Gas Laws: Combined Gas Law
The following problems may be solved using the relationships described by
either Charles’ or Boyles’ laws, together in the combined gas law. Show all
the steps to the solution of the problem.
V_{1}P_{1}T_{2} = V_{2}P_{2}T_{1}
1. Carbon dioxide occupies a 2.54 dm^{3} container at STP. What will
be the volume when
the pressure is 150 KPa and 26^{o}C?
V_{2} = [2.54
dm^{3}][101.3 KPa][26^{o}C + 273K] = 1.88 dm^{3
} [150 KPa
][273 K]
2. Oxygen occupies a fixed container of 5.5L at STP. What will happen to the
pressure if
the temperature rises to 300K?
P_{2 }= [5.5
L] [ 101.3 KPa][300 K] = 111.3 KPa
[5.5
L]
[273 K]
3. Methane is compressed in a closed 15.8 dm^{3} container at 101.3
KPa. If the volume
drops to 8.7 dm^{3} and the temperature begins at 25^{o}C
and then drops to 18^{o}C , what will
the pressure of the gas be?
P_{2 }= [ 101.3 KPa][15.8
dm^{3}][300 K] = 179.6 KPa
[8.7 dm^{3} ][273 K]
4. A helium balloon is fully inflated at 1.2 L. When the clerk is filling the
balloon, she stops
to make sure it is not going to explode and checks the
pressure. The pressure is 5.7 KPa
and the temperature at the store is 24^{o}C. The
balloon is 0.75L full. She stops when the
balloon is fully inflated and the pressure is 7.2 KPa. When
the customer takes the balloon
outside, it explodes. What was the temperature outdoors?
T = [24^{o}C +
273K][ 1.2 L][7.2 KPa] = 600 K
[0.75 L][5.7 KPa]
5. Oxygen gas is added to a rebreather at the same rate as it would be in the
open air.
The volume is 4.8 dm^{3} and the temperature is
25 ^{o}C. The pressure is1 atm. Once the
tank is lowered under the water the pressure increases
to 2 atm and the temperature
drops to 12^{o}C. Is the tank in danger
of exploding if it’s maximum volume is 5.0 dm^{3}?
V_{2} = [4.8
dm^{3}][1 atm][12^{o}C + 273K] = 2.1 dm^{3
}[2 atm][25^{o}C + 273K] not in
danger of exploding
6. Ozone is formed due to electricity passing through the air and splitting
some O_{2} atoms
which then join briefly to form O_{3}, ozone. Your
olfactory sense can detect 1.00 mL
ozone in 10 L of air at STP. You are surprised that the
noreaster is accompanied by
thunderstorms. You detect the scent of ozone in the air and
the pressure is 94.5 Kpa and
the temperature is 4 ^{o}C. What is the new
volume of ozone?
V_{2} = [1.00
mL][101.3 KPa][
273K] = 1.09 mL^{
}[94.5 KPa][4 ^{o}C + 273K]
7. You are researching the gases that keep lily pads afloat. The cell
vacuoles that contain the
oxygen that keeps the plant afloat are approximately
17.7 mL. They can expand and
contract with changes in temperature and pressure, but
that is the optimal volume at
25 ^{o}C and standard pressure. If the volume
drops below 14.2 mL the leaves are
submerged. You observe the lily pads in the pond are
below water level, so the volume
is down. If the pressure is 98.2 KPa, what is the
temperature?
T = [25^{o}C +
273K][17.7 mL ][101.3 KPa] = 246.6
K
[14.2 mL ][98.2
KPa]
8. You like to skin dive. The best corals are at a depth of approximately
10m. You take a
deep breath and dive. Your lung capacity is 2.4L total.
The air temperature is 32 ^{o}C and
the pressure is 101.3 Kpa. At 10 m the temperature is
21 ^{o}C and 141.2 Kpa. What is
the volume of your lungs?
V_{2} = [2.4
L][101.3 KPa][32 ^{o}C + 273K] = 1.66 L^{
} [141.2KPa][21 ^{o}C + 273K]
9. If you breathe 3.0 L of helium at 25 ^{o}C and 101.3 Kpa, you will
talk funny. You think
that would be fun. You breathe all the helium in a container
at 15 ^{o}C and 110.6 Kpa and
you aren’t talking funny. Why not?
V_{2} = [3.0
L][101.3 KPa][15^{o}C + 273K ] = 2.66 L^{
} [110.6KPa][25 ^{o}C + 273K] not enough
volume to talk funny
10. A researcher is studying the relationship between volume of burps and
stress. Burps due
to stress are just swallowed air. Your diaphragm
detects pressure as discomfort at
210.0 Kpa. (body temperature is 37 ^{o}C).
If you feel discomfort and you burp, into the
researcher’s balloon, the balloon slightly
inflates to 6.45 mL at 101.3 Kpa and 27 ^{o}C.
What volume did the burp occupy in your body?
V_{2} = [6.45
mL][101.3 KPa][37 ^{o}C + 273K] = 3.22 mL^{
} [210.0 KPa][27 ^{o}C + 273K]
