Subtitles section Play video Print subtitles 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.