϭ 1.3 L at 1.0 kPa; V ϭ ? at 1.0 atm

c. V ϭ 1.3 L at 1.0 kPa; V ϭ ? at 1.0 mm Hg

121. A particular balloon is designed by its manufacturer

to be inflated to a volume of no more than 2.5 L. If

the balloon is filled with 2.0 L of helium at sea level,

is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg, will the balloon burst?

122. What pressure is needed to compress 1.52 L of air at

755 mm Hg to a volume of 450 mL (at constant temperature)?

123. An expandable vessel contains 729 mL of gas at 22 °C.

What volume will the gas sample in the vessel have if

it is placed in a boiling water bath (100. °C)?

124. For each of the following sets of volume/temperature

data, calculate the missing quantity. Assume that the

pressure and the amount of gas remain constant.

a. V ϭ 100. mL at 74 °C; V ϭ ? at Ϫ74 °C

b. V ϭ 500. mL at 100 °C; V ϭ 600. mL at ? °C

c. V ϭ 10,000 L at 25 °C; V ϭ ? at 0 K

125. For each of the following sets of volume/temperature

data, calculate the missing quantity. Assume that the

pressure and the amount of gas remain constant.

a. V ϭ 22.4 L at 0 °C; V ϭ 44.4 L at ? K

b. V ϭ 1.0 ϫ 10Ϫ3 mL at Ϫ272 °C; V ϭ ? at 25 °C

c. V ϭ 32.3 L at Ϫ40 °C; V ϭ 1000. L at ? °C

126. A 75.2-mL sample of helium at 12 °C is heated to

192 °C. What is the new volume of the helium (assuming constant pressure)?



129. Given each of the following sets of values for three of

the gas variables, calculate the unknown quantity.

a. P ϭ 21.2 atm; V ϭ 142 mL; n ϭ 0.432 mol; T ϭ ? K

b. P ϭ ? atm; V ϭ 1.23 mL; n ϭ 0.000115 mol; T ϭ

293 K

c. P ϭ 755 mm Hg; V ϭ ? mL; n ϭ 0.473 mol; T ϭ

131 °C

130. Given each of the following sets of values for three of

the gas variables, calculate the unknown quantity.

a. P ϭ 1.034 atm; V ϭ 21.2 mL; n ϭ 0.00432 mol;

Tϭ?K

b. P ϭ ? atm; V ϭ 1.73 mL; n ϭ 0.000115 mol; T ϭ

182 K

c. P ϭ 1.23 mm Hg; V ϭ ? L; n ϭ 0.773 mol; T ϭ

152 °C

131. What is the pressure inside a 10.0-L flask containing

14.2 g of N2 at 26 °C?

132. Suppose three 100.-L tanks are to be filled separately

with the gases CH4, N2, and CO2, respectively. What

mass of each gas is needed to produce a pressure of

120. atm in its tank at 27 °C?

133. At what temperature does 4.00 g of helium gas have

a pressure of 1.00 atm in a 22.4-L vessel?

134. What is the pressure in a 100.-mL flask containing

55 mg of oxygen gas at 26 °C?

135. A weather balloon is filled with 1.0 L of helium at 23 °C

and 1.0 atm. What volume does the balloon have

when it has risen to a point in the atmosphere where

the pressure is 220 torr and the temperature is Ϫ31 °C?

136. At what temperature does 100. mL of N2 at 300. K and

1.13 atm occupy a volume of 500. mL at a pressure of

1.89 atm?

137. If 1.0 mol N2(g) is injected into a 5.0-L tank already

containing 50. g of O2 at 25 °C, what will be the total

pressure in the tank?

138. A gaseous mixture contains 12.1 g of N2 and 4.05 g of

He. What is the volume of this mixture at STP?

139. A flask of hydrogen gas is collected at 1.023 atm and

35 °C by displacement of water from the flask. The

vapor pressure of water at 35 °C is 42.2 mm Hg. What

is the partial pressure of hydrogen gas in the flask?

140. Consider the following chemical equation:

N2( g) ϩ 3H2( g) S 2NH3( g)

What volumes of nitrogen gas and hydrogen gas,

each measured at 11 °C and 0.998 atm, are needed to

produce 5.00 g of ammonia?



127. If 5.12 g of oxygen gas occupies a volume of 6.21 L at

a certain temperature and pressure, what volume will

25.0 g of oxygen gas occupy under the same conditions?



141. Consider the following unbalanced chemical equation:



128. If 23.2 g of a given gas occupies a volume of 93.2 L at

a particular temperature and pressure, what mass of

the gas occupies a volume of 10.4 L under the same

conditions?



What volume of oxygen gas, measured at 28 °C and

0.976 atm, is needed to react with 5.00 g of C6H12O6?

What volume of each product is produced under the

same conditions?



C6H12O6(s) ϩ O2( g) S CO2( g) ϩ H2O( g)



All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.



Chapter Review

142. Consider the following unbalanced chemical equation:

Cu2S(s) ϩ O2( g) S Cu2O(s) ϩ SO2( g)

What volume of oxygen gas, measured at 27.5 °C and

0.998 atm, is required to react with 25 g of copper(I)

sulfide? What volume of sulfur dioxide gas is produced under the same conditions?

143. When sodium bicarbonate, NaHCO3(s), is heated,

sodium carbonate is produced, with the evolution of

water vapor and carbon dioxide gas.

2NaHCO3(s) S Na2CO3(s) ϩ H2O( g) ϩ CO2( g)

What total volume of gas, measured at 29 °C and

769 torr, is produced when 1.00 g of NaHCO3(s) is

completely converted to Na2CO3(s)?

144. What volume does 35 moles of N2 occupy at STP?



445



146. A mixture contains 5.0 g of He, 1.0 g of Ar, and 3.5 g

of Ne. Calculate the volume of this mixture at STP.

Calculate the partial pressure of each gas in the mixture at STP.

147. What volume of CO2 measured at STP is produced

when 27.5 g of CaCO3 is decomposed?

CaCO3(s) S CaO(s) ϩ CO2( g)

148. Concentrated hydrogen peroxide solutions are explosively decomposed by traces of transition metal

ions (such as Mn or Fe):

2H2O2(aq) S 2H2O(l ) ϩ O2( g)

What volume of pure O2(g), collected at 27 °C and

764 torr, would be generated by decomposition of

125 g of a 50.0% by mass hydrogen peroxide solution?



145. A sample of oxygen gas has a volume of 125 L at

25 °C and a pressure of 0.987 atm. Calculate the volume of this oxygen sample at STP.



All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.



14

14.1 Water and Its Phase

Changes

14.2 Energy Requirements for

the Changes of State

14.3 Intermolecular Forces

14.4 Evaporation and Vapor

Pressure

14.5 The Solid State: Types

of Solids

14.6 Bonding in Solids



Liquids and Solids



Ice, the solid form of water, provides recreation

for this ice climber. (Vandystadt/Tips Images)



Liquids and Solids

Sign in to OWL at

www.cengage.com/owl to view

tutorials and simulations, develop

problem-solving skills, and complete

online homework assigned by your

professor.

Download mini-lecture videos

for key concept review and exam prep

from OWL or purchase them from

www.ichapters.com



447



Y



ou have only to think about water to appreciate how different the

three states of matter are. Flying, swimming, and ice skating are all done

in contact with water in its various states. We swim in liquid water and

skate on water in its solid form (ice). Airplanes fly in an atmosphere containing water in the gaseous state (water vapor). To allow these various activities, the arrangements of the water molecules must be significantly different in their gas, liquid, and solid forms.

In Chapter 13 we saw that the particles of a gas are far apart, are in

rapid random motion, and have little effect on each other. Solids are obviously very different from gases. Gases have low densities, have high compressibilities, and completely fill a container. Solids have much greater densities than gases, are compressible only to a very slight extent, and are

rigid; a solid maintains its shape regardless of its container. These properties indicate that the components of a solid are close together and exert

large attractive forces on each other.

The properties of liquids lie somewhere between those of solids and

of gases—but not midway between, as can be seen from some of the properties of the three states of water. For example, it takes about seven times

more energy to change liquid water to steam (a gas) at 100 °C than to melt

ice to form liquid water at 0 °C.



Robert Y. Ono/Corbis



H2O(s) S H2O(l)

H2O(l) S H2O(g)



Wind surfers use liquid water for recreation.



energy required Х 6 kJ/mol

energy required Х 41 kJ/mol



These values indicate that going from the liquid to

the gaseous state involves a much greater change

than going from the solid to the liquid. Therefore,

we can conclude that the solid and liquid states are

more similar than the liquid and gaseous states. This

is also demonstrated by the densities of the three

states of water (Table 14.1). Note that water in its

gaseous state is about 2000 times less dense than in

the solid and liquid states and that the latter two

states have very similar densities.

We find in general that the liquid and solid

states show many similarities and are strikingly different from the gaseous state (see Figure 14.1). The

best way to picture the solid state is in terms of

closely packed, highly ordered particles in contrast

to the widely spaced, randomly arranged particles of

a gas. The liquid state lies in between, but its properties indicate that it much more closely resembles

the solid than the gaseous state. It is useful to picture a liquid in terms of particles that are generally

quite close together, but with a more disordered

arrangement than for the solid state and with some

empty spaces. For most substances, the solid state

has a higher density than the liquid, as Figure 14.1

suggests. However, water is an exception to this rule.



448 Chapter 14 Liquids and Solids

Table 14.1 Densities of the Three

States of Water

State



Density (g/cm3)



solid (0 °C, 1 atm)



0.9168



liquid (25 °C, 1 atm)



0.9971



gas (100 °C, 1 atm)



5.88 ϫ 10Ϫ4



Gas



Liquid



Solid



Figure 14.1

Representations of the gas, liquid, and solid states.



Ice has an unusual amount of empty space and so is less dense than liquid

water, as indicated in Table 14.1.

In this chapter we will explore the important properties of liquids and

solids. We will illustrate many of these properties by considering one of the

earth’s most important substances: water.



14.1 Water and Its Phase Changes

OBJECTIVE:



The water we drink often has a

taste because of the substances

dissolved in it. It is not pure

water.



To learn some of the important features of water.

In the world around us we see many solids (soil, rocks, trees, concrete, and

so on), and we are immersed in the gases of the atmosphere. But the liquid

we most commonly see is water; it is virtually everywhere, covering about

70% of the earth’s surface. Approximately 97% of the earth’s water is found

in the oceans, which are actually mixtures of water and huge quantities of

dissolved salts.

Water is one of the most important substances on earth. It is crucial for

sustaining the reactions within our bodies that keep us alive, but it also affects our lives in many indirect ways. The oceans help moderate the earth’s

temperature. Water cools automobile engines and nuclear power plants. Water provides a means of transportation on the earth’s surface and acts as a

medium for the growth of the myriad creatures we use as food, and much

more.

Pure water is a colorless, tasteless substance that at 1 atm pressure

freezes to form a solid at 0 °C and vaporizes completely to form a gas at

100 °C. This means that (at 1 atm pressure) the liquid range of water occurs

between the temperatures 0 °C and 100 °C.

What happens when we heat liquid water? First the temperature of the

water rises. Just as with gas molecules, the motions of the water molecules

increase as it is heated. Eventually the temperature of the water reaches

100 °C; now bubbles develop in the interior of the liquid, float to the surface,

and burst—the boiling point has been reached. An interesting thing happens at the boiling point: even though heating continues, the temperature

stays at 100 °C until all the water has changed to vapor. Only when all of the

water has changed to the gaseous state does the temperature begin to rise



14.1 Water and Its Phase Changes



Figure 14.2



Steam

Water and steam



120



Temperature (°C )



The heating/cooling curve for

water heated or cooled at a

constant rate. The plateau at the

boiling point is longer than the

plateau at the melting point,

because it takes almost seven

times as much energy (and thus

seven times the heating time) to

vaporize liquid water as to melt

ice. Note that to make the

diagram clear, the blue line is

not drawn to scale. It actually

takes more energy to melt ice

and boil water than to heat

water from 0 °C to 100 °C.



140



449



100



Liquid water



80



g



60

40

20



tin



Ice and

water



0

−20



ea



g



lin

oo



H



C



Ice

Heat added at a constant rate



again. (We are now heating the vapor.) At 1 atm pressure, liquid water always

changes to gaseous water at 100 °C, the normal boiling point for water.

The experiment just described is represented in Figure 14.2, which is

called the heating/cooling curve for water. Going from left to right on

this graph means energy is being added (heating). Going from right to left

on the graph means that energy is being removed (cooling).

When liquid water is cooled, the temperature decreases until it reaches

0 °C, where the liquid begins to freeze (see Figure 14.2). The temperature remains at 0 °C until all the liquid water has changed to ice and then begins

to drop again as cooling continues. At 1 atm pressure, water freezes (or, in

the opposite process, ice melts) at 0 °C. This is called the normal freezing

point of water. Liquid and solid water can coexist indefinitely if the temperature is held at 0 °C. However, at temperatures below 0 °C liquid water

freezes, while at temperatures above 0 °C ice melts.

Interestingly, water expands when it freezes. That is, one gram of ice at

0 °C has a greater volume than one gram of liquid water at 0 °C. This has very

important practical implications. For instance, water in a confined space can

break its container when it freezes and expands. This accounts for the bursting of water pipes and engine blocks that are left unprotected in freezing

weather.

The expansion of water when it freezes also explains why ice cubes

float. Recall that density is defined as mass/volume. When one gram of liquid water freezes, its volume becomes greater (it expands). Therefore, the

density of one gram of ice is less than the density of one gram of water, because in the case of ice we divide by a slightly larger volume. For example, at

0 °C the density of liquid water is

1.00 g

ϭ 1.00 g/mL

1.00 mL

and the density of ice is

1.00 g

ϭ 0.917 g/mL

1.09 mL

The lower density of ice also means that ice floats on the surface of lakes

as they freeze, providing a layer of insulation that helps to prevent lakes and

rivers from freezing solid in the winter. This means that aquatic life continues to have liquid water available through the winter.



450 Chapter 14 Liquids and Solids



14.2 Energy Requirements for the

Changes of State

OBJECTIVES:



Remember that temperature is a

measure of the random motions

(average kinetic energy) of the

particles in a substance.



H2O



To learn about interactions among water molecules. • To understand and

use heat of fusion and heat of vaporization.

It is important to recognize that changes of state from solid to liquid and

from liquid to gas are physical changes. No chemical bonds are broken in

these processes. Ice, water, and steam all contain H2O molecules. When water is boiled to form steam, water molecules are separated from each other

(see Figure 14.3) but the individual molecules remain intact.

The bonding forces that hold the atoms of a molecule together are

called intramolecular (within the molecule) forces. The forces that occur

among molecules that cause them to aggregate to form a solid or a liquid are

called intermolecular (between the molecules) forces. These two types of

forces are illustrated in Figure 14.4.

It takes energy to melt ice and to vaporize water, because intermolecular forces between water molecules must be overcome. In ice the molecules

are virtually locked in place, although they can vibrate about their positions.

When energy is added, the vibrational motions increase, and the molecules

eventually achieve the greater movement and disorder characteristic of liquid water. The ice has melted. As still more energy is added, the gaseous state

is eventually reached, in which the individual molecules are far apart and interact relatively little. However, the gas still consists of water molecules. It

would take much more energy to overcome the covalent bonds and decompose the water molecules into their component atoms.

The energy required to melt 1 mole of a substance is called the molar

heat of fusion. For ice, the molar heat of fusion is 6.02 kJ/mol. The energy

required to change 1 mole of liquid to its vapor is called the molar heat of

vaporization. For water, the molar heat of vaporization is 40.6 kJ/mol at

100 °C. Notice in Figure 14.2 that the plateau that corresponds to the vaporization of water is much longer than that for the melting of ice. This occurs because it takes much more energy (almost seven times as much) to vaporize a mole of water than to melt a mole of ice. This is consistent with our

models of solids, liquids, and gases (see Figure 14.1). In liquids, the particles

(molecules) are relatively close together, so most of the intermolecular forces

are still present. However, when the molecules go from the liquid to the

gaseous state, they must be moved far apart. To separate the molecules

enough to form a gas, virtually all of the intermolecular forces must be overcome, and this requires large quantities of energy.



Figure 14.4

Intermolecular

forces



Figure 14.3

Both liquid water and gaseous

water contain H2O molecules. In

liquid water the H2O molecules

are close together, whereas in

the gaseous state the molecules

are widely separated. The

bubbles contain gaseous water.



H

O



Bonds



H

O



H

H



Bonds



Intramolecular (bonding) forces exist

between the atoms in a molecule and hold

the molecule together. Intermolecular

forces exist between molecules. These are

the forces that cause water to condense

to a liquid or form a solid at low enough

temperatures. Intermolecular forces are

typically much weaker than intramolecular

forces.



C H E M I S T R Y I N F OCUS

Whales Need Changes of State



Sperm whales are prodigious divers. They com-



Flip Nicklin/Minden Pictures



monly dive a mile or more into the ocean, hovering at that depth in search of schools of squid or

fish. To remain motionless at a given depth, the

whale must have the same density as the surrounding water. Because the density of seawater

increases with depth, the sperm whale has a sys-



ͦͦ



O

which is a liquid above 30 °C. At the ocean surface the spermaceti in the whale’s head is a liquid, warmed by the flow of blood through the

spermaceti organ. When the whale dives, this

blood flow decreases and the colder water

causes the spermaceti to begin freezing. Because

solid spermaceti is more dense than the liquid

state, the sperm whale’s density increases as it

dives, matching the increase in the water’s density.* When the whale wants to resurface, blood

flow through the spermaceti organ increases,

remelting the spermaceti and making the whale

more buoyant. So the sperm whale’s sophisticated density-regulating mechanism is based on

a simple change of state.

*For most substances, the solid state is more dense than

the liquid state. Water is an important exception.



A sperm whale.



EXAMPLE 14.1



tem that automatically increases its density as it

dives. This system involves the spermaceti organ

found in the whale’s head. Spermaceti is a waxy

substance with the formula

CH3—(CH2)15——O—C—(CH2)14—CH3



Calculating Energy Changes: Solid to Liquid

Calculate the energy required to melt 8.5 g of ice at 0 °C. The molar heat of

fusion for ice is 6.02 kJ/mol.

SOLUTION

Where Are We Going?

We want to determine the energy (in kJ) required to melt 8.5 g of ice at 0 °C.

What Do We Know?

• We have 8.5 g of ice (H2O) at 0 °C.

• The molar heat of fusion of ice is 6.02 kJ/mol.

What Information Do We Need?

• We need to know the number of moles of ice in 8.5 g.

How Do We Get There?

The molar heat of fusion is the energy required to melt 1 mole of ice. In this

problem we have 8.5 g of solid water. We must find out how many moles of



451



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