Fundamentals of General, Organic,
and Biological Chemistry
5th Edition
Chapter Eight
Gases, Liquids, and Solids
James E. Mayhugh
Oklahoma City University
2007 Prentice Hall, Inc.
Outline
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8.1 States of Matter and Their Changes
8.2 Gases and the Kinetic–Molecular Theory
8.3 Pressure
8.4 Boyle’s Law: The Relation Between Volume and Pressure
8.5 Charles’s Law: The Relation Between Volume and Temperature
8.6 Gay-Lussac’s Law: The Relation Between Pressure and Temperature
8.7 The Combined Gas Law
8.8 Avogadro’s Law: The Relation Between Volume and Molar Amount
8.9 The Ideal Gas Law
8.10 Partial Pressure and Dalton’s Law
8.11 Intermolecular Forces
8.12 Liquids
8.13 Water: A Unique Liquid
8.14 Solids
8.15 Changes of State
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8.1 States of Matter and Their
Changes
► Matter exists in any of three phases, or states—solid,
liquid, and gas, depending on the attractive forces
between particles, temperature, and pressure.
► In a gas, the attractive forces between particles are
very weak compared to their kinetic energy, so the
particles move about freely, are far apart, and have
almost no influence on one another.
► In a liquid, the attractive forces between particles are
stronger, pulling the particles close together but still
allowing them considerable freedom to move about.
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In a solid, the attractive forces are much stronger than
the kinetic energy of the particles, so the atoms,
molecules, or ions are held in a specific arrangement
and can only wiggle around in place.
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►Phase change or change of state: The transformation
of a substance from one state to another.
►Melting point (mp): The temperature at which solid
and liquid are in equilibrium.
►Boiling point (bp): The temperature at which liquid
and gas are in equilibrium.
►Sublimation: A process in which a solid changes
directly to a gas.
►Melting, boiling, and sublimation all have H > 0,
and S > 0. This means they are nonspontaneous
below and spontaneous above a certain temperature.
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8.2 Gases and the Kinetic-Molecular
Theory
► The behavior of gases can be explained by a group
of assumptions known as the kinetic–molecular
theory of gases. The following assumptions account
for the observable properties of gases:
► A gas consists of many particles, either atoms or
molecules, moving about at random with no
attractive forces between them. Because of this
random motion, different gases mix together quickly.
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► The amount of space occupied by the gas particles
themselves is much smaller than the amount of
space between particles. Most of the volume taken
up by gases is empty space, accounting for the ease
of compression and low densities of gases.
► The average kinetic energy of gas particles is
proportional to the Kelvin temperature. Thus, gas
particles have more kinetic energy and move faster
as the temperature increases. (In fact, gas particles
move much faster than you might suspect. The
average speed of a helium atom at room temperature
and atmospheric pressure is approximately 1.36
km/s, or 3000 mi/hr, nearly that of a rifle bullet.)
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► Collisions of gas particles, either with other
particles or with the wall of their container, are
elastic; that is, the total kinetic energy of the
particles is constant. The pressure of a gas against
the walls of its container is the result of collisions of
the gas particles with the walls. The number and
force of collisions determines the pressure.
► A gas that obeys all the assumptions of the kinetic–
molecular theory is called an ideal gas. All gases
behave somewhat differently than predicted by the
kinetic–molecular theory at very high pressures or
very low temperatures. Most real gases display
nearly ideal behavior under normal conditions.
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8.3 Pressure
► Pressure (P) is defined as a force (F) per unit area
(A) pushing against a surface; P = F/A.
► A barometer measures pressure as the height of a
mercury column. Atmospheric pressure presses
down on mercury in a dish and pushes it up a tube.
► Pressure units:
1 atm = 760 mm Hg = 14.7 psi = 101,325 Pa
1 mm Hg = 1 torr = 133.32 Pa
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Gas pressure inside a container is often measured
using an open-end manometer, a simple instrument
similar in principle to the mercury barometer.
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8.4 Boyle’s Law: The Relation Between
Volume and Pressure
► Boyle’s law: The volume of a gas is inversely
proportional to its pressure for a fixed amount of gas
at a constant temperature. That is, P times V is
constant when the amount of gas n and the
temperature T are kept constant.
► V  1/P or PV = k if n and T are constant
► If: P1V1 = k and P2V2 = k
► Then: P1V1 = P2V2
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The volume of a gas decreases proportionately as its
pressure increases. If the pressure of a gas sample is
doubled, the volume is halved.
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Graph (a) demonstrates the decrease in volume as
pressure increases, whereas graph (b) shows the
linear relationship between V and 1/P.
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Problem 8.41
►The volume of a balloon is 2.85 L at 1.00 atm. What
pressure is required to compress the balloon to a
volume of 1.70 L?
Use Boyle’s Law:
P1V1 = P2V2 now, solve for P2
divide both sides by V2
P1V1/V2 = P2
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P2 = P1V1/V2
P2 = (1.00 atm)(2.85 L)/(1.70 L)
= 1.68 atm
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8.5 Charles’ Law: The Relation Between
Volume and Temperature
► Charles’s law: The volume of a gas is directly
proportional to its Kelvin temperature for a fixed
amount of gas at a constant pressure. That is, V
divided by T is constant when n and P are held
constant.
► V  T or V/T = k if n and P are constant
► If: V1/T1 = k and V2/T2 = k
► Then: V1/T1 = V2/T2
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If the Kelvin temperature of a gas is doubled, its
volume doubles.
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As the temperature goes up, the volume also goes up.
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Problem 8.47
►A hot air balloon has a volume of 875 L. What is the
original temperature of the balloon if its volume
changes to 955 L when heated to 56oC?
Charles’ Law:
V1/T1 = V2/T2 now, solve for T1
divide both sides by V1
1/T1 = V2/V1T2
take reciprocal of both sides
T1 = V1T2/V2
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Make sure to use Kelvin degrees
T1 = V1T2/V2
T2 = 56oC + 273 = 329 K
T1 = (875 L)(329K)/(955 L)
= 301K convert to oC (subtract 273)
28oC
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8.6 Gay-Lussac’s Law: The Relation Between
Pressure and Temperature
► Gay-Lussac’s law: The pressure of a gas is directly
proportional to its Kelvin temperature for a fixed
amount of gas at a constant volume. That is, P
divided by T is constant when n and V are held
constant.
► P  T or P/T = k if n and V are constant
► If: P1/T1 = k and P2/T2 = k
► Then: P1/T1 = P2/T2
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As the temperature goes up, the pressure also goes up.
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Problem 8.52
►An aerosol can has an internal pressure of 3.85 atm at
25oC. What temperature is required to raise the
pressure to 18.0 atm?
►Use Gay-Lussac’s law
P1/T1 = P2/T2 Now, solve for unknown variable.
divide both sides by P2
P1/T1P2 = 1/T2
take reciprocal of both sides
T2 = T1P2/P1
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T2 = T1P2/P1
T1 = 25oC + 273
= 298 K
T2 = (298 K)(18.0 atm)/(3.85 atm)
= 1390 K (1117 oC)
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8.7 The Combined Gas Law
► Since PV, V/T, and P/T all have constant values for
a fixed amount of gas, these relationships can be
merged into a combined gas law for a fixed amount
of gas.
► Combined gas law: PV/T = k if n constant
► P1V1/T1 = P2V2/T2
► If any five of the six quantities in this equation are
known, the sixth can be calculated.
► See problems 8.8, 9, 54, 57, 60
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8.8 Avogadro’s Law: The Relation
Between Volume and Molar Amount
► Avogadro’s law: The volume of a gas is directly
proportional to its molar amount at a constant
pressure and temperature. That is, V divided by n is
constant when P and T are held constant.
► V  n or V/n = k if P and T are constant
► If: V1/n1 = k and V2/n2 = k
► Then: V1/n1 = V2/n2
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► The molar amounts of any two gases with the same
volume are the same at a given T and P.
► Standard temperature and pressure:
(STP) = 0C (273.15 K) and 1 atm (760 mm Hg)
► Standard molar volume of a gas at STP = 22.4 L/mol
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Problem 8.68
►What is the mass of CH4 in a sample that occupies a
volume of 16.5 L at STP?
1 mol of any gas at STP = 22.4 L
16.5 L x 1 mol/22.4 L x 16.0 g CH4/1 mol CH4
= 11.8 g CH4
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Density of gases g/L
Density of Helium:
1 mol/22.4 L x 4.00g He/mol He = 0.178 g/L
Density of Nitrogen:
1 mol/22.4 L x 28.0g N2/mol N2 = 1.25 g/L
Density of a gas is proportional to its Mol. Wt.
So… H2 < He < CH4 < CO = N2 < CO2
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8.9 The Ideal Gas Law
► Ideal gas law: The relationships among the four
variables P, V, T, and n for gases can be combined
into a single expression called the ideal gas law.
► PV/nT = R (a constant value) or PV = nRT
► If the values of three of the four variables in the
ideal gas law are known, the fourth can be
calculated.
► Values of the gas constant R:
For P in atm:
R = 0.0821 L·atm/mol·K
For P in mm Hg: R = 62.4 L·mm Hg/mol·K
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Problem 8.11
►An aerosol spray can of deodorant with a volume of
350 mL contains 3.2 g of propane gas (C3H8) as a
propellant. What is the pressure in the can at 20oC?
PV = nRT
solve for P
P = nRT/V
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Convert units
P = nRT/V
R = 0.0821 L.atm/mol.K
n = moles propane (C3H8)
= 3.2 g C3H8 x 1 mol C3H8/ 56 g C3H8
= 0.057 mol
T = K degrees = 20oC + 273
= 293 K
V = Liters = 350 mL x 1 L/1000 mL
= 0.350 L
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Now Solve for P
P = nRT/V
n
R
T
/ V
= (0.057 mol)(0.0821 L.atm/mol.K)(293 K)/0.350 L
= 3.9
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8.10 Partial Pressure and Dalton’s law
► Dalton’s law: The total pressure exerted by a gas
mixture of (Ptotal) is the sum of the partial pressures
of the components in the mixture.
► Dalton’s law Ptotal = Pgas1 + Pgas2 + Pgas3 + …
► Partial pressure: The contribution of a given gas in
a mixture to the total pressure.
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Dry Air at Sea Level
►Pressure at sea level is 760 mm Hg (1 atm)
►Percent composition of dry air is:
78% N2 (78% of the pressure is caused by N2)
21% O2 (21% of the pressure is caused by O2)
1% Ar (1% of the pressure is caused by Ar)
Ptotal = PN2 + PO2 + PAr
= (0.78)(760) + (0.21)(760) + (0.01)(760)
760 = 593 mm + 160 mm +
7 mm
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Problem 8.14
►Deep sea divers breathe a mixture of 98% He and
2% O2 at 9.50 atm of pressure. How does the partial
pressure of O2 in diving gas compare with its partial
pressure in normal air?
Normal air is 21% O2
PPO2 in air: (0.21 O2)(760 mm Hg) = 160 mm Hg
Tank pressure is 9.50 atm x 760 mm Hg/1 atm =
7220 mm Hg
PPO2 in tank = (0.02)(7220) = 144 mm Hg
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8.11 Intermolecular Forces in
Liquids
► Intermolecular force: A force that acts between
molecules and holds molecules close to one another.
There are three major types of intermolecular forces.
► Dipole–dipole forces are weak, with strengths on the
order of 1 kcal/mol
► London dispersion forces are weak, in the range 0.5–
2.5 kcal/mol. They increase with molecular weight
and molecular surface area.
► Hydrogen bonds can be quite strong, with energies
up to 10 kcal/mol.
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5.8 Polar Covalent Bonds and
Electronegativity
► Electrons in a covalent bond occupy the region
between the bonded atoms.
► If the atoms are identical, as in H2 and Cl2,
electrons are attracted equally to both atoms and
are shared equally.
► If the atoms are not identical, however, as in HCl,
the bonding electrons may be attracted more
strongly by one atom than by the other and thus
shared unequally. Such bonds are known as polar
covalent bonds.
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When charges separate in a neutral molecule, the
molecule has a dipole moment and is said to be polar.
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► In HCl, electrons spend more time near the chlorine
than the hydrogen. Although the molecule is overall
neutral, the chlorine is more negative than the
hydrogen, resulting in partial charges on the atoms.
► Partial charges are represented by a d- on the more
negative atom and d+ on the more positive atom.
► The ability of an atom to attract electrons is called
the atom’s electronegativity.
► Fluorine, the most electronegative element, assigned
a value of 4, and less electronegative atoms assigned
lower values.
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Elements at the top right of the periodic table are most
electronegative, those at the lower left are least
electronegative. Noble gases are not assigned values.
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►As a rule of thumb, electronegativity differences of
less than 0.5 result in nonpolar covalent bonds,
differences up to 1.9 indicate increasingly polar
covalent bonds, and differences of 2 or more indicate
ionic bonds.
►There is no sharp dividing line between covalent and
ionic bonds; most bonds fall somewhere in-between.
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5.9 Polar Molecules
►Entire molecules can be polar if electrons are
attracted more strongly to one part of the molecule
than to another.
►Molecules polarity is due to the sum of all
individual bond polarities and lone-pair
contribution in the molecule.
►Polarity has a dramatic effect on the physical
properties of molecules, particularly on melting
points, boiling points, and solubility.
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► Dipoles or polarity can be represented by an arrow
pointing to the negative end of the molecule with a
cross at the positive end resembling a + sign.
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►Just because a molecule has polar covalent bonds
does not mean that the molecule is polar overall.
►Carbon dioxide and tetrachloromethane molecules
have no net polarity because their symmetrical shapes
cause the individual bond polarities to cancel each
other out.
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Dipole–dipole forces: The positive and negative ends
of polar molecules are attracted to one another by
dipole–dipole forces. As a result, polar molecules have
higher boiling points than nonpolar molecules of
similar size.
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►Only polar molecules experience dipole–dipole
forces, but all molecules, regardless of structure,
experience London dispersion forces.
►(a) On average, the electron distribution in a nonpolar
molecule is symmetrical. (b) At any instant, it may be
unsymmetrical, resulting in a temporary polarity that
can attract neighboring molecules.
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A hydrogen bond is an attractive interaction between
an unshared electron pair on an electronegative O, N, or
F atom and a positively polarized hydrogen atom
bonded to another electronegative O, N, or F. Hydrogen
bonds occur in both water and ammonia.
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The boiling points of NH3, H2O, and HF are much
higher than the boiling points of their second row
neighbor CH4 and of related third-row compounds
due to hydrogen bonding.
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8.12 Liquids
► Molecules are in constant motion in the liquid state.
If a molecule happens to be near the surface of a
liquid, and if it has enough energy, it can break free
of the liquid and escape into a state called vapor.
► Once molecules have escaped from the liquid into
the gas state, they are subject to all the gas laws. The
gas molecules make their own contribution to the
total pressure of the gas above the liquid according
to Dalton’s law. We call this contribution the vapor
pressure of the liquid.
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► Vapor pressure rises with increasing temperature
until ultimately it becomes equal to the pressure of
the atmosphere. At this point, bubbles of vapor form
under the surface and force their way to the top; this
is called boiling.
► At a pressure of exactly 760 mm Hg, boiling occurs
at what is called the normal boiling point.
► If atmospheric pressure is higher or lower than
normal, the boiling point of a liquid changes
accordingly. At high altitudes, for example,
atmospheric pressure is lower than at sea level, and
boiling points are also lower.
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At a liquid’s boiling point, its vapor pressure is equal
to atmospheric pressure. Commonly reported boiling
points are those at 760 mm Hg.
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8.13 Water: A Unique Liquid
► Water covers nearly 71% of the Earth’s surface, it
accounts for 66% of the mass of an adult human
body, and it is needed by all living things.
► Water has the highest specific heat of any liquid,
giving it the capacity to absorb a large quantity of
heat while changing only slightly in temperature.
► As a result, large lakes and other bodies of water
tend to moderate the air temperature and the human
body is better able to maintain a steady internal
temperature under changing outside conditions.
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► Water has an unusually high heat of vaporization
(540 cal/g), it carries away a large amount of heat
when it evaporates.
► Your body relies on the cooling effect of water
evaporation.
► Most substances are more dense as solids than as
liquids because molecules are more closely packed
in the solid than in the liquid. Water, however, is
different. Liquid water has a maximum density of
1.000 g/mL at 3.98°C but then becomes less dense as
it cools. When it freezes, its density decreases still
further to 0.917 g/mL. Ice floats on liquid water, and
lakes and rivers freeze from the top down. If the
reverse were true, fish would be killed in winter.
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8.14 Solids
► There are many different kinds of solids. The most
fundamental distinction between solids is that some
are crystalline and some are amorphous.
► Crystalline solid: A solid whose atoms, molecules,
or ions are rigidly held in an ordered arrangement.
Crystalline solids can be further categorized as ionic,
molecular, covalent network, or metallic.
► Amorphous solid: A solid whose particles do not
have an orderly arrangement.
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A summary of the different types of solids and their
characteristics is given below.
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8.15 Changes of State
► When a substance changes state, energy added is used
to overcome attractive forces instead of increasing
kinetic energy so temperature does not change.
► Heat of fusion: The quantity of heat required to
completely melt a substance once it has reached its
melting point.
► Heat of vaporization: The quantity of heat required to
completely vaporize a substance once it has reached its
boiling point.
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A heating curve for water, showing the temperature
and state changes that occur when heat is added.
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Chapter Summary
►According to the kinetic–molecular theory of gases,
the behavior of gases can be explained by assuming
that they consist of particles moving rapidly at
random, separated from other particles by great
distances, and colliding without loss of energy.
►Boyle’s law says that the volume of a fixed amount
of gas at constant temperature is inversely
proportional to its pressure.
►Charles’s law says that the volume of a fixed amount
of gas at constant pressure is directly proportional to
its Kelvin temperature.
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Chapter Summary Cont.
►Gay-Lussac’s law says that the pressure of a fixed
amount of gas at constant volume is directly
proportional to its Kelvin temperature.
►Avogadro’s law says that equal volumes of gases at
the same temperature and pressure contain the same
number of moles.
►The four gas laws together give the ideal gas law,
PV = nRT, which relates the effects of temperature,
pressure, volume, and molar amount.
►At 0°C and 1 atm pressure, called standard
temperature and pressure (STP), 1 mol of any gas
occupies a volume of 22.4 L.
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Chapter Summary Cont.
►The pressure exerted by an individual gas in a
mixture is called the partial pressure. Dalton’s law:
the total pressure exerted by a mixture is equal to the
sum of the partial pressures of the individual gases.
►There are three major types of intermolecular forces,
which act to hold molecules near one another in
solids and liquids. Dipole–dipole forces occur
between polar molecules. London dispersion forces
occur between all molecules as a result of temporary
molecular polarities. Hydrogen bonding, the strongest
of the three forces, occurs between a hydrogen atom
bonded to O, N, or F and a nearby O, N, or F atom.
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Chapter Summary Cont.
►Crystalline solids are those whose constituent
particles have an ordered arrangement; amorphous
solids lack internal order. There are several kinds of
crystalline solids, ionic solids, molecular solids,
covalent network solids, and metallic solids,.
►The amount of heat necessary to melt a given amount
of solid at its melting point is its heat of fusion.
Molecules escape from the surface of a liquid
resulting in a vapor pressure of the liquid. At a
liquid’s boiling point, its vapor pressure equals
atmospheric pressure. The amount of heat necessary
to vaporize a given amount of liquid at its boiling
point is called its heat of vaporization.
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