Daniel L. Reger
Scott R. Goode
David W. Ball
http://academic.cengage.com/chemistry/reger
Chapter 6
The Gaseous State
Solid Phase
• A solid has fixed shape
and volume.
Solid Br2 at low
temperature
Liquid Phase
• A liquid has fixed volume
but no definite shape.
• The density of a solid or a
liquid is given in g/mL.
Liquid Br2
Gas Phase
• A gas has no fixed
volume or definite shape.
• The density of a gas is
given in g/L whereas
liquids and solids are in
g/mL.
Gaseous Br2
Pressure of a Gas
• Pressure is the
force per unit area
exerted on a
surface.
• The pressure of the
atmosphere is
measured with a
barometer.
Manometers
• Both open and closed end
manometers measure pressure
differences.
Units of Pressure
• One atmosphere of pressure (1 atm) is the
normal pressure at sea level. The SI unit of
pressure is the pascal (Pa), but is a very small
unit and is not used frequently by chemists.
1 Pa 
1 atm = 760 mm Hg
1 atm = 760 torr
1 torr = 133.3 Pa
1 atm = 14.7 psi
1kg
m s
2
1 atm = 101.3 kPa
1 atm = 1.01 bar
1 atm = 29.9 in Hg
Boyle’s Law
• Increasing the
pressure on a gas
sample, by
addition of
mercury to an
open ended
manometer,
causes the volume
to decrease.
Boyle’s Law
• A plot of volume
versus 1/P is a
straight line.
• V = k1 x
1
P
Example: Changing P and V
•
A sample of a gas occupies 5.00 L at 0.974
atm. Calculate the volume of the gas at 1.00
atm, when the temperature held is constant.
Charles’s Law
• A plot of volume versus
temperature is a
straight line.
• Extrapolation to zero
volume yields absolute
zero in temperature:
-273o C.
• V = k2 x T, where T is
given in units of kelvin.
Avogadro’s Hypothesis
Equal volumes
of gases at
constant T and P
contain the same
number of
particles.
• The pressure in
both containers is
the same, but the
mass of the gases
is different.
•
Avogadro’s Law
• A plot of the volume
of all gas samples,
at constant T and
P, vs. the number
of moles (n) of gas
is a straight line.
• V = k3 x n
Example: Changing P, T and V
• A sample of a gas occupies 4.0 L at 25o
C and 2.0 atm of pressure. Calculate the
volume at STP (T = 0 oC, P = 1 atm).
Test Your Skill
• A sample of a gas occupies 200 mL at
100o C. If the pressure is held constant,
calculate the volume of the gas at 0o C.
Ideal Gas Law
• The ideal gas law combines the
three gas laws into a single
equation:
PV = nRT
.
.
where: R = 0.08206 L atm/mol K
• The volume of one mole of an ideal
gas at STP is 22.4 L
Ideal Gas Law Calculation
• Calculate the number of moles of argon
gas in a 30 L container at a pressure of
10 atm and temperature of 298 K.
Ideal Gas Law Calculation
• Calculate the number of moles of argon
gas in a 30 L container at a pressure of
10 atm and temperature of 298 K.
PV = nRT
PV
n=
RT
n=
(10 atm)(30 L)
(0.0821 L  atm/K  mol)(298
K)
= 12 mol
Molar Mass and Density
• The ideal gas law can be used to
calculate density (mass/volume) and
molar mass (mass/moles) of a gas.
• At constant pressure and temperature
the density of a gas is proportional to its
molar mass, so the higher the molar
mass, the greater the density of the gas.
Example: Molar Mass
• Calculate the molar mass of a gas if a
1.02 g sample occupies 220 mL at 95o C
and a pressure of 750 torr.
Gases and Chemical Equations
• The ideal gas law can be used to
determine the number of moles, n, for
use in problems involving reactions.
• The ideal gas law relates n to the volume
of gas just as molar mass is used with
masses of solids and molarity is used
with volumes of solutions.
Example: Gases with Equations
• Calculate the volume of O2 gas formed in
the decomposition of 2.21 g of KClO3 at
STP.
2KClO3(s)  2KCl(s) + 3O2(g)
Gas Volumes in Reactions
Example: Gas Volumes in Reactions
• Calculate the volume of NH3 gas
produced in the reaction of 4.23 L of H2
with excess N2 gas. Assume the
volumes are measured at the same
temperature and pressure.
Dalton’s Law of Partial Pressure
• The pressure exerted by each gas in a
mixture is called its partial pressure.
• For a mixture of two gases A and B, the
total pressure, PT, is
PT = PA + PB
Pressure of a Mixture of Gases
Example: Partial Pressures
• Calculate the pressure in a container that
contains O2 gas at a pressure of 3.22
atm and N2 gas at a pressure of 1.29
atm.
Mole Fraction
• Mole fraction (c, chi) is the number
of moles of one component of a
mixture divided by the total number
of moles of all substances present in
the mixture.
• c A + cB + cC = 1
• The partial pressure of any gas, A, in
a mixture is given by: PA = cA x PT
Mole Fraction
• Mole fraction of the yellow gas is 3/12 =
0.25 and the mole fraction of the red gas
is 9/12 = 0.75
Example: Partial Pressure
• Calculate the partial pressure of Ar gas
in a container that contains 2.3 mol of Ar
and 1.1 mol of Ne and is at a total
pressure of 1.4 atm.
Collecting Gases over Water
• Water vapor is
also present in a
sample of O2 gas
collected over
water.
Example: Collecting Gases
• Sodium metal is added to excess water,
and H2 gas produced in the reaction is
collected over water with the gas volume
of 1.2 L. If the pressure is 745 torr and
the temperature 26o C, what was the
mass of the sodium? The vapor
pressure of water at 26o C is 25 torr.
2Na(s) + 2H2O(l) H2(g) + 2NaOH(aq)
Kinetic Molecular Theory of Gases
1. Gases consist of small particles that are
in constant and random motion.
2. Gas particles are very small compared to
the average distance that separates them.
3. Collisions of gas particles with each other
and the walls of the container are elastic.
4. The average kinetic energy of gas
particles is proportional to the temperature
on the Kelvin scale.
Average Speed of a Gas
• Gas particles
move at different
speeds.
• Average speed is
called the root
mean square
(rms) speed, urms,
and is the square
root of the average
squared speed.
Maxwell-Boltzmann
distribution curves
Average Speed of a Gas
u rms 
3RT
molar mass
R = 8.314 J/mol.K;
molar mass in
kilograms per mole
Effusion and Diffusion
• Effusion - the
passage of a gas
through a small hole
into an evacuated
space.
• Gases with low molar
masses effuse more
rapidly.
• Diffusion is the
mixing of particles
due to motion.
Deviations from Ideal Behavior
• Gases deviate from the ideal gas
law at high pressures.
Deviations from Ideal Behavior
• The assumption that gas particles are
small compared to the distances
separating them fails at high pressures.
• The observed value of PV/nRT will be
greater than 1 under these conditions.
Forces of Attraction in Gases
• The forces of attraction
between closely spaced gas
molecules reduce the impact
of wall collisions.
• These attractive forces cause
the observed value of PV/nRT
to decrease below the
expected value of 1 at
moderate pressures.
Ideal Gases
• A gas (O2 below) deviates from ideal gas
behavior at low temperatures (near the
condensation point ) and high pressures.
van der Waals Equation
• The van der Waals equation corrects for
attractive forces and the volume occupied
by the gas molecules.
2

an
P 
2

V


 V  nb   nRT


• a is a constant related to the strength of the
attractive forces.
• b is a constant that depends on the size of the
gas particles.
• a and b are determined experimentally for each
gas.