Combined Gas Law
- To use Boyle's Law we have to make sure the temperature and number
of moles stays constant.
- To use Charles' Law we have to make sure the pressure and number of moles
stays constant.
- To keep the moles constant is relatively easy, because we just have to make
sure there are no leaks in the gas container. Keeping temperature or pressure
constant is more difficult because they influence each other.
- To overcome this we can do two sets of calculation, one using Boyle's Law,
and then one using Charles' Law. Here is the example from the front side of
the Combined Gas Law Sheet.
"You blow a methane bubble with a volume of 200.0mL at a pressure of
1.00 atm and a temperature of 20.0°C. Because methane is lighter than
air, the bubble floats upward until it reaches and an altitude where the pressure
is 0.600 atm and a temperature of -10.0°C."
- Using Boyle's Law we can calculate the new volume of the bubble just
due to the pressure change:
Sea Level |
High Altitude |
P1 = 1.00 atm |
P2 = 0.600 atm |
V1 = 200.0 ml |
V2 = ? |
- Using Charles' Law we can take this new larger bubble due to the pressure
change and let it cool down due to the temperature change:
Warm High Altitude
|
Cool High Altitude |
T1 = 20.0°C = 293 K |
T2 = -10.0°C = 263 K |
V1 = 333 ml |
V2 = ? |
- Notice that the V2 from the first problem was substituted
for the V1 in the second problem. We can substitute this algebraically
as follows:
- Voila we have the Combined Gas Law! This can be used to
solve any of the problems we have encountered so far, even those in which
pressure, volume, or temperature do remain constant. In problems such
as these the constant property will mathematically cancel out on each
side.
-
Solving the above problem using the Combined Gas Law is as follows:
Warm Sea Level |
Cool High Altitude |
P1 = 1.00 atm |
P2 = 0.600 atm |
V1 = 200.0 mL
|
V2 = ? |
T1 = 293 K
|
T2 = 263 K |