Pre-AP Chapter 13 – States of Matter
1. Kinetic Theory
• The particles in a gas are considered to be small, hard spheres with an
insignificant volume.
• The motion of the particles in a gas is rapid, constant, and random.
• All collisions between particles in a gas are perfectly elastic.
Kinetic Theory and a Model for Gases
 Particles in a gas are in rapid, constant motion.
 Gas particles travel in straight-line paths.
 The gas fills the container.
2. Gas Pressure
Gas pressure results from the force exerted by a gas per unit surface area of an object.
Gas pressure is the result of simultaneous collisions of billions of rapidly moving
particles in a gas with an object
• An empty space with no particles and no pressure is called a vacuum.
• Atmospheric pressure results from the collisions of atoms and molecules in air
with objects.
A barometer is a device that is used to measure atmospheric pressure.
3. Kinetic Energy and Temperature
Average Kinetic Energy
The particles in any collection of atoms or molecules at a given temperature have a
wide range of kinetic energies. Most of the particles have kinetic energies somewhere
in the middle of this range.
The Kelvin temperature of a substance is directly proportional to the average kinetic
energy of the particles of the substance.
4. Absolute zero (0 K, or –273.15°C) is the temperature at which the motion of
particles theoretically ceases.
• Particles would have no kinetic energy at absolute zero.
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• Absolute zero has never been produced in the laboratory.
5. Liquids Substances that can flow are referred to as fluids. Both liquids and gases are
fluids.
Liquids
• Particles closer together than gas particles
• Particles are attracted to one another (intermolecular forces)
• Particles can flow, or move and slide around one another
• To escape a liquid and become a gas, a particle must have enough kinetic energy
to overcome the intermolecular forces.
• The interplay between the disruptive motions of particles in a liquid and the
attractions among the particles determines the physical properties of liquids.
6. Evaporation
The conversion of a liquid to a gas or vapor is called vaporization. When such a
conversion occurs at the surface of a liquid that is not boiling, the process is called
evaporation.
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In an open container, molecules that evaporate can escape from the container.
In a closed container, the molecules cannot escape. They collect as a vapor above
the liquid. Some molecules condense back into a liquid.
During evaporation, only those molecules with a certain minimum kinetic energy
can escape from the surface of the liquid.
7. Vapor Pressure is a measure of the force exerted by a gas above a liquid.
 In a system at constant vapor pressure, a dynamic equilibrium exists between
the vapor and the liquid. The system is in equilibrium because the rate of
evaporation of liquid equals the rate of condensation of vapor.
Vapor Pressure and Temperature Change
 An increase in the temperature of a contained liquid increases the vapor
pressure.
 The particles in the warmed liquid have increased kinetic energy. As a result,
more of the particles will have the minimum kinetic energy necessary to
escape the surface of the liquid.
8. Boiling Point
When a liquid is heated to a temperature at which particles throughout the liquid have
enough kinetic energy to vaporize, the liquid begins to boil (not just as surface as in
evaporation.)
The temperature at which the vapor pressure of the liquid is just equal to the external
pressure on the liquid is the boiling point (bp).
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Boiling Point and Pressure Changes
 Because a liquid boils when its vapor pressure is equal to the external pressure,
liquids don’t always boil at the same temperature.
 At a lower external pressure, the boiling point decreases.
 At a higher external pressure, the boiling point increases.
Altitude and Boiling Point
Normal Boiling Point
Because a liquid can have various boiling points depending on pressure, the normal
boiling point is defined as the boiling point of a liquid at a pressure of 101.3 kPa.
9. Properties of Liquids
 Fluidity – the ability to flow
 Viscosity – a measure of the resistance of a liquid to flow
 Surface Tension – a measure of the inward pull by particles in the interior
 Capillary Action - Due to cohesion and adhesion, water will rise
 Cohesion – the attraction between identical molecules
 Adhesion – attraction between different molecules
10. How are the structure and properties of solids related?
 The general properties of solids reflect the orderly arrangement of their
particles and the fixed locations of their particles.
 The melting point (mp) is the temperature at which a solid changes into a
liquid.
 In a crystal, the particles are arranged in an orderly, repeating, threedimensional pattern called a crystal lattice. The shape of a crystal reflects the
arrangement of the particles within the solid.
 The smallest group of particles within a crystal that retains the geometric
shape of the crystal is known as a unit cell.
A crystal lattice is a repeating array of any one of fourteen kinds of unit cells.
There are from one to four types of unit cells that can be associated
with each crystal system. Three kinds of unit cells can make up a cubic
crystal system.
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11. Non-Crystalline Solids
 An amorphous solid lacks an ordered internal structure.
 Rubber, plastic, asphalt, and glass are amorphous solids.
 A glass is a transparent fusion product of inorganic substances that have cooled to
a rigid state without crystallizing.
12. Sublimation : The change of a substance from a solid to a vapor without passing
through the liquid state is called sublimation.
Ex: When solid iodine is heated, the crystals sublime, going directly from the
solid to the gaseous state. When the vapor cools, it goes directly from the gaseous
to the solid state.
Ex: dry ice (carbon dioxide), moth balls, air freshener, freeze-dried foods
13. Phase Diagrams
 A phase diagram is a graph that gives the conditions of temperature and pressure
at which a substance exists as solid, liquid, and gas (vapor).
 The conditions of pressure and temperature at which two phases exist in
equilibrium are indicated on a phase diagram by a line separating the phases.
 The triple point describes the only set of conditions at which all three phases can
exist in equilibrium with one another.
14. Phase Changes
Phase Changes that Require Energy – Melting, Vaporization and Sublimation
Phase Changes that Release Energy – Condensation, Deposition, Freezing
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15. Properties of Gases
Why are gases easier to compress than solids or liquids are?
Compressibility is a measure of how much the volume of matter decreases under
pressure. When a person collides with an inflated airbag, the compression of the gas
absorbs the energy of the impact.
Compressibility
Gases are easily compressed because of the space between the particles in a gas.
• The distance between particles in a gas is much greater than the distance between
particles in a liquid or solid.
• Under pressure, the particles in a gas are forced closer together.
• At room temperature, the distance between particles in an enclosed gas is about 10
times the diameter of a particle.
Factors Affecting Gas Pressure
The amount of gas, volume, and temperature are factors that affect gas pressure. Four
variables are generally used to describe a gas. The variables and their common units are
pressure (P) in kilopascals
volume (V) in liters
temperature (T) in kelvins
the number of moles (n)
You can use kinetic theory to predict and explain how gases will respond to a change of
conditions. If you inflate an air raft, for example, the pressure inside the raft will increase.
Collisions of particles with the inside walls of the raft result in the pressure that is exerted
by the enclosed gas. Increasing the number of particles increases the number of
collisions, which is why the gas pressure increases. If the gas pressure increases until it
exceeds the strength of an enclosed, rigid container, the container will burst.
16. Forces of Attraction
Intermolecular Forces – can hold together identical or different particles. These include
dispersion forces, dipole-dipole forces and hydrogen bonds.
17. Ideal Gas Law PV=nRT
The gas law that includes all four variables—P, V, T, and n—is called the ideal gas law.
Where n is the number of moles. The ideal gas constant (R) has the value 8.31
(kPa·L)/(mol·K).
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You can solve for R by considering 1 mole of gas at standard temp (273 K) and
standard pressure (101.3 kPa) has a volume of 22.4 L. Solve for R….you get 8.31
(kPa·L)/(mol·K).
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18. The Combined Gas Law P1V1 T2=P2V2T1
The combined gas law describes the relationship among the pressure, temperature,
and volume of an enclosed gas. The combined gas law allows you to do calculations
for situations in which only the amount of gas is constant.
15. Boyle’s Law: Pressure and Volume P1V1=P2V2
If the temperature is constant, as the pressure of a gas increases, the volume decreases.
Boyle’s law states that for a given mass of gas at constant temperature, the volume of the
gas varies inversely with pressure.
16. Charles’s Law: Temperature and Volume V1T2=V2T1
As the temperature of an enclosed gas increases, the volume increases, if the pressure
is constant. Charles’s law states that the volume of a fixed mass of gas is directly
proportional to its Kelvin temperature if the pressure is kept constant.
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17. Gay-Lussac’s Law: Pressure and Temperature P1T2=P2T1
As the temperature of an enclosed gas increases, the pressure increases, if the
volume is constant. When a gas is heated at constant volume, the pressure
increases. Gay-Lussac’s law states that the pressure of a gas is directly proportional
to the Kelvin temperature if the volume remains constant. A pressure cooker
demonstrates Gay-Lussac’s Law.
18. Avogadro’s Principle
Avogadro studied the relationship between the
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number of
atoms of a gas and the resulting volume. His results took two forms:
1. Avogadro’s Hypothesis: Equal volumes of gases under the same conditions of
temperature and pressure contain equal numbers of molecules, (particles).
This hypothesis proposes, (correctly), that the composition of a gas is irrelevant to its
volume. The only important variables are: pressure, temperature, and number of moles.
Moreover, it is possible to calculate a molar volume of gases which is the same for
all gases.
At STP, 1.00 mole of any gas has a volume of 22.414 Liters.
This “molar volume” value can be used in the equation:
Sample volume of gas = (moles of gas)(22.414 Liters/mole)
Example: What is the volume of 3.5 moles of helium at STP?
Example: What is the mass of 35.0L of nitrogen gas at STP?
2. Avogadro’s Law: The volume of a gas, at a given temperature and pressure, is
directly proportional to the quantity of gas molecules.
V1
n1
= V2
n2
(if the number of moles doubles, then the volume doubles; all other things remaining
equal)
Example: If you have 0.85 moles of a gas that occupies 350mL, what would the volume
of 1.20 moles be at the same temperature and pressure?
20. Dalton’s Law
Dalton’s law of partial pressures states that, at constant volume and temperature, the
total pressure exerted by a mixture of gases is equal to the sum of the partial pressures
of the component gases.
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Example: What is the partial pressure of hydrogen gas in a mixture of hydrogen and
helium if the total pressure is 600.0 mmHg and the partial pressure of helium is 438
mmHg?
Ex. What is the pressure of dry hydrogen if it is collected over water at 45.0 oC?
21. Ideal Gas Law Application: Molar Mass
n = m/M or
# mol = mass in grams/molar mass in grams per mole
Substitute m for n in PV=nRT to give you PV=mRT
M
Ex: Find the molar mass of an unknown gas that has a volume of 72.5 mL at a
temperature of 68OC, a pressure of 0.980 atm, and a mass of 0.207 g.
22. Ideal Gas Law Application: Density
Ex: The density of a gas was found to be 2.0 g/L at 1.50 atm and 27OC. What is the
molar mass of the gas?
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23. Graham’s Law
 Diffusion is the tendency of molecules to move toward areas of lower
concentration until the concentration is uniform throughout.
 During effusion, a gas escapes through a tiny hole in its container.
 Gases of lower molar mass diffuse and effuse faster than gases of higher molar
mass. A helium filled balloon will deflate sooner than an air-filled balloon.
Helium atoms are less massive than oxygen or nitrogen molecules. So the
molecules in air move more slowly than helium atoms with the same kinetic
energy.
Graham’s law of effusion: for 2 gases at the same temperature, the gas with
the lighter molar mass moves faster.
Rate A
Molar Mass B
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Rate B
Molar Mass A
Example: How many times more rapidly does helium effuse than oxygen gas?
Example: Ammonia effuses at a rate that is 2.93 times larger than that of an unknown
gas. What is the molecular mass of the unknown gas?
24. Behavior of Real Gases
While the Kinetic Theory, Boyle's Law and Charles' Law explain gas behavior
pretty well, they do not explain it perfectly, because real gases do not behave exactly like
ideal gases.
A. Real molecules take up volume and have mass.
1. At high pressures, the size of the gas particles becomes important.
2. The rate of gas diffusion depends upon its mass. Light molecules diffuse quickly,
while heavier molecules diffuse more slowly.
B. Real molecules have slight attractions and repulsion for each other.
1. Dispersion Forces - non-polar molecules have a slight attraction for each other. The
larger the atom or molecule, the stronger the attraction.
2. Dipole Interactions - Polar molecules attract each other. The positive and negative
ends act like magnets to attract opposite charges. At low temperatures gases will
condense to form liquids due to these attractions.
25. Gas Law Stoichiometry
If the conditions are at STP, you can use the molar volume of 22.414L/mol in
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place of the molar mass – either at the beginning or at the end of the problem.
If the conditions are not at STP, then you would use the ideal gas law either at the
beginning or at the end of the problem.
Example: In the decomposition of manganic carbonate what mass of manganic carbonate
would produce 38.0L of carbon dioxide at STP?
Example: In the problem above, if you produce 13.8L of carbon dioxide at 725 mmHG
and 28.0oC, what mass of manganic carbonate did you start with?
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