Combined Gas Law
This gas law combines Boyle’s, Charles’s, and Gay-Lussac’s laws. It describes the relationship
between pressure, volume, and temperature of a gas when the amount of gas is constant.
P1V1 = P2V2
T1
T2
Conversions
K = °C + 273
1 cm3 (cubic centimeter) = 1
mL (milliliter)
1.
1 dm3 (cubic decimeter) = 1L
L (liter) = 1000 mL
Standard Conditions
0.00 °C = 273 K
1.00 atm = 760.0 mm Hg =
101.325 kPa = 101,325 Pa
If a compressed air cylinder for scuba diving contains 6.0 L of gas at 18oC and 200. atm
pressure, what volume does the gas occupy at 1.0 atm and 25oC? Answer: 1.23 x 103 L
2. A weather balloon has contains 222 L of He a 20oC and 760. mm Hg. What is the volume of
the balloon when it ascends to an altitude where the temperature is -40oC and 540. mm Hg?
Answer: 249 L
3. A scientist has a sample of gas that was collected several days earlier. The sample has a
volume of 392 mL at a pressure of 0.987 atm and a temperature of 21oC. On the day the gas
was collected, the temperature was 13oC and the pressure was 0.992 atm. What volume did
the gas have on the day it was collected? Answer: 379 mL
4.
Assuming a fixed amount of gas complete the following table.
a.
b.
c.
P1
1.03 atm
107 kPa
0.029 atm
V1
1.65 L
3.79 L
249 mL
T1
19oC
73 oC
?K
P2
0.920 atm
?
0.098 atm
V2
?
7.58 L
197 mL
T2
46 oC
217 oC
293 K
Gay-Lussac’s Law
Gay-Lussac’s Law states for a fixed amount of gas at constant volume, the pressure of a gas is
P1 P2
proportional to its Kelvin temperature. The formula used is:
=
T1 T2
1. A tire on a bicycle stored in a cool garage at 18oC had a pressure of 80psi. WHat is the
pressure inside the tire after riding the bike at 43oC? Answer: 87 psi
2. A pressure cooker is used to cook food in a closed pot. By heating the contents of a pressure
cooker at constant volume, the pressure increases. If the steam inside the pressure cooker
is initially at 100.oC and 1.00 atm,, what is the final temperature of the steam if the pressure
is increased to 1.05 atm? Answer: 392 K
3. If a plastic container at 1.0oC and 750 mmHg is heated in a microwave oven to 80oC, , what is
the pressure inside the container? Answer: 966 mmHg
4. A container filled with helium gas has a pressure of 127.5 kPa at a temperature of 290. K.
What is the temperature when the pressure is 3.51 kPa? Answer: 7.98 K
5. Assuming a fixed amount of gas at constant pressure, complete the following table:
a.
b.
c.
T1
302 K
? oC
263 K
P1
152 kPa
0.777 atm
0.39 atm
T2
11.0 K
192.0 oC
?K
P2
?
5.6 atm
0.058 atm