1

TOPIC 1- IDEAL GASES

Examples of Solved Problems

1. A rigid tank contains CO2 at 29 oC and a pressure of 120 kPa. Determine the internal gas

pressure when the tank and its contents are heated to 90 oC?

Solution:

From the question, a rigid tank means that V, the volume of the system is constant, P and T

are changing. Apply Gay-Lussac’s law:

2

2

1

1

T

P

T

P= or

K

KkPa

T

TPP

)27329(

)27390(120

1

212

+

+×== =144 kPa

2. Exactly 200 cm3 of hydrogen is collected over water at 25

oC and 900.5 torr. Compute the

standard volume of dry hydrogen. The vapor pressure of water at 25 oC is 23.8 torr.

Solution:

The total pressure = pressure of hydrogen (dry) + vapor pressure of water ,

Pressure of dry hydrogen = (total pressure) - (vapor pressure of water)

= (900.5 torr)-(23.8 torr) = 876.7 torr = P1

Converting to standard state (STP: 273 K, 1 atm =760 torr),

torrK

Kcmtorr

P

T

T

VPV

760298

2732007.876 3

2

2

1

112

×

××=×= = 211.4 cm

3

3. 10.00 g of a gas mixture of nitrogen and methane, containing 30.4 wt % of nitrogen, occupies

a volume of 10.00 cm3 at a definite pressure and a temperature of 10

oC. Assuming that the

mixture follows Dalton’s law, calculate the total pressure of the mixture of gases in kPa.

Solution:

Mass of N2 = =× g00.10100

4.303.04 g , mol of N2 =

0.28

04.3= 0.1086 mol

Mass of CH4 =10.00 - 13.04 = 6.96 g , mol of CH4 = 16

96.6= 0.435 mol

Total of mol = 0.544 mol

Total pressure =V

RTntotal = )10(00.10

)15.27310)(314.8(544.0333

11

−−

−−+

cmLcm

KmolkPaKLmol

= 1.28×105 kPa

2

4. A mixture of N2 and O2 is contained in a glass bulb of 5 cm3

capacity at 24 oC. The pressure

is 870 bar, and the mass of the gas in the bulb is 5.08 g. What is the average molar mass, and

what is the mole fraction of O2?

Solution:

From density Vm /=ρ , M

RT

M

RT

V

m

V

nRTP ×=×== ρ

0.2090.2090.2090.209=−

−=

+−=

+=

+=

+=×+=×+=

=×

==−

−

−−

2832

2884.28

,3228)1(

1)()(

84.28)870)(105(

)297)(08314.0)(08.5(

2

2

2222

2

2

2

2

222

2222

2

2

1

3

11

O

OO

OONN

O

total

O

N

total

N

total

OONN

total

ONON

X

XX

MXMX

Mn

nM

n

n

n

MnMn

nmm

PV

RTmmM

molgbarL

KmolbarKLg

VP

mRTM

5. After 2.10 mol of NH3 gas is placed in a 1600-cm3 box at 25

oC, the box is heated to 600 K.

At this temperature, the ammonia is partially decomposed to N2 and H2, and a pressure

measurement gives 8.85 MPa. Find the number of moles of NH3 present at 600 K.

Solution:

• You must write the balance equation, the initial mol, reacting mol and the final mol

bellow.

• Convert MPa to Pa or kPa, cm3 to liter or m

3.

2NH2 → N2 + 3H2

Initial mol 2.10 0 0

Reacting mol 2x + x +3x

Final mol 2.10-2x x 3x

.839.2

100

1

1

10

600314.8

160085.8

600)314.8(

160085.8

32

36

113

3

113

3

mol

cm

m

MPa

Pa

KmolKmPa

cmMPa

KmolKmPa

cmMPa

RT

PVnTotal

=

×××

×=

×==

−−

−−

Find x from nTotal = 2.10 -2x+ 4x = 2.10 +2x =2.839 , x =0.3693

3NHn = 2.10-2(0.3693) = 0.714 mol

3

Exercise 1a– Perfect gas or ideal gas

1. Could 55 g of argon (39.95 g mol-1

) gas in a vessel of volume 1.8 dm3 exert a

pressure of 21 bar at 35 °C if it behaved as a perfect gas? If not, what

pressure would it exert? (19.6 bar)

2. A perfect gas undergoes isothermal compression, which reduces its volume by

1.08 L. The final pressure and volume of the gas are 1.79 atm and 2.41 L,

respectively. Calculate the original pressure of the gas in atm. (1.24)

3. A sample of H2 gas was found to have a pressure of 130 kPa when the

temperature was 28°C. What can its pressure be expected to be when the

temperature is 12°C? (123 kPa)

4. The mass composition of dry air at sea level is approximately N2: 75.5 %;

O2:23.2 %; Ar: 1.3 %. What is the partial pressure of N2 when the total

pressure is 780 torr? (608 torr)

5. A sealed flask with a capacity of 200 µL contains 1.5 g of ethane. The flask is

so weak that it will burst if the pressure exceeds 1.2 GPa. At what temperature

will the pressure of the gas exceed the bursting temperature? (577.3 K)

6. The density of a gaseous compound was found to be 12.3 kg dm−3

at 53 oC

and 900 bar. What is the molar mass of the compound? (370.4 g/mol)

7. A glass bulb of volume 0.136 L contains 0.7031 g of gas at 579 torr and

99.5ºC. What is the molar mass of the gas? (207 g/mol)

8. Ten grams of methane is mixed with 10 g of ethane and held at 35 oC at 0.870

atm. What is the mole fraction of ethane and what is the volume of the ideal

mixture? (0.347, 27.8 L)

9. A sample of oxygen was collected by displacement of water occupied a

volume of 50.0 mL at STP. What volume would be oxygen gas occupy if it

was dry and at SATP? The vapor pressure of water at STP is 3.2 kPa.

(52.8 mL)

10. Prove that the equation PV/T = k1 for m constant and V/m = k2 for T and P

constant lead to PV/mT = a constant.

4

Exercise 1b

1. A vessel of volume 2.40 dm3 contains 4.00 mol H2 and 1.00 mol N2 at

273.15 K initially. All the N2 reacted with sufficient H2 to form NH3.

Calculate the total pressure of the final mixture, in bar. (28.39)

2. A compressed cylinder of gas contains 1.50 kg of N2 gas at a pressure of

20 MPa and a temperature of 17 ºC. Calculate the mole of gas has been

released into the atmosphere if the final pressure in the cylinder is 18

MPa? Assume ideal behavior and that the gas temperature is

unchanged.(2.10 )

3. Nitrogen tetraoxide (N2O4) gas is placed in a 600-cm3 glass vessel, and the

reaction; N2O4 = 2NO2

goes to equilibrium at 25 oC. The density of the gas at equilibrium at 756

mmHg is 3.176 g L-1

. Assuming that the gas mixture is ideal, what is the

partial pressure (in atm) of the NO2 at equilibrium? (0.300)

4. Two bulbs A and B were vacuumed and are connected to one another

through a small tube. Two mole of H2 gas was injected through A. If the

volumes of the two bulbs are same and total volume is 11.0 L, and at 25 oC,

calculate the pressure in the bulb A at equilibrium, in kPa.(451)

5. A Dumas experiment to determine molar mass is conducted in which a gas

sample’s P, T, and V are determined. If a 1.89-g sample is held in 0.35 dm3

at 308 K and 120.13 kPa, what would the sample’s volume be at 200.15 K,

at constant pressure, and what is the molar mass of the sample? (0.23 L,

115.10 g/mol)

Problems 1

1. A rigid vessel of volume 0.5 m3 (Vessel X) containing H2 at 200 K and a

pressure of 60 kPa is connected to a second rigid vessel of volume 0.8 m3

(Vessel Y) containing Ar at 300 K at a pressure of 40 kPa. A valve

separating the two vessels is opened and both are cooled to a temperature

of 150 K. What is the final pressure (kPa) in the vessels? (29.62)

2. A sample of propane (C3H8) is placed in a closed vessel together with an

amount of O2 that is 4 times the amount needed to completely oxidize the

propane to CO2 and H2O at constant temperature. Calculate the mole

fraction of O2 in the resulting mixture after oxidation assuming that the

H2O is present as a gas. (0.682)

3. A mole of air (80 % nitrogen and 20 % oxygen by volume) at 27 oC is

brought into contact with liquid water, which has a vapor pressure at 26.7

mmHg at this temperature.

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a) What is the volume of the dry air if the pressure is 1 bar.

b) What is the final volume of the air saturated with water vapor if the total

pressure is maintained at 1 bar?

c) What are the mole fraction of H2O in the moist air? Assume the gases

are ideal. (24.94 L, 25.87 L, 0.0356)

4. A mixture of methane and ethane is contained in a glass bulb of 500 cm3

capacity at 25 o C. The pressure is 1.25 bar and the mass of gas in the bulb is

0.530 g. Calculate: (a) The average molar mass.(b) The mole fraction of

ethane. (21.00 g mol-1

, 0.357)

5. A container is divided into two compartments. The left compartment holds

an ideal gas A at 400 K and 4 atm of pressure. The right compartment is

filled with an ideal gas B at 400 K and 6 atm. The partition between the

compartments is then removed and the gases are allowed to mix. The mole

ratio of A and B in the mixture is found to be 2:5. If the total volume of the

container is 30 L, determine the original volumes of both compartments

and the total pressure of the mixture.(11.3L,18.8 L,5.3 atm)

6. Gas X is contained in one piston cylinder arrangement, while gas Y is

contained in another similar setup cylinder separately.

a) It is experimentally determined that the density of gas X at 0 o

C and

pressure 1 atm is 1.784 g L-1

. Calculate the molar mass for gas X.

b) The temperature and pressure in both cylinders are now changed to

identical new values, and the ratio for the density of X to Y, ρx /ρy is

1.248. Calculate the molar mass of gas Y. (39.98 g mol-1

, 32.04 g mol-1

)

7. A mixture of gases A (M = 28 g mol-1

) and B (M = 32 g mol-1

) is contained

in a glass bulb of 300 mL at temperature 30 o

C. The pressure and mass for

the mixture of these gases are 1.25 atm and 0.442 g respectively. Calculate

the average molar mass of the gas mixture and the mole fraction of gas B.

(29.31 g mol-1

, XB = 0.329, XA = 0.671)

8. A container with a volume of 4 L and temperature 25 oC contains 1.1 mol

N2 gas and 2.7 mol H2 gas. This mixture is exploded using sparks and the

reaction is left for completion. The container is then cooled to the initial

temperature. Assuming that both gases are ideal, calculate mol fractions

and partial pressures for all species in the container before and after the

reaction in atm.( 6.72, 16.51, 1.22, 11.00)

9. The following gases are produced from exploding 5.0 mL of

nitroglycerine, C3H5(NO3)3 at 25 oC and a final pressure of 1 atm:

4C3H5(NO3)3 (l) → 6N2(g) + O2(g) + 12CO2(g) + 10 H2O(l)

Calculate the volume ( in L) occupied by the gas and the partial pressure,

in atm of nitrogen if the density of nitroglycerine is 1.59 g mL-1

. Assume

all gases behave ideally. (4.066, 0.315)