Chemistry B2A
Chapter 13
Gases
States of matter: the physical state of matter depends on a balance between the kinetic
energy of particles, which tends to keep them apart, and the attractive forces between them,
which tend to bring them together. The attractive forces between molecules are the same in all
three states (gas, liquid, and solid). However, in the gaseous state, the kinetic energy of the
molecules is great enough to overcome the attractive forces between them. Kinetic energy
increases with increasing temperature.
Kinetic molecular theory (properties of an ideal gas):
1. Gases consist of particles, either atoms or molecules, constantly moving through space in
straight lines, in random directions.
2. The average kinetic energy of gas particles is proportional to the temperature in kelvins.
The higher temperature, the faster they move, and the greater their kinetic energy.
3. Molecules collide with each other, much as billiard balls do, bouncing off each other and
changing directions (they may exchange kinetic energies).
4. Gas particles have no volume.
5. There are no attractive forces between gas particles (they do not stick together after a
collision occurs).
6. Molecules collide with the walls of the container, and these collisions constitute the
pressure of the gas.
Pressure: the force per unit area.
P=
Force (F)
Area (A)
Pressure has the different units: atmosphere, torr, mm Hg, in. Hg, Pascal, bar.
1.000 atm = 760.0 torr = 760.0 mm Hg = 101,325 Pascals = 29.92 in. Hg = 1.000 bar
Barometer: we use a barometer to measure atmospheric pressure. A barometer consists of a
long glass tube that is completely filled with mercury and then inverted into a pool of mercury
in a dish. The difference in the heights of the two mercury levels is a measure of the
atmospheric pressure.
Dr. Behrang Madani
Chemistry B2A
Bakersfield College
Manometer: we use a manometer to measure the pressure of a gas in a container. One type of
manometer consists of a U-shaped tube mercury. One arm has been evacuated and sealed and
has zero pressure. The second arm is connected to the container. The difference between the
two mercury levels gives the pressure directly in mm Hg.
Gas laws:
Boyle’s law: for a fixed mass of an ideal gas at a constant temperature, the volume of the gas
is inversely proportional to the applied pressure.
P1V1 = P2V2
P1 V1
P2 =
V2
V2=
P1 V1
P2
Charles’s law: for a fixed mass of an ideal gas at a constant pressure, the volume of gas is
directly proportional to the temperature in Kelvin (K).
V1 V 2
=
T1 T 2
Dr. Behrang Madani
Chemistry B2A
Bakersfield College
V2=
V1 T2
T1
T2 =
T 1 V2
V1
Gay-Lussac’s law: for a fixed mass of an ideal gas at constant volume, the pressure is
directly proportional to the temperature in Kelvin (K).
P1 P 2
=
T1 T 2
P2 =
P1 T 2
T1
T2 =
T1 P2
P1
Combined gas law: the three gas laws can be combined:
P1 V1 P2 V2
=
T1
T2
Avogadro’s law: the volume of a gas is directly proportional to the number of moles of gas if
temperature and pressure remain constant.
V1 V2
=
n1 n 2
Note: Equal volumes of gases at the same temperature and pressure contain equal numbers of
molecules (regardless of their identity).
Ideal gas law: under most experimental conditions, real gases behave sufficiently like ideal
gases.
PV = nRT
Dr. Behrang Madani
Chemistry B2A
Bakersfield College
n: amount of the gas in moles (mol)
R: a constant for all gases (universal gas constant)
V: volume of the gas in liters (L)
T: temperature of the gas in Kelvins (K)
P: pressure of the gas in atmospheres (atm)
Note: at the Standard Temperature and Pressure (STP) (T = 0°C (273K) and P = 1.000 atm),
one mole of any gas occupies a volume of 22.4 L.
R=
PV (1.000 atm) (22.4 L)
L. atm
=
= 0.0821
nT
(1.00 mol) (273 K)
mol. K
Dalton’s law of partial pressure: in a mixture of gases, each molecule acts independently of
all the others. The total pressure, PT, of a mixture of gases is the sum of the partial pressures
of each individual gas.
PT = P1 + P2 + P3 + …
Partial pressure: the pressure that a gas in a mixture of gases would exert if it were alone in
the container.
ntotal is the sum of the number of moles of the gases in the mixture. Therefore, for a mixture of
ideal gases, it is the total number of moles of particles that is important, not the identity of the
individual gas particles or the nature of the gas particles. Thus:
1. The volume of the individual gas particles (atom or molecule) must not be very
important.
2. The forces among the particles must not be very important.
Dr. Behrang Madani
Chemistry B2A
Bakersfield College
Gas Stoichiometry: we can calculate the number of moles, mass, and number of molecules
of a gas at STP condition if we know the pressure, volume, and temperature for a given
sample of gas.
Example: Calculate the volume of oxygen gas produced at 1.00 atm and 25.0°C by the
complete decomposition of 10.5 g of potassium chlorate. The balanced equation for the
reaction is:
2KClO3(s) → 2KCl(s) + 3O2(g)
Dr. Behrang Madani
Chemistry B2A
Bakersfield College