The most important thing to remember about Boyle's Law is that it only holds when the temperature and amount of gas are constant. A state of constant temperature is often referred to as isothermal conditions. When these two conditions are met, Boyle's law states that the volume V of a gas varies inversely with its pressure P. The equation below expresses Boyle's law mathematically:
|PV = C|
You will get the most mileage out of another incarnation of Boyle's law:
|P1V1 = P2V2|
Boyle used a manometer to discover his gas law. His manometer had an odd "J" shape: As you can see from , there are two ends to Boyle's manometer. One end is open to the atmosphere. The other end is sealed, but contains gas at atmospheric pressure. Since the pressure on both ends of the tube is the same, the level of mercury is also the same.
Next Boyle added mercury to the open end of his manometer. The volume of the gas at the closed end of the manometer decreased, but since gas can't get in or out of the closed end, the amount of gas does not change. Likewise we can assume that the experiment occurs under isothermal conditions. Boyle's law should hold, meaning that the initial volume times pressure should equal the volume times pressure after the additional mercury was added. Let's use the equation below on the gas at the sealed end:
|P1V1 = P2V2|
After Boyle added mercury, the volume of the gas, V2, drops to 50 mL. To find the value of P2, rearrange the equation above and plug in values:
|=||(100 mL)(760 mm Hg)/(50 mL)|
|=||1520 mm Hg|
Boyle's manometer is only one of the many kinds of manometers you'll face. Don't be disheartened; all manometers are practically the same. Realize that each end of a manometer can only be:
Let's try this procedure with a manometer in which one end is open to the atmosphere (760 mm Hg) and the other is sealed off to a vacuum. At the end that is sealed off with a vacuum, P = 0 mm Hg. At the end open to the atmosphere, P = 760 mm Hg. The difference between the two pressures is 760 mm Hg, so the height h must correspond to 760 mm Hg, the atmospheric pressure. Thus this manometer has the same function as a barometer; it measures atmospheric pressure.
There are a few other flavors of manometer, but you can handle them if you remember that h is the pressure difference between the two sides of the manometer. Note that the side of the manometer with the highest pressure also has the lowest level of Hg.