WS Gas Laws - KEY
Combined Gas Law
P
1
V
1
= P
2
V
2
T
1
T
2
STP: 273 K & 1.00 atm
Concepts: (circle one choice)
1. If the volume of a container of gas is reduced, what will happen to the pressure inside the container? increase or decrease
2. What happens to the volume of a gas when it is cooled to a lower temperature? increase or decrease
3. What happens to the pressure in a rigid container when it is slowly warmed? increase or decrease
Sample Calculations: (Remember: ALL temperatures MUST be in K , NOT o C )
1. A sample of gas at 240 K and 670 mmHg occupies a 0.128 L volume. What volume will the gas occupy at 198 K if the pressure remains constant?
P
1
V
1
X
2
V
2
(0.128 L) = V
2
. (0.128) (198) = V
2
= 0.106 L
T
1
T
2
(240 K) (198 K) (240)
2. A sample of gas is in a steel container at –75.0°C and 1.48 atm. At what temperature will the sample have a pressure of 7.35 atm?
K = -75 + 273 = 198 K
P
1
V
1
= P
2
X (1.48 atm) = (7.35 atm) T
2
(1.48) = (7.35) (198) T
2
= (7.35)(198) = 983 K
T
1
T
2
(198 K) T
2
(1.48)
3. In an airplane, a gas sample occurs at a volume of 1.50 L at 760 mmHg. Suppose, while flying, the airplane loses pressure and the volume of the gas increases to 11.40 L. What is the pressure in the airplane if the temperature is constant?
P
1
V
1
= P
2
V
2
(760 mmHg)(1.50 L) = P
2
(11.40 L) (760)(1.50) = P
2
= 100 mmHg
T
1
X
2
(11.40)

P
1
V
1
= P
2
V
2
T
1
T
2
Calculations: ( ALL temperatures MUST be in K , NOT o C )
STP: 273 K & 1.00 atm
101.3 kPa, 760 mmHg, 760 torr
4. A balloon of air occupies 10.0 liters at 25.0°C and 1.00 atm. What volume will it occupy if it is placed in a freezer at -10.0°C and the pressure is constant?
8.83 L P
1
V
T
1
1
= P
2
V
T
2
2
10L = V
2
298K 263K
10 x 263 = V
298
2
5. A 0.0500 L sample of a gas is contained in a syringe with a pressure gauge attached. Initially, the gauge indicates a pressure of 1.00 atm. The plunger is pushed so that the pressure reads 1.45 atm. What is the new volume of the gas?
0.0345 atm
P
1
V
1
= P
2
V
2
T
1
T
2
1 x .05 = 1.45 x V
2
1 x .05 = V
1.45
2
6. A sample of gas at 15.0°C and 760 mmHg is heated to 375 K, and the volume is held constant. What is the new pressure of the gas?
990 mmHg (or 1.30 atm)
P
1
V
1
= P
2
V
2
T
1
T
2
760 = P
288
2
375
760 x 375 = P
288
2
7. A gas in a flexible container occupies 0.250 L and 202.6 kPa. If the temperature is constant, what volume does the gas occupy when the pressure is 152.0 kPa?
0.333 L
P
1
V
1
= P
2
V
2
T
1
T
2
202.6 x .250 = 152.0 x V
2
202.6 x .250 = V
152.0
2
8. An inflated balloon occupies a volume of 3.20 L at 25.0°C. What volume will the balloon occupy at
50.0°C if the pressure is constant?
3.49 L P
1
V
1
= P
2
V
2
3.20 L = V
2
3.20 x 325 = V
2
T
1
T
2
298K 325K 298
9. Suppose a used aerosol can contains a gas at 760 mmHg and 25.0°C. If this can is heated in a fire to
500°C, what will be the pressure of the gas inside the can?
1970 mmHg (or 2.59 atm)
P
1
V
1
= P
2
V
2
760mmHg = P
2
T
1
T
2
300K 775K
760 x 775 = P
300
2
10. The gas in an aerosol container has a pressure of 3.00 atm at 57.0°C. What will be the new pressure if the temperature is lowered to -173°C? Assume the volume stays the same.
0.909 atm
P
1
V
1
= P
2
V
2
T
1
T
2
3 atm = P
2
332K 102K
3 x 102 = P
2
332

P
1
V
1
= P
2
V
2
T
1
T
2
Calculations: (cont.) ( ALL temperatures MUST be in K , NOT o C )
STP: 273 K & 1.00 atm
101.3 kPa, 760 mmHg, 760 torr
11. A gas with a volume of 40.0 L at a pressure of 0.900 atm is allowed to expand until the pressure drops to
0.200 atm. Assuming the temperature is constant, what is the new volume?
180 L P
1
V
T
1
1
= P
2
V
T
2
2
0.900atm x 40.0L = 0.200atm x V
2
0.900 x 40.0 = V
0.200
2
12. The pressure in an automobile tire is 2.00 atm at 27.0°C. At the end of a journey on a hot sunny day, the pressure has risen to 2.20 atm. What is the temperature of the air in the tire? Assume the volume of gas has not changed.
330 K P
1
V
1
= P
2
V
2
T
1
T
2
2.00atm = 2.20atm
302K T
2
T
2
= 2.20 x 302
2.00
13. 5.00 L of air at 0.00°C is warmed to 100°C. What is the new volume if the pressure doesn’t change?
6.83 L
P
1
V
T
1
1
= P
2
V
T
2
2
5.00 L = V
2
275K 375K
5.00 x 375 = V
275
2
14. Suppose we have a sample of ammonia gas with a volume of 3.50 L at a pressure of 170.2 kPa. The gas is compressed to a volume of 1.35 L at a constant temperature. Calculate the final pressure.
4.37 atm
170.2 kPa x 3.50 L = P
2
x 1.35 L
15. A sample of methane gas has a volume of 3.80 L at 278 K. If the sample is heated to 355 K at a constant pressure, what would be the new volume?
4.85 L
P
1
P
V
T
1
1
V
T
1
1
1
= P
= P
2
V
T
2
2
V
T
2
2
2
3.80 L = V
2
278K 355K
1.35 L
3.80 x 355 = V
278
2
170.2 x 3.50 = P
2
16. What volume will be occupied by nitrogen in a 50.0 L cylinder at a pressure of 125 atm when it expands into a space where the pressure is 733 mmHg?
6483 L P
1
V
1
= P
2
V
2
T
1
T
2
125 atm x 50.0L = .964 atm x V
2
125 x 50.0 = V
.964
2
17. A balloon of gas occupies 2.50 L at 780 mmHg and 20.0
o
C. What new volume will the gas occupy at
25.0
o
C if pressure is constant?
2.54 L P
1
V
1
= P
2
V
T
1
T
2
2
2.50 L = V
2
298K 400K
2.50 x 400 = V
295
2

P
1
V
1
= P
2
V
2
T
1
T
2
Calculations: (cont.) ( ALL temperatures MUST be in K , NOT o C )
STP: 273 K & 1.00 atm
101.3 kPa, 760 mmHg, 760 torr
For these questions, use all 6 variables in the combined gas law ( none are held constant ).
18. A sample of gas at 240 K and 670 mmHg occupies a 1.28 L volume. What volume will the gas occupy at
-75.0°C if the pressure is changed to 680 mmHg?
K = -75 + 273 = 198 K
1.04 L
P
1
V
1
= P
2
V
2
T
1
T
2
670 mmHg x 1.28 L = 680 mmHg V
2
240 K 198 K
670 x 1.28 x 198 = V
2
240 x 680
19. A 0.700 L gas sample gas sample at STP is compressed to a volume of 0.200 L, and the temperature is increased to 30.0°C. What is the new pressure of the gas?
K = 30.0 + 273 = 303 K
3.88 L
P
1
V
1
= P
2
V
2
T
1
T
2
1atm x 0.700L = P
2
x 0.200L
273K 303 K
1 x 0.700 x 303 = V
2
273 x 0.200
20. A sample of gas has a volume of 2.00 L at 25.0°C and 1.08 atm. What volume will it have at 100°C and
1.50 atm?
1.80 L
P
1
V
1
= P
2
V
2
T
1
T
2
1.08 atm x 2.000L = 1.50 atm x V
298K 373 K
2
1.08 x 2.000 x 373 = V
2
298 x 1.5
21. A 0.150 L sample of gas at 15.0°C and 99.8 kPa. What is the new volume at STP?
P
1
V
1
= P
2
V
2
99.8 kPa x 0.150 L = 101.3 kPa x V
2
99.8 x 0.150 x 273 = V
2
0.140 L
T
1
T
2
288K 273 K 288 x 101.3
22. A 2.50 L sealed flask is filled with gas at 780 mmHg and 273 K. What is the temperature of the gas in o C at
851 mmHg if the volume is constant?
24.9
o C P
1
V
1
= P
2
V
2
T
1
T
2
780 mmHg = 851 mmHg
273K T
2
T
2
= 851 x 273
780
T
2
= 297.9K - 273
23. A helium-filled balloon has a volume of 50.0 L at 25°C and 745 mmHg. What volume will the balloon have at STP?
44.9 L
P
1
V
T
1
1
= P
2
V
T
2
2
745 mmHg x 50.00 L = 760mmHg x V
298K 273 K
2
745 x 50.00 x 273 = V
298 x 760
2