0 | 40

RT

PV

P, atm

1.0

80

Section: IPLCO D AILY PRACTICE PAPER

TOPIC: GASEOUS STATE

1. 1 mole each of O2, SO2, Xe and Kr with Vander Waals constants (atm.L2mol-2) 1.378, 6.803, 4.250

and 2.349 respectively is kept separately in four different vessels of equal volumes at identical temperature. Their pressures are observed to be P1, P2, P3 and P4 respectively. On the basis of

this data alone, which of the following may be expected to be true?

a) P1 < P2< P3 < P4 b) P2 < P1 < P3 < P4 c)P2 < P3 < P4 < P1 d) P3 < P2 < P4 < P1

2. The correct order of normal boiling points of O2, N2, NH3 and CH4, for whom the values of van-

der Waals constant ‘a’ are 1.360, 1.390, 4.170 and 2.253 L2. atm.mol-2 respectively, is

a) O2< N2 < NH3 < CH4 b) O2< N2 < CH4 < NH3

c) NH3 < CH4 < N2 < O2 d) NH3 < CH4 < O2 < N2

3. The Vander Waals equation of state for a non-ideal gas can be rearranged

to give

PVRT

= VV−b

− aVRT for 1 mole of gas. The constants a & b are

positive numbers. When applied to H2 at 80K, the equation gives the curve

as shown in the figure. Which one of the following statements is(are) correct ?

a) at 40 atm the two terms V / (V-b) & a/VRT are equal

b) at 80 atm the two terms V/(V-b) & a/VRT are equal

c) at 80 atm the gas has condensed

d) at a pressure greater than 80 atm, the term V/(V-b) is greater than a/VRT.

4. The molecular radius for a certain gas = 1.25 Å. What is a reasonable estimate of the magnitude of the Vander Waals constant, b, for the gas?

a) 0.98 x 10-2 litre/mole b) 1.43 x 10-2 litre/mole

c) 1.97 x 10-2 litre/mole d) 3.33 x 10-2 litre/mole

5. A mixture of methane and ethene in the mole ratio X:Y has a mean molecular weight 20. What would be the mean molecular weight if the same gases are mixed in the ratio Y : X

a) 22 b) 24 c) 20.8 d) 19

2V

A B

V

Fig. 1

Condition B

Condition A

C, speed

n

6. A mixture of two gases A and B in the mole ratio 2 : 3 is kept in a 2 litre vessel. A second 3 litre vessel has the same two gases in the mole ratio 3 : 5. Both gas mixtures have the same temperature and same pressure. They are allowed to intermix and the final temperature and pressure are the same as the initial values, the final volume being 5 litres. Given that the molar masses are MA and MB, what is the mean molar mass of the final mixture?

a)

77M A+123MB

200 b)

123M A+77MB

200 c)

77M A+123MB

250 d)

123M A+77MB

250

7. A sample of air is saturated with benzene (vapor pressure = 100 mm Hg at 298 K) at 298K, 750mm Hg pressure. If it is suddenly compressed to one third of its initial volume, the final pressure of the system is

a) 2250 torr b) 2150 torr c) 2050 torr d)1950 torr

8. Vander Waal’s constant ‘a’ will be highest for which of the following in gaseous state?

a) CHCl3 b) NH3(g) c) H2O(g) d) C6H14(g)

9. H2 and N2 are contained in two separate isothermal vessels connected by a thin tube as shown in

Fig. 1. When the valve separating the two vessels is opened, which of the following will be true for the final state?

a) Mass of H2 in vessel A = Mass of H2 in vessel B.

b) Mass of N2 in vessel A = Mass of N2 in vessel B.

c) Mass of H2 in vessel A = Mass of H2 in vessel A.

d) Total pressure will be same in vessels A and B.

10. On heating vapours of S8(g) decomposes to S2(g). Due to this, the Vander Waal’s constant ‘b’for

the resulting gas

a) increases b) decreases c) remains same d) changes unpredictably

11. An amount of 1.00 g of a gaseous compound of boron and hydrogen occupies 0.820 liter at 1.00

atm and 30C. The compound is (R = 0.0820 liter atm mole-1 0 K−1 ; at. wt: H = 1.0, B = 10.8)

a) BH3 b) B4H10 c) B2H6 d) B3H12 (E) B5H14

12. The curves in the Fig. represent two different Maxwell - Boltmann velocity distributions for the same gas sample under two different

V=2HtP=530torr N2

V=3litersP=195torr O2

closedbefore

open

P = ?

after

conditions, A and B. Which of the following statements about conditions A and B is true?

a) The temperature for B is greater than for A.

b) The average kinetic energy for A is greater than for B.

c) The intermolecular attractive forces are greater for A than for B.

d) A and B correspond to the same temperature but different volumes.

13. The cylinders in a particular automobile engine have a total volume of 6.15liters (about 380cu in.).

Assume that air fills this volume, at 1.00 atm and 270C, and is one fifth oxygen by volume. What weight of pure octane (C8H18, mol wt. = 114) is necessary to combine exactly with the oxygen

(mol wt. = 32)?

2C8H 18+2502→16CO2+18H 2O (R = 0.082 liter atm mole-1 deg-1)

a) 0.092g b) 0.13g c) 0.46g d) 5.6g e)72 g

14. The stopcock between a 3-liter bulb containing oxygen at 195 torr and a 2-litre bulb containing nitrogen at 530 torr is opened. After equilibration the pressure is which one of the following? (Assume that T is constant).

a) 329 torr b) 362 torr

c) 396 torr d) 725 torr

15. The human body discharges about 960 g of CO2 per day. If the cabin for an astronaut has a

volume of 7600 liters (about 270 cu ft) and the partial pressure of CO2(mol wt. = 44) must be

maintained at not more than 4.1 torr at 270C cabin temperature. What weight of CO2 must be

removed on the first day of the voyage? (Assume that the initial partial pressure of CO2 is zero).

a) 73g b) 145g c) 815g d) 887g

SECTION – B

Objective QuestionsMore than one option is/are correct

28. Which of the following is/are correct?

a) All real gases are less compressible than ideal gas at high pressure

Valve-1 Valve-2

N20.82atm He

0.0 atm

6.0L A

10.0C B

4.0L C

He4.1 atm

b) H2 and He are more compressible than ideal gas for all values of pressure

c) For H2 and He the compressibility factor z=( PVnRT )<1

for all gases at low pressure

d) The compressibility factor of real gases in independent of temperature

29. Which of the following is correct under the same conditions of pressure and temperature?

a) H2 gas diffuses four times faster than oxygen gas

b) H2 gas diffuses 2.83 times faster than CH4 gas

c) He escapes at a rate 2 times as fast methane does

d) He escapes at a rate 4 times as much as sulphurdioxide

30. Which of the following relationship is/are not true

a) Most probable velocity Cmp = √ 2 RTm b)

pV=23KT

c) Compressibility factor z= PVnRT d) Average kinetic energy of a gas =

12 kT

31. The RMS velocity an ideal gas in a closed container of fixed volume is increased from 5 × 104 cm/s to 10 × 104cm/s. Which of the following statement correctly explains how the changes is accomplished

a) By heating the gas, the temperature is decreased

b) By heating the gas, the pressure quadrupled

c) By heating the gas, the temperature is quadrupled

d) By heating the gas, the pressure is doubled

32. Rate of effusion of an ideal gas through a hole depends upon

a) the pressure of the gas b) the molecular weight of the gas

c) surface area of the hole d) shape of the hole

SECTION – C

(COMPREHENSION TYPE)

Comprehension – I

The figure given below shows three glass chambers that are connected by valves of negligible volume. At the outset of an experiment the valves are closed and the chambers contain the gases as detailed in the diagram. All the chambers are at the temperature of 300k and external pressure of 1.0 atm

223k 273k

373k

Ideal gas

Fig. (b)

z

T

N2 CO2 H2

He CH4

Ideal gas

200 1000P

Fig. (a)

z

33. What will be the work done by N2 gas when the valve-2 is opened and valve-1 remaining closed?

a) 8.2 atm b) -8.2 atm c) 0 d) -3.28 atm

34. Which of the following represents the total kinetic energy of all the gas molecules after both valves are opened?

a) 2836.2J b) 3280.0J c) 4520.6J d) 4988.4J

35. Suppose that after both valves are opened the entire apparatus is cooled to lower temperature the final internal pressure to 1.0atm what will be the contribution of N2 gas to this final pressure

a) 0.4 atm b) 0.35 atm c) 0.3 atm d) 0.25 atm

Comprehension – II

Vander Waal’s equation explains the behaviour of real gases under different conditions of temperature and pressure. Gases obey ideal gas equation only at low pressure and high temperature. Thus these real gases deviate from ideal behaviour and the extent of deviation is studied in terms of a quantity called compressibility factor ‘Z’. Gases are said to behave ideally when z = 1, and undergo positive deviation when z > 1 and undergo negative deviation when z <1, where z = PV / nRT.

At the same temperature and pressure the extent of deviation depends upon the nature of the gas. Figure (a) shows the variation of z with pressure of different gases at constant temperature and figure (b) shows the variation of z with pressure of a real gas at different temperatures.

36. A real gas is more compressible than an ideal gas. The compressibility factor (z) is

a) 1 b) > 1 c) < 1 d)

37. Positive deviation from ideal behaviour takes place because of

a) molecular interaction between atoms

PVnRT

>1

b) molecular interaction between atoms

PVnRT

<1

c) finite size of atoms and

PVnRT

>1

d) finite size of atoms

PVnRT

<1

38. For which of the gases z is always greater than 1 at ordinary temperatures

a) CO2 b) CH4 c) N2 d) H2

SECTION – D

(MATCHING TYPE)

39.

Column – I Column - II

i(V−b )( pα aV 2

)=RT A 22.4L

ii RN av

B Kinetic equation for ideal gases

iii Molar volume C Equation for real gas

iv

PV =

13 mnc2

D Boltoman constant

40.

Column – I Column - II

i Vapor pressure of liquid A Vander Waal’s constant b

ii Co volume B PV / nRT

iii Compressibility factor C Universal gas constant

iv Work done (degree-1 mol-1) D Depends of T and nature of liquid

SECTION – E

Subjective Questions

41. The molar volume of helium at 10.1325M Pa and 273 K is 0.011075 of its molar volume at 101.325k Pa at 273K. Calculate radius of helium atom.

42. At 273.15K and under a pressure of 10.132M Pa the compressibility factor of O 2 is 0.927. Calculate the mass of O2 necessary to fill a gas cylinder of 100 cm3

capacity under the given conditions.

43. A certain amount of gas present in container of unknown volume shows a pressure of 750mm. A small amount of gas is taken out and measured a volume of 2dm’ when expanded to 600mm.

The pressure of the gas remaining in the container was 700mm. Calculate volume of container if all the measurement were done at same temperature.

44. Vander Waal’s constant ‘b’ for N2 and H2 has the values 0.039L/mol and 0.0266 L/mol. The density of solid N2 in 1g/cc. Assuming the molecules in solid to be close packed with same % age void calculate the density of solid H2 (g/cc).

45. A gas at 250k and 15 atm has a molar volume 12% smaller than calculated from perfect gas equation. Calculate ‘Z’ and volume of gas. Which are dominating attractive or repulsive forces?

46. A mixture of Cs2 and H2S when oxidized yields a mixture of CO2, SO2, H2O, (steam) which exerts a pressure of 748.8mm in a 60L vessel at 327C. To oxidize SO2 in the mixture 700mL of 2N I2 were required. Calculate mole fraction of Cs2 is mixture.

47. Explain variation of Vander Waal’s constant in the following compounds

n-pentane iso-pentane

a. 19.01 18.05

b. 0.146 0.1417

48. Two flasks of equal volumes connected by a narrow tube of negligible volume at 300K contain each 22.4 gm of oxygen gas at 0.5 atm pressure. One of the flasks is immersed in a bath kept at 400K, while the other remains at 300K. Find the final pressure and number of moles of O2 in each flask.

49. n moles of oxygen when enclosed in a 2 liter bulb exert a pressure of 2.0 atm at T0C. On introducing 0.1 mole nitrogen into same bulb, it became necessary to cool it to 0 0C to maintain the same pressure. Find the values of n and T.

50. 2 moles each of hydrogen and oxygen were filled in a balloon and a small hole is pierced. After one hour, 0.4 mole of oxygen diffuse out. What will be the mole fraction of hydrogen in the balloon? Temperature remains constant.

GASEOUS STATE1) C 2) B 3) D 4) C 5) B6) A 7) C 8) C 9) D 10) B11) C 12) B 13) C 14) A 15) C16) D 17) A 18) C 19) D 20) B

21) B 22) B 23) C 24) D 25) C26) C 27) C 28) A,C 29) A,B,C,D 30) A,C31) B,C 32) A,B,C 33) C 34) D 35) D36) C 37) A 38) D 39) I-C,II-D,III-A,IV-B 40) I-D,II-A,III-B,IV-C41) 267pm 42) V = 9774 dm3 43) 3.9530 : 1.677:1 44) 24dm3 45) 0.10546) 0.8 47) 0.4 48) 1 49) 0.5714 atm, 0.6 mole at 400, 0.8 mole at 300

50) 1033 51) --- 52) 60.19 ml 53)