For a gas, pressure and volume are inversely
proportional. If you keep everything else constant, then as the pressure on a gas goes
up, its volume goes down. As the volume a gas occupies goes up, its pressure goes down. If you exert pressure on a gas, you can compress
it – make it take up less space. Imagine a hard container that measures how many times
gas particles bang against the sides. The more the gas particles bang against the sides,
the higher the gas pressure on the container. If you make the container smaller, you compress
the gas. The particles of gas will run into the sides more often per second, so that means
higher pressure. If you keep the amount of gas particles constant, but you make the size
of the container bigger, there will be fewer collisions per second with the sides. That
registers as lower pressure. Robert Boyle stated the inverse relationship
between pressure and volume as a Gas Law. Boyle’s Law says that for a given amount
of gas, at fixed temperature, pressure and volume are inversely proportional. P ∝ 1/V.
You can write this mathematically as P=k/V where
P=pressure V=volume, and
k=is a proportionality constant. We can rearrange this equation so it reads
PV=k, or the product of pressure and volume is a constant, k.  Very often Boyle’s law is used to compare
two situations, a “before” and an “after.” In that case, you can say P1V1=k, and P2V2
=k, so you can write Boyle’s law as P1V1=P2V2. Let’s see an example. Example 1: A tire with a volume of 11.41 L
reads 44 psi (pounds per square inch) on the tire gauge. What is the new tire pressure
if you compress the tire and its new volume is 10.6 L?
Write out Boyle’s Law, and substitute in what we know.
This is one of those “before and after” situations, so we write P1V1=P2V2
(44 psi)(11.41L)=(P2)(10.6L) solve for P2 (divide both sides by 10.6L)
(44 psi)(11.41L)/10.6L=P2 P2=47.36 psi (There are 2 significant figures
in the measurement 44 psi, so we round our answer to 2 sig figs)=47 psi Example 2: Here’s another example: A syringe
has a volume of 10.0 ccs (or 10 cubic centimeters). The pressure is 1.0 atm. If you plug the end
so no gas can escape, and push the plunger down, what must the final volume be to change
the pressure to 3.5 atm? P1V1=P2V2
(1.0 atm)(10.0 cm3)=3.5 atm (V2) solve for V2 (divide both sides by 3.5 atm)
(1.0 atm)(10.0 cm3) / 3.5 atm=V2 V2=2.9 cm3 (2.9 ccs) Boyle’s law relates pressure and volume,
but there are other gas laws which relate the other essential variables associated with
a gas. Charles’s Law is the relationship between temperature and volume.
Gay-Lussac’s Law is the relationship between pressure and temperature. And the combined
gas law puts all 3 together: Temperature, Pressure, and Volume. Notice that to use any
of these laws, the amount of gas must be constant. Avogadro’s Law describes the relationship
between volume and the amount of a gas (usually in terms of n, the number of moles). When
we combine all 4 laws, we get the Ideal Gas Law. To decide which of these gas laws to
use when solving a problem, make a list of what information you have, and what information
you need. If a variable doesn’t come up, or is held constant in the problem, you don’t
need it in your equation.