States:
There are three common states of matter: solid, liquid and gas. Each state has some general traits which all types of matter in this state follow.
Phases Characteristics:
Density Shape Thermal Expansion Compressible
Solid High
Liquid Medium
Gas VERY Low fixed takes shape of the container takes shape of the container
Very Little
Very Little
Lots
Very Little
Very Little
Very Easily
Before you begin your studies of Kinetic Molecular Theory, you need to know what the word means. Kinetic refers to things in motion; molecular deals with molecules; a theory is a hypothesis that has been supported with experimental evidence. Now, we need to define terms. You know what these terms are, but for the discussion of this unit, we will define them differently than normal.
Temperature is a measure of the average kinetic energy of the molecules in a sample.
Since KE = ½ mv 2 , the change in temperature of a sample is caused by a change in velocity (speed) of the molecules in that sample.
Volume of a sample is the space that the particles take up (not much differently than it is normally thought of).
Pressure of a gas sample is caused by the molecules of that sample colliding with the walls of the container. Pressure = Force / Area, so in order for a gas to exert more pressure on its container, there must be more collisions or more forceful collisions.

Kinetic Molecular Theory is guided by the following assumptions:
1. The molecules of an ideal gas (an ideal gas is a gas that follows the assumptions of kinetic molecular theory) are in constant, random, straight-line motion. Gas molecules are constantly moving very, very fast and their direction is completely random. They move in straight lines within their container.
The molecules in an ideal gas can be considered dimensionless points. This assumption can be made because molecules are very, very small compared with the empty space in a gas
2. sample. Therefore, you can assume that the volume of a gas sample is equal to the size of the container that it is held.
3. The collisions between molecules in an ideal gas with each other and the walls of its container are completely elastic. Elastic collisions mean that no energy is lost or gained when the molecules collide.
4. There are no attractive or repulsive forces in an ideal gas. This means that the molecules of an ideal gas do not like or hate each other, they are indifferent. If they pass by another gas molecule, they don’t even notice them, they just go about their business. This assumption is totally false, but as long as the molecules of the gas have plenty of space, they really won’t interact with each other.
5.
Units of Gasses:
2

6.
Nature of Gas Pressure:
The pressure of a gas is a measure of force applied over a given area. For example, pounds per square inch. The force being applied is due to the impact of gas particles on some object.
7.
Right this second, as you read these notes, billions of gas particles – N
2
, O
2
, CO
2
, Ar, H
2
O – are slamming into your eyes. Yes, your eyes and all of the rest of your body. The air is acting in the same fashion that water does when you submerge yourself. You feel the water pressing you as you dive deeper. You feel it on your eardrums. Just as you feel it when you come back down a mountain, say Mt. Hood.
8.
Why do your ears hurt or feel uncomfortable when traveling up and down mountains? There is air pressing on your eardrums, so why are your eardrums not constantly hurting? Because your body equalizes the pressure. Normal atmospheric pressure is 14.7 psi. This means that the air is pressing on everything with a pressure of 14.7 psi. Your eardrums are no exception. Your body has countered this by applying a pressure of 14.7 psi in the inside of your eardrums. This results in no net pressure and your eardrum rests happily undisturbed. But when you drive up a mountain you get an uncomfortable feeling, maybe even painful, why? The pressure in your head is now greater than that outside your head and your eardrum is pressing outward. This stress to the drum is uncomfortable, for some it is even incapacitating.
The "popping" of your ears is your head equalizing the pressure, which as you travel up is some value less than 14.7 psi. As you travel back down the mountain your drums will be pressed in until your head can re-equalize the pressure.

9.
Evangelista Torricelli's Barometer:
The barometer picture here was invented by Evangelista
Torricelli. This was one of the first methods used to measure atmospheric pressure, and it is still used today. Today, most instruments named barometers are not this large and contain no mercury, they work on other principals of physics. But the name has been applied to all instruments used to measure atmospheric pressure.
10.
The apparatus is set up by taking a tube filled with Hg, placing your thumb over the top, inverting the tube and submerging the open end in another container, a dish, also filled with Hg. The
Hg in the tube falls, leaving a vacuum at the top of the tube. But not all of the Hg drains out of the tube. What force is holding this dense liquid up against gravity’s pull? Air pressure. Normal atmospheric pressure will hold a column of Hg 760 mm tall.
This is one of our units listed above for atmospheric pressure; it is equivalent to the Torr, obviously named after Torricelli.
11.
Gas Laws:
There are several laws used to describe the behavior of gasses.
What follows are descriptions of the most important. There about 8 laws we will discuss. These laws we will be discussing pressure, temperature, volume and moles or numbers of gas particles.
When doing these problems, keep in mind that there are only 4 parameters to consider: P, T,
V, and n. For many of these problems you will be keeping two of the four parameters steady as you modify one of these four and calculate that modification of the fourth parameter.
12.
Boyle's Law:
This law defines the relationship between pressure and volume if temperature and amount of gas is held constant. If the volume of a container is increased, the pressure decreases. If the volume of a container is decreased, the pressure increases. The law is described by the following equation:
P
1
V
1
= P
2
V
2
Example: A sample of gas is in a 2.00 L contain at a pressure of 740.0 mmHg. What is the new pressure of the sample if the container’s volume is reduced to 1.25 L?
Answer: This problem is solved by inserting values into the given equation:
(740.0 mmHg) (2.00 L) =(X) (1.25 L)
Solving for X will give you a new pressure of 1184 mmHg.

Charles's Law:
This law defines the relationship between volume and temperature if pressure and amount of particles are held constant. If the temperature of a gas is increased, the volume of the gas will increase. If the temperature of a gas is decreased, the volume of the gas will decrease. This is a direct relationship. One goes down, so does the other.
Picture the gas particles flying around inside a balloon. If you were to put the balloon in the freezer, the gas particles would slow down, therefore they would not hit the balloon walls as hard and the balloon would shrink in size.
V
1
T
1

V
2
T
2
or V
1
T
2
= V
2
T
1
Example: A gas is collected and found to fill 2.85 L at 25.0°C. What will be its volume at standard temperature?
Answer: Convert 25.0°C to Kelvin and you get 298 K. Standard temperature is 273 K. We plug into our equation like this:
2 .
85 L
298 K

V
2
273 K
Solving for the new volume gives a value of 2.61 liters. The volume has decreased as the temperature has decrease.
Gay-Lussac's Law:
This law characterizes the relationship between pressure and temperature when volume and amount are held constant. If the temperature of a container is increased, the pressure increases.
If the temperature of a container is decreased, the pressure decreases. This is another example of a direct relationship. One goes up, so does the other.
Think about this law in this manner, if the gas particles are moving faster, as happens when the temperature of a gas is increased, the force of the impact will increase. Therefore, increasing the temperature will increase the pressure exerted by a gas.
Example: 10.0 L of a gas is found to exert 97.0 kPa at 25.0°C. What would be the required temperature (in Celsius) to change the pressure to standard pressure?
Answer: Change 25.0°C to 298.0 K and remember that standard pressure in kPa is 101.325.
Insert values into the equation and get:

The answer is 311.3 K, but the question asks for Celsius, so you subtract 273 to get the final answer of 38.3°C, but then you knew that. Right?
Avogadro's Law:
This law gives the relationship between volume and number of gas particles when pressure and temperature are held constant. Remember the number is measured in moles. If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases. Another direct relationship.
The volume of a container holding a gas will increase with increasing numbers of gas particles because there are more particles impacting the wall of the container.
Example: A 5.00 L sample of a gas is known to contain 0.965 mol. If the amount of gas in this container is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?
Answer:
V
1 n
2
= V
2 n
1
(5.00 L) (1.80 mol) = (x) (0.965 mol)
Combined Gas Law:
To derive the Combined Gas Law, follow these steps:
Step 1: Write Boyle's Law
P
1
V
1
= P
2
V
2
Step 2: Multiply by Charles’s Law
V
1
T
2
= V
2
T
1
P
1
V
1
2
/ T
1
= P
2
V
2
2
/ T
2
Step 3: Multiply by Gay-Lussac's Law
P
1
T
2
= P
2
T
1
P
1
2 V
1
2 / T
1
2 = P
2
2 V
2
2 / T
2
2
Step 4: Take the square root to get the combined gas law:
P
1
V
1
/ T
1
= P
2
V
2
/ T
2

As a side note:
If we include Avogadro’s Law the following equation is generated:
P
1
V
1
/ n
1
T
1
= P
2
V
2
/ n
2
T
2
Example:
A 2.00 L sample of a gas is collected at 25.0°C and 745.0 mmHg. What is the volume at STP?
You have to recognize that five values are given in the problem and the sixth is the only unknown. Also, remember to change the Celsius temperatures to Kelvin.
When problems like this are solved it is very helpful to write out all the variables in the equation as shown below:
Next fill in the data given in the problem. Here is the right-hand side filled in with the STP values:
You can be pretty sure that the term "STP" will appear in these types of problems. I recommend you memorize these standard conditions.
Here are all the given values:
Insert the values in their proper places in the combined gas law equation:
P
1
V
1
/ T
1
= P
2
V
2
/ T
2

and solve for x.
PV = nRT: The Ideal Gas Law:
The derivation of this law is a lot of math. So, I will just give you the equation and examples of how to use it.
The Numerical Value for R:
R's value can be determined many ways. This is just one way:
We will assume we have 1.000 mol of a gas at STP. The volume of this amount of gas under the conditions of STP is known to a high degree of precision. We will use the value of 22.414 L.
By the way, 22.414 L at STP has a name. It is called molar volume. It is the volume of ANY ideal gas at standard temperature and pressure. As far as you are concerned, all the gasses we discuss will behave as ideal gasses. So, if you have a sample of gas containing 6.022 x 10
23
gas particle, this sample of gas will have a volume of 22.414 L, or about 5 gallons. Think about an object that is 5 gallons. I picture an office water cooler bottle, or a one of those LARGE buckets of paint.
Let's plug our numbers into the equation:
(1.000 atm) (22.414 L) = (1.000 mol) (R) (273.15 K)
Notice how atmospheres were used as well as the exact value for standard temperature.
Solving for R gives 0.08206 L atm / mol K, when rounded to four significant figures. This is usually enough. Remember the value. You'll need it for problem solving.
Notice the weird unit on R. Say out loud "liter atmospheres per mole Kelvin."
This is not the only value of R that can exist. It depends on which units you select. Those of you that take more chemistry or physics will most likely meet up with 8.3145 Joules per mole Kelvin, but that's for another course. We will only use the 0.08206 value in gas-related problems.
Example: A sample of gas with a mass of 2.1025 grams is found to occupy a volume of 2.850 L at 22.0°C at a pressure of 740.0 mmHg. How many moles of the gas are present?
Notice that the units for pressure MUST be in atm., so the 740.0 mm Hg must be converted first.
740.0 mm Hg ÷ 760.0 mm Hg/atm = 0.9737 atm
However, the unrounded-off value should be used in the calculation just below.
Now, plug into the equation:
(0.9737 atm) (2.850 L) = (n) (0.08206 L atm / mol K) (295.0 K)

and solve for n = 0.115 mol
Example: Using the problem above, what is the molar mass of the gas?
This is a very common use of this law and the odds are very good you will see this type of question on a test.
The key is to remember the units on molar mass: grams per mole. We know from the problem statement that 2.1025 grams of the gas is involved and we also know how many moles that is.
We know that from doing the calculation above and getting 0.1146 mol.
So all we have to do is divide the grams of gas by how many moles it is:
2.1025 g ÷ 0.1146 mol = 18.34 g/mol
With a molar mass of 18.34 g per mol can you make an educated guess as to what gas this might be?
Let's go over those steps for using the Ideal Gas Law to calculate the molar mass of the gas:
1.
You have to know the grams of gas involved. Usually the problem will just give you the value, but not always. You might have to calculate it.
2.
You are going to have to calculate the moles of gas. Use PV = nRT and solve for n. Make sure to use L, atm and K.
3.
Divide grams by moles and there's your answer.
For any pure gas (let's use helium) PV = nRT holds true. Therefore, P is directly proportional to n if V and T remain constant. As n goes up, so would P. Or the reverse.
Suppose you were to double the moles of helium gas present. What would happen?
Answer: the gas pressure doubles.
However, suppose the new quantity of gas added was a DIFFERENT gas. Suppose that, instead of helium, you added neon.
What would happen to the pressure?
Answer: the pressure doubles, same as before.
Dalton's Law immediately follows from this example since each gas is causing 50% of the pressure. Summing their two pressures gives the total pressure.
Written as an equation, it looks like this:
P
He
+ P
Ne
= P total

Dalton's Law of Partial Pressures: Each gas in a mixture creates pressure as if the other gases were not present. The total pressure is the sum of the pressures created by the gases in the mixture. P total
= P
1
+ P
2
+ P
3
+ .... + P n
Where n is the total number of gases in the mixture.
The only necessity is that the two gases do not interact in some chemical fashion, such as reacting with each other.
The pressure each gas exerts in mixture is called its partial pressure.
Example:
A container holds three gases: oxygen, carbon dioxide, and helium. The partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. What is the total pressure inside the container?
P
T
= P
O
2
+ P
CO
2
+ P
He
PT = 2 atm + 3 atm + 4 atm = 9 atm
Graham's Law:
Consider samples of two different gases at the same Kelvin temperature.
Since temperature is proportional to the kinetic energy of the gas molecules, the kinetic energy
(KE) of the two gas samples is also the same.
In equation form, we can write: KE
1
= KE
2
Since KE = (1/2) mv
2
, (m = mass and v = velocity) we can write the following equation: m
1 v
1
2
= m
2 v
2
2
Note that the value of one-half cancels out.
The equation above can be rearranged algebraically into the following:
The square root of (m
1
/ m
2
) = v
2
/ v
1
You may wish to assure yourself of the correctness of this rearrangement.
Another way you may see this written is:

Rate
1
Rate
2

MM
2
MM
1
Rate
1
of gas 1
Rate
2
of gas 2
MM
1
molar mass of gas 1
MM
2
molar mass of gas 2
This last equation is the modern way of stating Graham's law.
This is a good way to determine the ratio of the speeds of the gasses.
This will tell you which gas will make it through a small hole quicker, i.e. the small holes you find in a balloon. For example, which gas will leave the balloon quicker?
This diagram depicts the curve of temperature verses time of a given substance. Starting with a solid that is melted into a liquid that is boiled to a vapor. As heat is added this is the shape of the curve generated. Flat lines are due to intermolecular forces being broken, solid ice turning to liquid water, liquid water being turned into steam. Once boiling begins the temperature remains fixed at the boiling point until all of the liquid is converted to gas. Thus, at the boiling point liquid and gas coexist in equilibrium. Similarly, solid and liquid coexist in equilibrium at the melting or boiling point.
The angled lines are where the temperature is rising in a given phase. So, flat lines indicate a phase change is occurring and angled lines indicate no phase change.
The first angled line is the rising of temperature of a solid. Once the melting temperature has been reached, the line becomes flat and a phase change begins. The energy needed for this to

occur is called the Heat of Fusion and is defined as that amount of heat needed to melt a specific mass of a specific substance. If this curve were a cooling curve the line would be called the Heat of Solidification, defined as that amount of heat given off a specific mass of a specific substance when it freezes. Yes, freezing is exothermic. It usually gets warmer right when it begins to snow.
The second angled line is the rising of temperature of a liquid. Once the boiling or vaporization has been reached, the line again becomes flat, indicating a phase change is occurring. The energy needed for this to occur, the Heat of Vaporization, is that amount of heat needed to vaporize a specific mass of a specific substance. If this curve were a cooling curve the line would be called the Heat of Condensation, defined as that amount of heat given off a specific mass of a specific substance when it condenses. Yes, condensing is exothermic. It usually gets warmer right when it begins to rain.