Chemistry: Boyle's Law (Gas Laws) with 2 example problems

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 is proportional to 1 over V. You can write this mathematically as P equals K over V, where P equals pressure, V equals volume, and K is a proportionality constant. We can rearrange this equation so it reads PV equals 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 equals K, and P2V2 equals K. So you can write Boyle's law as P1V1 equals P2V2. Let's see an example. A tire with a volume of 11.41 liters 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 liters? Write out Boyle's law and substitute in what we know. This is one of those before and after situations, so we write P1V1 equals P2V2. 44 psi times 11.41 liters equals P2 times 10.6 liters. Solve for P2. Divide both sides by 10.6 liters. 44 psi times 11.41 liters divided by 10.6 liters equals P2. P2 equals 47.36 psi. There are two significant figures in the measurement 44 psi, so we round our answer to two sig figs, 47 psi. Here's another example. A syringe has a volume of 10.0 cc or 10 cubic centimeters. The pressure is 1.0 atmospheres. 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 atmospheres? P1V1 equals P2V2. 1.0 atmospheres times 10.0 centimeters cubed equals 3.5 atmospheres times V2. Solve for V2. Divide both sides by 3.5 atmospheres. 1.0 atmospheres times 10.0 centimeters cubed divided by 3.5 atmospheres equals V2. V2 equals 2.9 centimeters cubed or 2.9 cc. Boyle's law relates pressure and volume, but there are other gas laws which relate the other essential variables associated with a gas. Charles' 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 three 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 four 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.