Gases: Chapter 10
10.1 – Characteristics of Gases
• Physical properties of gases are all similar.
• Composed mainly of nonmetallic elements with
simple formulas and low molar masses.
• Unlike liquids and solids, gases
 expand to fill their containers.
 are highly compressible.
 have extremely low densities.
• Two or more gases form a homogeneous
mixture.
10.2 -- Pressure
• Pressure = force per unit
area (P = F/A)
• SI Unit = N/m2 = 1 pascal
(Pa). kPa is more common
• Atmospheric pressure (the
force exerted by the
atmosphere on a given
surface area) -- measured
with a barometer:
• 1 atm = 760mmHg = 760
torr = 101.3kPa
• Standard pressure = 1atm
• Manometer –
measures the
difference in pressure
between atmospheric
pressure the pressure
of a gas in a container.
• Pgas = Patm + h
• Note:
• h is positive if Pgas > Patm
• h is negative if Pgas < Patm
10.3 – the Gas Laws
• Boyle’s Law: At a constant temp., the pressure and
volume of a gas are inversely proportional.
• PV = a constant, or P1 x V1 = P2 x V2
• Charles’s Law: The volume of a fixed amount of gas
at constant pressure is directly proportional to
its Kelvin temperature
• V1/T1 = V2/T2
• (note: temp must be
• in Kelvin)
• Avogadro’s Law: At a fixed T and P, the volume of
a gas is directly proportional to the number of moles
of gas.
• At STP (1atm and 0°C), 1 mole of a gas = 22.4L
(molar volume of a gas at STP)
10.4 – The Ideal Gas Law
• The Ideal Gas Law (an ideal gas is a hypothetical gas
that follows the ideal gas law under all pressure,
volume, and temperature conditions)
• PV=nRT
• R=.0821 L atm/mol K (see other values on page 408)
• The Combined Gas Law
10.5 – Applications of the Ideal Gas Law
• Determination of Gas Densities: using the ideal gas
law, set the volume equal to 1L and solve for moles (that
gives you moles/L) – then convert to g/L using the molar
mass.
• Or use the following equation:
• d = MP/RT, where M is the molar mass of the gas
• (note: this equation is not on the equation sheet, so
you would have to memorize it)
Determination of the molar mass of a gas: calculate
moles with the ideal gas equation, then divide
mass/moles
• Or use the following equation:
• M = mRT/PV, where M is the molar mass.
• (note: this equation is also not on the equation
sheet)
• Gases in Reaction Stoichiometry
• Law of Combining Volumes: If all the gases in the
reaction are at the same conditions, then the mole ratio
is also the volume ratio.
• For other problems, use the ideal gas law to relate
the moles of a gas to other gas units, such as volume
and pressure (you can’t use the 22.4L/mole
conversion if the conditions aren’t STP)
10.6 – Gas Mixtures and Partial Pressures
• If two gases that don’t react are combined in a container, they
act as if they are alone in the container.
• Dalton’s Law of Partial Pressures:
• Ptotal = P1 + P2 + P3 + …
• Mole fraction = moles of one component / total # of moles in
mixture.
• For gases in a mixture, the mole fraction = the pressure
fraction (Pgas/Ptotal)
• So, PA = Ptot x XA
• Collecting a gas over
water:
• -there’s a mixture of the
desired insoluble gas
and water vapor
• Ptotal = Pbar = Pgas + PH2O
10.7 – The Kinetic-Molecular Theory of Gases
1) Gases consist of large numbers of molecules that are in
continuous, random motion.
2) The combined volume of all the molecules of the gas is
negligible relative to the total volume in which the gas is
contained.
3) Attractive and repulsive forces between gas molecules are
negligible.
4) Energy can be transferred between molecules during
collisions, but the average kinetic energy of the molecules
does not change with time, as long as the temperature of
the gas remains constant.
5) The average kinetic energy of the molecules is proportional
to the absolute (kelvin) temperature
• The Maxwell-Boltzmann distribution describes the
distribution of particle speeds in an ideal gas. Notice that:
• 1. As the molar mass of the gas increases, the speed of the
molecules decreases and the range gets smaller.
• 2. As the temp. increases, the speed increases and the range
gets larger.
How Fast Do Gas Molecules Move?
• Temperature is related to the
average kinetic energy of the gas
molecules.
• Individual molecules can have
different speeds of motion.
• The figure shows three
different speeds:
 ump is the most probable speed (most
molecules are this fast).
 uav is the average speed of the
molecules.
 urms, the root-mean-square speed, is
the one associated with the average
kinetic energy.
 Molar mass
10.8 – Molecular Effusion and Diffusion
Effusion is the escape of
gas molecules through a
tiny hole into an
evacuated space.
Diffusion is the spread of
one substance throughout a
space or a second
substance.
Graham’s Law of Effusion
• Graham’s Law relates the molar mass of
two gases to their rate of speed of travel.
• The “lighter” gas always has a faster rate of
speed.
10.9 – Real Gases: Deviations from Ideal
Behavior
The assumptions made in the kinetic-molecular model
(negligible volume of gas molecules themselves, no attractive
forces between gas molecules, etc.) break down at high
pressure and/or low temperature.
Real Gases
 In the real world, the behavior of gases only conforms to the
ideal-gas equation at relatively high temperature and low
pressure. This is because real gases do have volumes and do
attract one another.
 At high pressures, the volumes of the gas molecules are not
negligible, so the gas volume would be slightly greater than that
predicted by the Ideal Gas Law.
 At low temps, the attractive forces are not negligible, which
lessens the forces with which gas molecules hit the wall of their
container, giving a lower pressure than would be predicted by the
Ideal Gas Law