Without even knowing what gases are made of (OK, they’re made of atoms and molecules) we can understand how they behave on a macroscopic level. Gases are a form of ordinary matter that is much less dense than liquids or solids. Because of this they tend to fill completely any containers they are in and are very compressible.
Everyone has experience working with gases and taking advantage of their properties. If you have ever blown up a balloon, used a straw, inflated a tire, complained about the weather, or taken a deep breath then you already know how this topic relates to “real life”.
There are four mathematical variables used to describe the behavior of gases. Pressure (P), Volume (V), Temperature (T), and amount (n). There are some common units of measurement for each of these variables so your first task will be to become familiar with them.
One more thing: Using these variables will help you to understand the ideal gas laws. Why are they called ideal? It’s not because they are the best possible laws gases could follow. Nor is it because they are the best scientific laws anyone ever found. No, it is because the gases we will discuss are ‘idealized’. That is, they are not real gases and no real gases act the way these equations say they will. But, and this is important, almost all gases come very, very close to acting exactly according to the ideal gas laws. So even though they are not perfect, they are very useful.
| Volume | Unit | Symbol | Convert | Example |
| Cubic Meter | m3 | 1000 L | a large fish tank | |
| Liter | L |
0.001 m3 1000 mL |
a 2 L bottle of soda | |
| Milliliter | mL |
1/1000 L 0.001 L |
a drop from an eyedropper | |
| Pressure | Unit | Symbol | Convert | Example |
| Atmosphere | atm |
760 Torr 14.7 lb/in2 |
The ‘normal’ amount of pressure exerted by Earth’s atmosphere | |
| Torr | torr |
0.00132 atm 0.0193 psi |
Atmos. pressure can drop to 740 torr during a storm | |
|
lbs. per square in. |
psi lb/in2 |
0.0680 atm 51.7 torr |
A car tire might be rated for 35 psi |
|
| Temperature | Unit | Symbol | Convert | Example |
| Fahrenheit | °F | °C · 9/5 + 32 |
32°F water freezes 212°F water boils |
|
| Celsius | °C | (°F -32) · 5/9 |
0°C water freezes 100°C water boils |
|
| Kelvin | K | °C + 273 |
77 K liquid nitrogen boils 273 K water freezes 373 K water boils |
|
| Amount | Unit | Symbol | Convert | Example |
| Mole | mol |
1 mol of C = 6.02 x 1023 atoms of C |
1 mol of C atoms weighs exactly 12 g |
First, a helpful note about using the units given above. You will need to be able to change a number given in one unit into another unit. For instance, you might have a problem to solve in which a volume is given in cubic meters (m3). But the formula you will end up using requires that all volumes be given in liters. How do you go about changing over? Use a technique called Unit Analysis. Here’s how it works:
1000 L Put the unit you need on top of the unit factor
1.2 m3 x -------- = 1,200 L (1.2 x 103 L)
1 m3 Put the unit you’re getting rid of on the bottom
OK, what’s a unit factor?
It is just another name for a conversion factor: a factor you multiply by number in one unit to make it a number in another unit. The word unit is a bit of a pun in the phrase ‘unit factor’. First, it means you’re dealing with units: liters (L), atmospheres (atm), or whatever. Second, it means that the factor is equal to the number one. Let me show you what I mean:
1 m
1 m = 100 cm --> divide both sides by 100 cm --> ----- = 1
100 cm
Equivalently:
100 cm
1 m = 100 cm --> divide both sides by 1 m --> ----- = 1
1 m
What happens when you multiply by one? You get the same number again, right? So using a unit factor does not change the quantity! Just the units.
The key is picking the right unit factor. The hint you need is in the first example above. Find out what one unit (say liters) is equivalent to in another unit (say milliliters). In this case 1 L = 1,000 mL. That means the unit factor is either (1 L)/(1,000 mL) or (1,000 mL)/(1 L). If the number you need to convert is in mL and you want L then use the first factor. If the number you need to convert is in L and you want mL use the second factor. Here, try a few problems to see if you get what I’m talking about:
Now that you know a bit about the units you will be using you are ready to start working with the mathematical laws that we will use to build up the Ideal Gas Law. (This should sound momentous and important.) The first law we will examine is known as Boyle’s Law and was first quantified and mathematically modelled by Robert Boyle is about the year 1662. The law, in words, says the following:
That is, the higher the pressure, the smaller the volume; the lower the pressure, the larger the volume. This relationship can be expressed in the formula:
P · V = constant or more algebraically: P · V = k (only when T and n are constant)
By the way, what is pressure? The key to understanding pressure is to think about force per unit area. Which unit expresses that idea most clearly? What do you think causes the force?
As you work through the following problems try to stop briefly after finding each solution and imagine what the answer means physically. Many people say that chemistry is very abstract, and it is, but with these problems you can very often think about the answers in a clear, physical way. If you do this, you will also have a leg up on making sure your solution is correct. If your volume is a negative number and you try to imagine a negative volume, then you will know you did something wrong!
V V — = constant or — = k (only when P and n are constant) T T
V V — = constant or — = k (only when T and P are constant) n n
PV = nRT is the combined form of the ideal gas law.
This formula is good for static situations
how about when variables are changing?
This formula combines all the gas laws we have used up to now.
P1V1 P2V2 P1V1 P2V2
R = ------ = ------ or ------ = ------ because moles usually don't change
n1T1 n2T2 T1 T2 (ex., n1 = n2 = 1)
R is called the so-called ‘gas constant’ and has a value of 0.0821 L·atm/K·mol