Boyle's Law and the Manometer
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|
C is a constant unique to the temperature and mass of gas involved. plots pressure versus volume for a gas that obeys Boyles law.
You will get the most mileage out of another incarnation of Boyle's law:
|P 1 V 1 = P 2 V 2|
The subscripts 1 and 2 refer to two different sets of conditions. It is easiest to think of the above equation as a "before and after" equation. Initially the gas has volume and pressure V 1 and P 1 . After some event, the gas has volume and pressure V 2 and P 2 . Often you will be given three of these variables and asked to find the fourth. You should realize that this is a simple case of algebra. Separate the knowns and unknowns on two different sides of the "=" sign, plug in the known values, and solve for the unknown.
Boyle used a manometer to discover his gas law. His manometer had an odd "J" shape:
Next Boyle added mercury to the open end of his manometer.
|P 1 V 1 = P 2 V 2|
The pressure of the gas before mercury is added is equal to the atmospheric pressure, 760 mm Hg (let's assume that the experiment is run at o C so that 1 torr = 1 mm Hg). So P 1 = 760 mm Hg. The volume V 1 is measured to be 100 mL.
After Boyle added mercury, the volume of the gas, V 2 , drops to 50 mL. To find the value of P 2 , rearrange the equation above and plug in values:
|P 2||=||P 1 V 1/V 2|
|=||(100 mL)(760 mm Hg)/(50 mL)|
|=||1520 mm Hg|
If you look back at , you'll notice that the difference P 2 - P 1 = 760 mm Hg, and that this exactly equals the difference in mercury levels on the two sides, h . In fact, Boyle's manometer illustrates a truism common to all manometers: h corresponds to the difference in pressure between the two ends of the manometer.
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:
- sealed and contain a vacuum ( P = 0 )
- open to the atmosphere ( P = P atm )
- open to a sample of gas with pressure P
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.
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.