# Gas Laws

Gas has existed since the beginning of time; oftentimes, it was referred to as “air” or “oxygen;” however, in the late 18th century, “air” became known as gas, and people were able to distinguish between different types of gas. Towards the end of the 18th century, scientists started testing and developing laws that later became known as the “gas laws.” These laws describe properties of gases, and how they react in different situations. In order to understand the gas laws, we need to define a few terms:

**Gas**: a substance consisting of widely spread particles; it can expand indefinitely.
This is also the third state of matter; it is not a solid or a liquid.

**Pressure**: the measure of force applied by another substance (such as a gas).
It is commonly abbreviated as “P” (a capital letter P). Pressure can be measured
in millimeters of Mercury (mmHg), torr, atmospheres (atm), Pascals (Pa), and kilopascals
(kPa). All of the following measurements are the same, just different units, so
you can use them to convert from one to the other. For the ideal gas law, the pressure
will need to be in atmospheres. The conversions between these are as follows:

760 mmHg = 760 torr = 1.00 atm = 101,325 Pa = 101.325 kPa

If you need help setting up the conversions between pressure measurements, please refer back to the Mole section which also explains how to set up dimensional analysis.

**Volume**: the numerical amount of space occupied by a solid, liquid, or gas.
It is commonly abbreviated as “V” (a capital letter V). Volume, in this situation,
will be most often measured in liters, L.

**Temperature**: the measurement of the amount of energy seen in the motion of
particles in a solid, liquid or gas. It can be measured on three scales: Fahrenheit,
Celsius (sometimes referred to as Centigrade) and Kelvin. It is commonly abbreviated
as “T” (a capital letter T). Temperature, in this situation, will most often be
measured in Kelvin, K.

**n**: a lowercase “n” stands for the number of moles of a gas. This is a measurement
in moles, so if you are given a mass in grams or kilograms, be sure to change it
to moles first.

**R**: when dealing with gas laws, R is a constant that means .0821 (L*atm)/(mol*K).
The units are read as “liter-atmospheres per mole-Kelvin.” This label combines volume
(measured in liters, L), pressure (measured in atmospheres, atm), mass (measured
in moles, mol), and temperature (measured in Kelvins, K).

**STP**: STP stands for “standard temperature and pressure” and refers to conditions
of 273 K (0 degrees C) and 1 atm.

Now that you are familiar with the above listed terms, we can begin studying the gas laws. We will state them in order from first discovered to most recently discovered. We will try to put them in common terms, but note that your teacher / instructor may have had a different way of presenting this, so make sure to get live help when you need it!

## Boyle’s Law

*1622*

This law is about pressure and volume relationships, therefore it assumes constant
temperature, meaning the temperature does not change. The subscripts on the letters
(example: P_{1}) are important: letters with the subscript 1 mean before
the change (the change refers to some part of the chemical equation changing, whether
it’s a change in state or a change in amount, etc), and letters with the subscript
2 mean after the change.

P_{1}V_{1} = P_{2}V_{2}

or like this:

This law states that pressure and volume are inversely proportional. That means
that as one gets larger, the other gets smaller. The 1 and 2 indicate change. P_{1}
would be before the pressure change, and P_{2} would be after the pressure
change.

This law can also be written like this:

PV = k_{1} which means that pressure multiplied by volume gives you a constant,
k. This is not the same constant for every reaction; it differs from gas to gas.

## Charles’s Law

*1787*

This law is about volume and how it relates to temperature, so constant pressure is assumed (meaning we assume that the pressure does not change). This law says that volume is directly proportional to absolute temperature. Temperature in this law is measured in Kelvins, K. The law is written in the following way:

V = k_{2}T

or

Simply stated, this law implies that as volume increases, temperature also increases at the same rate. The top equation shows that if you multiply T (temperature) by a constant, you will get the volume, V. The second equation is a more practical application of the law, which will help you when you’re given 3 of the 4 listed items.

## Gay-Lussac’s Law

*1809*

This law is about how pressure and temperature relate, which means the law assumes a constant volume of gas (meaning we assume the volume is not variable—it does not change). This law says that pressure is directly proportional to temperature. The given formula for this equation is:

P = k_{3}T

or

Simply stated, this law implies that as pressure increases, temperature also increases at the same rate. The top equation shows that if you multiply T (temperature) by a constant, you will get the pressure, P. The second equation is a practical application of the law, which will help you when you’re given 3 out of the 4 listed items; you can solve for the last value.

## Avogadro’s Law

*1811*

You may remember an earlier discussion of Avogadro in the Mole section of the Chemistry Help
page. As a reminder, Avogadro’s number is 6.02 x 10^{23} atoms in a mole.
Although it is always the same number of particles, the mass and weight vary by
element with each element’s properties. The law states that the volume a gas takes
up is directly proportional to the number of moles of gas there are. The equation
is:

V = k_{4}n

which means that the number of moles, n, multiplied by a constant, k, yields a specific
volume, V. There is not another application of the law, because it does not involve
changing conditions (there is no V_{1} and V_{2}).

## Ideal Gas Law

*1834, 1856*

Now, after all of these laws came about, another scientist (Emile Clapeyron) decided that they could all be combined into one “ideal” gas law. This is the equation for the ideal gas law:

PV = nRT

In other words, pressure multiplied by volume equals the number of moles multiplied by the gas constant (R = .0821 L*atm/mol*K) multiplied by the temperature. The ideal gas law is used when you are given 3 of the 4 variables (you always have R, so that doesn’t count as a variable). For example, you could use this equation to find pressure if you were given volume, number of moles, and temperature. The equation would look like this:

This equation is easily manipulated by using some simple Algebra—just pretend like you’re solving for x, and whatever you’re looking for (in this case, pressure) is x, so you have to get it on a side by itself. Most of the time, it will simply involve multiplying and/or dividing by the other variables that you’ve been given already.

As this section concludes, we want to make sure you’re aware of one more thing. All of these gas laws are based on “ideal” gases. Ideal gases have the following properties:

1. All gas molecules are in motion, and move randomly.

2. Each time the gas particles collide, kinetic energy is conserved (this is called elasticity).

3. The volume of the molecules of gas is negligible (meaning so small it’s not worth stating).

4. Gases do not attract or repel other gas molecules (there are no IMAFs).

5. The kinetic energy of a gas is directly proportional to its temperature (in Kelvins), and is the same for all gases at the same temperature.

Most gases found in nature do not meet all of these qualifications for ideal gas; however, they follow the rules closely enough that we can still use all of the equations above in theory, and it will not present a significant difference from what occurs in nature.