This ubiquitous equation is known throughout the world.
People use it as a password to their website, and as a button slogan. I think my high school chemistry teacher made us write it on stickers and put them on our foreheads..... (oh dear)
The ideal gas equation summarizes the discoveries about the behavior of gases into one neat and tiny equation. Let's start with the left side:
This is Boyle. Boyle's law states that the pressure increases as the volume decreases. This is known in science as an inverse relationship: P ~ 1/V. The best illustration of this is scuba diving. When a scuba diver goes down into the depths of the ocean the pressure increases. (Makes sense when you think of tons and tons of water weighing down on the ocean floor). As the pressure increases, the volume of the diver's lungs decreases. As the scuba diver rises to the surface, the pressure slowly decreases and the lungs can expand again. When a diver gets "the bends" the person swam upward too quickly and did not allow pressure/volume equilibration to relieve excess pressure. A scuba diver's lungs can actually explode in such a situation. (Like removing the lid on something tightly compressed in a jar- it springs out)
The left side is equal to nRT. Charles's law told us that volume and temperature are directly proportional: as temperature increases, volume increases. Think about the amount of space something takes up when it is moving slowly versus the amount of space it would take moving quickly. This is why you can get a half-filled balloon to perk up by warming it with a hair dryer. The partially filled balloon seems to suddenly have more air (even though it doesn't) when the particles start moving faster.
We also know P ~ T (direct proportionality). Think about the pressure exerted by air in a balloon. Does it exert more or less pressure at room temperature or when heated with a hair dryer? As the hair dryer heats up the molecules inside they move faster and increase their volume. In the process they exert a higher and higher pressure on the walls of the balloon.
The joys of lecturing.....Today is PV=nRT
