Chapter 10 Outline: Gases
10.1 Characteristics of Gases
Substances that are liquids or solids under ordinary conditions but can be in a gaseous
state called vapor. Gases expand spontaneously to fill its container because according to Kinetic
Molecular Theory, gases do not have intermolecular forces. Therefore, the volume of a gas
equals the volume of a its container. Gases are also highly compressible: when pressure is
applied to a gas, its volume readily decreases. Two or more gases form a homogenous mixture.
10.2 Pressure
Pressure is defined in science as the force that acts on a given area. P = force/area.
Gases exert a pressure on any surface with which they are in contact.
 Atmospheric Pressure and the Barometer
o Different units of measurement for pressure and how they were discovered.
o 1 atm = 760. mmHg = 760. Torr = 1.01325 x 105 (101.3 kPa) = 1.01325 bar
10.3 The Gas Laws
 The Pressure-Volume Relationship: Boyle’s Law
o P1V1 = P2V2
o Pressure and volume are inversely related. As pressure decreases, volume
increase, and as pressure increases, volume decreases. (Assuming constant
temperature)
o Ex. Putting more air into a balloon increases the volume, because the individual
pressures from the helium molecules are exerting pressure on the inside of the
balloon. The balloon must increase the volume in order to alleviate the amount
of pressure.
 The Temperature-Volume Relationship: Charles’ Law
o V1/T1 = V2/T2
o Volume and temperature are directly related. As temperature increases, the
volume increases, and as the temperature decreases, the volume decreases
(Assuming constant pressure)
o Ex. Decreasing the temperature of a gas inside of a balloon under constant
pressure, will decrease the volume because the average kinetic energy of the
molecules is decreasing; their speed is decreasing, which decreases pressure.
(How often gas particles hit the walls of a container)
 The Quantity-Volume Relationship: Avogadro’s Law
o Gay-Lussac
 P1/T1 = P2/T2
 Temperature and pressure and directly related. Increasing temperature
increases pressure and decreasing temperature decreases pressure.
(Assuming constant volume)
o Avogadro’s Hypothesis
 Equal volumes of gases at the same temperature and pressure contain
equal numbers of molecules.

22.4 L of any gas at standard conditions contain 6.02 x 1023 (or 1 mol) gas
molecules.
 Standard conditions are 273 K or 0°C and 1 atm
o Avogadro’s Law
 V1/n1 = V2/n2
 Number of moles is directly related to volume. If the numbers of moles
doubles, the volume doubles. (Assuming constant temperature and
pressure)
10.4 The Ideal-Gas Equation
 PV = nRT
o P = pressure
o V = volume
o n = number of moles
o R = gas constant
o T = temperature
 An ideal gas is a hypothetical gas whose pressure, volume, and temperature
relationships are described completely by the ideal-gas equation.
 R is the gas constant and its units depend on the units of P, V, n, and T. Temperature
must be in Kelvin. Pressure is typically measured in atmospheres, and volume in liters.
There are two gas constants:
o 0.0821 L x atm/mol x K
 Typically used the most
o 8.314 J/mol x K
 The volume occupied by 1 mol of ideal gas at STP, 22.41 L, is known as the molar volume
of an ideal gas at STP.
 Relating the Ideal-Gas Equation and the Gas Laws
o Combined Gas Law
 P1V1/T1 = P2V2/T2
 Assumes that number of moles stays constant while pressure, volume,
and temperature change.
10.5 Further Applications of the Ideal-Gas Equation
 Gas Densities and Molar Mass
o Density = mass/volume.
o The density of a gas depends on its pressure, molar mass, and temperature. The
higher the molar mass, and pressure, the denser the gas. The higher the
temperature, the less dense the gas.
o When we have equal molar masses of two gases at the same pressure but
different temperatures, the hotter gas is less dense than the cooler one, so the
hotter gas rises.
o Another version of the ideal-gas law can be used to find the molar mass of a gas:
 MM = dRT/P

 MM = molar mass
 d = density
 R = gas constant
 T = temperature
 P = pressure
Volumes of Gases in Chemical Reactions
o The coefficients in a balanced chemical equation tells us the relative amounts (in
moles) of reactants and products in a reaction.
10.6 Gas Mixtures and Partial Pressures
 Dalton’s Partial Pressure
o Pt = P1 + P2 + P3 + …
 Pt = total pressure in the container
 P1/2/3… = partial pressure of a certain gas in the mixture
o The total pressure of a mixture of gases equals the sum of the pressures of each
individual gas molecule if it were by itself. The pressure exerted by a particular
component of a mixture of gases is called the partial pressure of that
component.
 Partial Pressures and Mole Fractions
o Px = (moles of gas “X”/total moles of gas in container) x Pt
 Px = Partial pressure of a certain gas in a mixture
 Pt = total pressure in the container
o Mole fraction – X. A dimensionless number that expresses the ratio of the
number of moles of one component in a mixture to the total number of moles in
the mixture.
10.7 The Kinetic-Molecular Theory of Gases
Gas laws do not work without these assumptions. These guidelines help explain how
gases behave under ideal conditions. The most ideal conditions for gases are low pressure, high
temperature, and low number of moles.
1. Properties of Gases
a. Made of particles
b. No definite volume
c. Definite mass
2. Forces of gases
a. No repulsive or attractive forces between particles.
i. Negligible INTER molecular forces but INTRA molecular still exists.
1. Intermolecular forces are forces that take place between
molecules.
2. Intramolecular forces are forces that take place between the
atoms in the molecules (ex. Ionic, metallic, and covalent bonds)
3. Energy
a. Elastic collisions, no energy loss
4. Movement
a. Gas particles move in a continuous, random motion, linear path.
5. Speed
a. Average kinetic energy of gas particles depends on the temperature of the gas.
AVE and temperature are directly related.
 Distributions of Molecular Speed
o The molecules in a sample of gas have an average kinetic energy and hence have
an average speed, the individual molecules are moving at different speeds.
10.8 Molecular Effusion and Diffusion
 Effusion – The escape of gas molecules through a tiny hole.
 Diffusion – The spread of one substance throughout a space or throughout a second
substance.
 Graham’s Law of Effusion
o


Or relative ratea =

o The effusion rate of a gas is inversely proportional to the square root of its molar
mass.
o The gas with the lowest molecular weight will escape the fastest.
Diffusion and Mean Free Path
o Because of molecular collisions, the direction of motion of a gas molecule is
constantly changing. Therefore, the diffusion of a molecule from one point to
another consists of many short, straight-line segments as collisions buffet it
around in random directions.
10.9 Real Gases: Deviations from Ideal Behavior
 Ideal gases are thought to have no attractions for one another, and occupy no space,
but real molecules do take up space, and are attracted to one another.
 At low pressures, the combined volume of the gas molecules is negligible relative to the
container volume. At high pressures the unoccupied volume available to the molecules
is less than the container volume, therefore, gas volumes tend to be slightly greater
than those predicted by the ideal-gas equation. Attractive forces between molecules
come into play at the short intermolecular distances found when molecules are
crowded together at high pressures. Because of these attractive forces, the impact of a
given molecule with the container wall is lessened.
 Temperature determines how effective attractive forces between gas molecule are in
causing deviations from ideal behavior at lower pressures.


o Ex. As a gas cools, the average kinetic energy of the molecules decreases. This
drop in kinetic energy means the molecules will be more likely to stick to each
other than bounce off each other.
The van der Waals equation is an equation of state for gases that modifies the ideal-gas
equation to account for intrinsic molecular volume and intermolecular forces.