Ley de Los Gases Ideales-ejercicios Resueltos

7/29/2019 Ley de Los Gases Ideales-ejercicios Resueltos

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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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Ley de Los Gases Ideales-ejercicios Resueltos

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