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Physics, 6th
Edition
19-22. A 16-L tank contains 200 g of air (M = 29 g/mol) at 270C. What is the absolute pressure
of this sample? [ T = 270
+ 2730
= 300 K; V = 16 L = 16 x 10-3
m3
]
PVm
RT; PmRT
(200 g)(8.314 J/molK)(300 K)
; P = 1.08 x 106 Pa
M MV (29 g/mol)(16 x 10-3m
3)
19-23. How many kilograms of nitrogen gas (M = 28 g/mol) will occupy a volume of 2000 L at
an absolute pressure of 202 kPa and a temperature of 800C? [ T = (80 + 273) = 353 K ]
m MPV (28 g/mol)(202,000 Pa)(2 m3 )PV RT; m ;
M RT (353 K)(8.314 J/molK)
m = 3854 g; m = 3.85 kg
19-24. What volume is occupied by 8 g of nitrogen gas (M = 28 g/mol) at standard temperature
and pressure (STP)? [ T = 273 K, P = 101.3 kPa ]
PVm
RT; VmRT
(8 g)(8.314 J/molK)(273 K); V = 6.40 x 10
-3m
3
M MP
(28 g/mol)(101,300 Pa)
V = 6.40 x 10-3
m3; V = 6.40 L
19-25. A 2-L flask contains 2 x 1023
molecules of air (M = 29 g/mol) at 300 K. What is the
absolute gas pressure?
N NRT (2 x 1023molecules)(8.314 J/molK)(300 K)
PV RT; P
NA NAV (6.023 x 1023molecules/mol)(2 x 10-3m3 )
P = 414 kPa
19-26. A 2 m3
tank holds nitrogen gas (M = 28 g/mole) under a gauge pressure of 500 kPa. If
the temperature is 270C, what is the mass of gas in the tank? [ T= 27
0+ 273
0= 300 K ]
m MPV (28 g/mol)(500,000 Pa)(2 m3 )
PV RT; m ; m = 11.2 kg
M RT (300 K)(8.314 J/molK)
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264
The Ideal Gas Law
19-21. Three moles of an ideal gas have a volume of 0.026 m3
and a pressure of 300 kPa. What
is the temperature of the gas in degrees Celsius?
PVnRT; TPV
nR
(300, 000 Pa)(0.026 m3)
(3 mol)(8.314 J/molK)
T = 313 K; tC = 3130273
0; tC = 39.7
0C
Challenge Problems
19-34. A sample of gas occupies 12 L at 70C and at an absolute pressure of 102 kPa. Find its
temperature when the volume reduces to 10 L and the pressure increases to 230 kPa.
V1 = 12 L = 12 x 10-3
m3; V2 = 10 L = 10 x 10
-3m
3; T1 = 7
0+ 273
0= 280 K
P1V1
P2V2 ; T
P2V2T1
(230 kPa)(10 L)(280 K); T
= 526 K
T T2
PV (102 kPa)(12 L m
3)
21 2 1 1
19-35. A tractor tire contains 2.8 ft3
of air at a gauge pressure of 70 lb/in.2. What volume of air
at one atmosphere of pressure is required to fill this tire if there is no change in
temperature or volume? [ P2 = 70 lb/in.2
+ 14.7 lb/in.2
= 84.7 lb/in.2
]
PV (84.7 lb/in.2)(2.8 ft
3)
PVP V ; V 2 2 ; V2 = 16.1 ft3.
1 1 2 2 2
1 14.7 lb/in.2
19-36. A 3-L container is filled with 0.230 mol of an ideal gas at 300 K. What is the pressure of
the gas? How many molecules are in this sample of gas?
PnRT
(0.230 mol)(8.314 J/molK)(300 K)
; P = 191 kPa n N
V 3 x 10-3
m3
N
N = nNA = (0.230 mol)(6.023 x 1023
molecules/mol) = 1.39 x 1023
molecules
19-38. How many grams of air (M = 29 g/mol) must be pumped into an automobile tire if it is to
have a gauge pressure of 31 lb/in.2
Assume the volume of the tire is 5000 cm3
and its
temperature is 270C?
P = 31 lb/in.2
+ 14.7 lb/in.2
= 45.7 lb/in.2; V= 5000 cm
3= 5 L
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m PVM (45.7 lb/in.2 )(5 x 103m3 )
PV RT; m ;M RT (8.314 J/molK)(300 K)
m = 9.16 x 10-5
g or m = 9.16 x 10-8
kg
19-37. How many moles of helium gas (M = 4 g/mol) are there in a 6-L tank when the pressure
is 2 x 10
5
Pa and the temperature is 27
0
C? What is the mass of the helium?
n PV
RT
(2 x 106Pa)(6 x 10-3m3 );
(8.314 J/mol K)(300 K)n = 0.481 mol
n m
; m = nM = (0.481 mol)(4 g/mol) ; m = 1.92 gM
*19-41. What is the density of oxygen gas (M = 32 g/mol) at a temperature of 230C and
atmospheric pressure?
PVm
RT; m
PM
(101, 300 Pa)(32 g/mol)
1320 g/m3
M V RT (8.314 J/molK)(296 K)
= 1.32 kg/m3
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