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• 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 “beforeand anafter.”

• 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 thosebefore and aftersituations, 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