Gaseous State Vedantu notes

4. Single correct Questions

5. Q-1: What is the ratio of molecules having speeds in the range of 2ump and 2ump
+du to the number of molecules having speeds in the range of ump and ump +du ?
A
B
C
D
2 e-3
2 e-4
4 e-3
4 e-4

6. Q- What is the ratio of molecules having speeds in the range of 2ump and 2ump +du
to the number of molecules having speeds in the range of ump and ump +du ?
A
B
C
D
2 e-3
2 e-4
4 e-3
4 e-4

7. Solution:

8. Q-2: A modified form of Vander waal’s equation of state for 1.0 mole of gas is
given as:
Where α and β are constant
Select correct statements:
(I) The second virial coefficient ‘B’ is
(II) The Boyle’s temperature TB is
(III) The second virial coefficient ‘B’ is
(IV) The Boyle’s temperature TB is
A B
C D
I ,II I , II , IV
I , IV I , II , IV

12. Q- A modified form of Vander waal’s equation of state for 1.0 mole of gas is given
as:
Where α and β are constant
Select correct statements:
(I) The second virial coefficient ‘B’ is
(II) The Boyle’s temperature TB is
(III) The second virial coefficient ‘B’ is
(IV) The Boyle’s temperature TB is
A B
C D
I ,II I , II , IV
I , IV I , II , IV

13. Q-3:
Infinite number of flasks are connected to one another as shown above. The
volume and pressure in each flask vary as shown. The stopcocks are initially
closed. The common pressure, when all the stopcocks are opened, is : (Assume
constant temperature)
A
B
C
D
P
till infinity

14. Q-
Infinite number of flasks are connected to one another as shown above. The
volume and pressure in each flask vary as shown. The stopcocks are initially
closed. The common pressure, when all the stopcocks are opened, is : (Assume
constant temperature)
A
B
C
D
P
till infinity

15. Solution:

16. Q-4: To an evacuated vessel with movable piston under external pressure of 1
atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68
atm at 0oC) are introduced. Considering the ideal gas behaviour, the total volume
(in litre) of the gases at 0oC is close to
A
B
C
D
5
6
8
7

17. Q- To an evacuated vessel with movable piston under external pressure of 1 atm.,
0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm at
0oC) are introduced. Considering the ideal gas behaviour, the total volume (in
litre) of the gases at 0oC is close to
A
B
C
D
5
6
8
7

19. Q-5: If Pd v/s. P(where P denotes pressure in atm and d denotes density in gm/L) is
plotted for He gas (assume ideal) at a particular temperature. If ,
then the temperature will be
A
B
C
D
160 K
320 K
80 K
None of these

20. Q- If Pd v/s. P(where P denotes pressure in atm and d denotes density in gm/L) is
plotted for He gas (assume ideal) at a particular temperature. If ,
then the temperature will be
A
B
C
D
160 K
320 K
80 K
None of these

21. Solution:

22. Q-6: One mole of a monoatomic real gas satisfies the equation p(V - b) = RT where
b is a constant. The relationship interatomic potential V(r) and interatomic
distance r for the gas is given by
A B
C D

23. Q- One mole of a monoatomic real gas satisfies the equation p(V - b) = RT where b
is a constant. The relationship interatomic potential V(r) and interatomic distance
r for the gas is given by
A B
C D

24. Solution:
At large interionic distances (because a → 0) the P.E. would remain
constant. However, when r → 0; repulsion would suddenly increase.

25. Q-7: A closed tank has two compartments A and B, both filled with oxygen
(assumed to be ideal gas). The partition separating the two compartments is
fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a
new partition which can slide and conduct heat but does NOT allow the gas to
leak across (Figure 2), the volume (in m3) of the compartment A after the
system attains equilibrium is
A
B
C
D
2.22
3.22
4.23
1.23

26. Q- A closed tank has two compartments A and B, both filled with oxygen
(assumed to be ideal gas). The partition separating the two compartments is
fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a
new partition which can slide and conduct heat but does NOT allow the gas to
leak across (Figure 2), the volume (in m3) of the compartment A after the
system attains equilibrium is
A
B
C
D
2.22
3.22
4.23
1.23

27. Solution:

28. Solution:

29. Q-8: 11 moles N2 and 12 moles of H2 mixture reacted in 20 litre vessel at 800 K. After
equilibrium was reached, 6 mole of H2 was present. 3.58 litre of liquid water is
injected in equilibrium mixture and resultant gaseous mixture suddenly cooled to
300K .What is the final pressure of gaseous mixture? Neglect vapour pressure of
liquid solution. Assume (i) all NH3 dissolved in water (ii) no change in volume of
liquid (iii) no reaction of N2 and H2 at 300 K
A
B
C
D
18.47 atm
60 atm
22.5 atm
45 atm

30. Q- 11 moles N2 and 12 moles of H2 mixture reacted in 20 litre vessel at 800 K. After
equilibrium was reached, 6 mole of H2 was present. 3.58 litre of liquid water is
injected in equilibrium mixture and resultant gaseous mixture suddenly cooled to
300K .What is the final pressure of gaseous mixture? Neglect vapour pressure of
liquid solution. Assume (i) all NH3 dissolved in water (ii) no change in volume of
liquid (iii) no reaction of N2 and H2 at 300 K
A
B
C
D
18.47 atm
60 atm
22.5 atm
45 atm

31. Solution:

32. Q-9: Two closed vessel A and B of equal volume containing air at pressure P1 and
temperature T1 are connected to each other through a narrow open tube. If the
temperature of one is now maintained at T1 and other at T2 (where T1 >T2) then what
will be the final pressure?
A
B
C
D

33. Q- Two closed vessel A and B of equal volume containing air at pressure P1 and
temperature T1 are connected to each other through a narrow open tube. If the
temperature of one is now maintained at T1 and other at T2 (where T1 >T2) then what
what will be the final pressure?
A
B
C
D

34. Solution:

35. Q-10: If 250 mL of N2 over water at 30°C and a total pressure of 740 torr is mixed
with 300 mL of Ne over water at 25°C and a total pressure of 780 torr, what will be
the total pressure if the mixture is in a 500 mL vessel over water at 35°C.
(Given : Vapour pressure (Aqueous tension) of H2O at 25°C, 30°C and 35°C are 23.8,
31.8 and 42.2 torr respectively. Assume volume of H2O(l) is negligible in final
vessel)
A
B
C
D
760 torr
828.4 torr
807.6 torr
870.6 torr

36. Q- If 250 mL of N2 over water at 30°C and a total pressure of 740 torr is mixed with
300 mL of Ne over water at 25°C and a total pressure of 780 torr, what will be the
total pressure if the mixture is in a 500 mL vessel over water at 35°C.
(Given : Vapour pressure (Aqueous tension) of H2O at 25°C, 30°C and 35°C are 23.8,
31.8 and 42.2 torr respectively. Assume volume of H2O(l) is negligible in final
vessel)
A
B
C
D
760 torr
828.4 torr
807.6 torr
870.6 torr

37. Solution:

38. Q-11: If the slope of 'Z' (compressibility factor) v/s 'P' curve is constant
particular temperature (300 K) and very high pressure, then calculate diameter of
the molecules.
(Given : NA = 6.0 x 1023, R = 0.0821 atm. lit mol-1 K-1)
A
B
C
D
7.5 Å
5 Å
2.5 Å
1.25 Å

39. Q- If the slope of 'Z' (compressibility factor) v/s 'P' curve is constant
particular temperature (300 K) and very high pressure, then calculate diameter of
the molecules.
(Given : NA = 6.0 x 1023, R = 0.0821 atm. lit mol-1 K-1)
A
B
C
D
7.5 Å
5 Å
2.5 Å
1.25 Å

40. Solution:

41. Multiple correct Questions

42. Q-12: Following represents the Maxwell distribution curve for an ideal gas at two
temperature T1 and T2. Which of the following option(s) are true?
A
B
C
D
Total area under the two curves is independent of moles of gas
Umps decreases as temperature decreases
T1 > T2 and hence higher the temperature, sharper the curve
The fraction of molecules having speed = Umps decreases as
temperature increases

43. Q- Following represents the Maxwell distribution curve for an ideal gas at two
temperature T1 and T2. Which of the following option(s) are true?
A
B
C
D
Total area under the two curves is independent of moles of gas
Umps decreases as temperature decreases
T1 > T2 and hence higher the temperature, sharper the curve
The fraction of molecules having speed = Umps decreases as
temperature increases

44. Solution:
(A) ∵ area under the curve gives fraction of molecules and total area is constant.
(B) umps , decreases with decrease in temperature.
(C) T2 is higher temperature
(D) As seen from graph; ∴ A, B, D

45. Q-13: Choose the correct options
A
B
C
D
At low pressure (nearly 1 atm), compressibility factor for H2 gas is
greater than 1 at 273 K.
Compressibility factor for a vander Waal’s gas at its critical
condition is less than 1
Boyle’s temperature of a gas is lesser than its critical temperature.
Vander Waal’s constant ‘a’ for NH3 is greater than that of CH4.

46. Q- Choose the correct options
A
B
C
D
At low pressure (nearly 1 atm), compressibility factor for H2 gas is
greater than 1 at 273 K.
Compressibility factor for a vander Waal’s gas at its critical
condition is less than 1
Boyle’s temperature of a gas is lesser than its critical temperature.
Vander Waal’s constant ‘a’ for NH3 is greater than that of CH4.

47. Solution:

48. Q-14: Following graph is constructed for the fixed amount of the gas.
A
B
C
D
From 1 - 2 pressure will increase
From 2 - 3 pressure remains constant
Gas pressure at (3) is greater at state (2)
Grom 1 - 2 pressure will decrease

49. Q- Following graph is constructed for the fixed amount of the gas.
A
B
C
D
From 1 - 2 pressure will increase
From 2 - 3 pressure remains constant
Gas pressure at (3) is greater at state (2)
from 1 - 2 pressure will decrease

50. Solution:

51. Q-15: For two gases A and B , P vs V isotherms are drawn at T K as shown TA and TB.
are critical temperature A and B respectively.
Which of the following is/are True ?
A
B
C
D
TA <T <TB
TA>TB>T
Pressure correction term will be more negligible for gas B at TK
The curve for gas B will be similar shape as for gas A if T>TB

52. Q-15: For two gases A and B , P vs V isotherms are drawn at T K as shown TA and TB.
are critical temperature A and B respectively.
Which of the following is/are True ?
A
B
C
D
TA <T <TB
TA>TB>T
Pressure correction term will be more negligible for gas B at TK
The curve for gas B will be similar shape as for gas A if T>TB

53. Q-16: Which of the following statements are correct ?
A
B
C
D
It is not possible to compress a gas at a temperature below TC
At a temperature below TC, the molecules are close enough for the
attractive forces to act and condensation occurs
No condensation takes place above TC
Boyle's temperature always greater than TC.

54. Q- Which of the following statements are correct ?
A
B
C
D
It is not possible to compress a gas at a temperature below TC
At a temperature below TC, the molecules are close enough for the
attractive forces to act and condensation occurs
No condensation takes place above TC
Boyle's temperature always greater than TC.

55. Q-17: Which of the following is correct for critical temperature ?
A
B
C
D
It is the highest temperature at which liquid and vapour can
coexist
At a certain point on isotherm graph, slope is zero.
At this temperature, the gas and the liquid phases have different
critical densities
All are correct

56. Q- Which of the following is correct for critical temperature ?
A
B
C
D
It is the highest temperature at which liquid and vapour can
coexist
At a certain point on isotherm graph, slope is zero.
At this temperature, the gas and the liquid phases have different
critical densities
All are correct

57. Q-18: Select incorrect statements for real gas.
A
B
C
D
In low pressure region repulsive forces dominates
Volume of gas particles is not negligible in low pressure region
Gas behaves idealy at low pressure & low temperature
In high pressure region attractive forces dominates

58. Q- Select incorrect statements for real gas.
A
B
C
D
In low pressure region repulsive forces dominates
Volume of gas particles is not negligible in low pressure region
Gas behaves idealy at low pressure & low temperature
In high pressure region attractive forces dominates

59. Q-19: Compressibility of real gas will be less than ideal gas when
(T = temp. of gas Tb = Boyle's temperature of gas)
A
B
C
D
At very high pressure when T > Tb
At very high pressure when T < Tb
At low pressure when T > Tb
At low pressure when T < Tb

60. Q- Compressibility of real gas will be less than ideal gas when
(T = temp. of gas Tb = Boyle's temperature of gas)
A
B
C
D
At very high pressure when T > Tb
At very high pressure when T < Tb
At low pressure when T > Tb
At low pressure when T < Tb

61. Integer Type Questions

62. Q-20: Consider the following graph of drawn at low pressure and
inversion temperature, using the virial form of vander waal’s equation :
Find critical molar volume (Vc) in cm3?

63. Solution:
6

64. Q-21: A bulb of constant volume is attached to a manometer tube open at other
end as shown in figure. The manometer is filled with a liquid of density (1/3)rd
that of mercury. Initially h was 228 cm. Through a small hole in the bulb gas
leaked causing pressure decrease as . If value of h is 114 cm after 7
minutes.
Calculate value of k in units of hour-1. (Report answer in multiple of 10-1)
[Use : In (4/3) = 0.28 & density of Hg = 13.6 g/ml] . The small hole 7 minutes.

65. Solution:
24

66. Q-22: According to Maxwell's distribution of molecular speeds, the following
graph has been drawn for two different samples of gases A and B at
temperature T1 and T2 respectively. Then, give the correct set of INCORRECT
statements : Report your answer as sum of the numbers of incorrect
statements. For example, if statements (1) & (2) are incorrect, then report
answer as (1 + 2) = 3.
(1) If T1 = T2, then gas B can be SO2 and gas A can be CO2.
(2) If gases A and B are CO2 & N2O, then T1 > T2.
(3) If T1 < T2, then gases A and B cannot be CO2 and SO2 respectively
(4) None of these

67. Solution:
6

68. Q-23: Consider the following figure at 500 K. Assuming ideal gas behaviour,
calculate the total pressure if the barriers are removed from the compartment.
Assume that the volume of barriers is negligible .
Gas A
1 L
1 atm
Gas B
1.5 L
2 atm
Gas C
2.5 L
4 atm
Gas D
2 L
3 atm

69. Solution:
2.85 atm

70. Q-24:
If above tube is placed vertically with the open end upward then find the length of
the air column.

71. Solution:

72. Q-25: Two moles of an ideal gas undergoes the following process. Given that
is , then calculate the value of (x + y)

73. Solution:
P
T
P ∝ T (400K, 4)
(300K, 3)

74. Q-26: The graph of compressibility factor (Z) vs. P for one mole of a real gas is
shown in following diagram. The graph is plotted at constant temperature 273 K. If
the slope of graph at very high pressure , then calculate
volume of one mole of real gas molecules (in L /mol)

75. Solution:

76. Q-27: A flask has 10 gas particles out of which four particles are moving at 7 ms-1
and the remaining are moving at the same speed of ' X' ms-1 . If the r.m.s. of the gas
is 5 ms-1, what is the value of X?

77. Solution:

78. Q-28: If an ideal gas at 100 K is heated to 109 K in a rigid container, the pressure
increases by X%. What is the value of X?

79. Solution:

80. Matrix Match Questions

81. Q-29: Match gases under specified conditions listed in Column-I with their
properties / laws in Column-II.
A
B
C D
A – p, s ; B – r ; C – p, q ; D – r A – r, s ; B – r ; C – p, q ; D – p
A – s ; B – r ; C – p, q ; D – r A – p ; B – r ; C – q ; D – r

82. Match gases under specified conditions listed in Column-I with their properties /
laws in Column-II.
A
B
C D
A – p, s ; B – r ; C – p, q ; D – r A – r, s ; B – r ; C – p, q ; D – p
A – s ; B – r ; C – p, q ; D – r A – p ; B – r ; C – q ; D – r

83. Solution:
(A) For H2 gas at high pressure Z > 1.
(B) For any gas at P ~ 0, Z ~ 1 i.e. ideal behaviour.
(C) For CO2 gas at normal pressure and temperature Z < 1.
(D) For any gas at very large molar volume i.e. P ~ 0, Z ~ 1 i.e. ideal behaviour of gas.

84. Paragraph Type Questions

85. Paragraph Type Question
When a sample of ideal gas is changed from an initial state to a final state, various
curves can be plotted for the process like P - V curve, V - T curve P - T curve etc.
For example, P - V curve for a fixed amount of an ideal gas at constant temperature is
rectangular hyperbola, V - T curve for a fixed amount of an ideal gas at constant
pressure is a straight line and P - T curve for a fixed amount of an ideal gas at
constant volume is again a straight line. However, the shapes may vary if the
constant parameters are also changed.
Now, answer the following questions:

86. Q-30: Which of the following statements is correct regarding a fixed amount of
ideal gas undergoing the following
A
B
C
D
Root mean square (RMS) speed of gas molecules
increases during the process A → B
Density of the gas increases during the process A → B
Such a graph is not possible
If Pa = 4PA, then VA = 4VB (where PA, VA, PB, & VB represent
pressure and volume values at states A and B.

87. Q- Which of the following statements is correct regarding a fixed amount of ideal
gas undergoing the following
A
B
C
D
Root mean square (RMS) speed of gas molecules
increases during the process A → B
Density of the gas increases during the process A → B
Such a graph is not possible
If Pa = 4PA, then VA = 4VB (where PA, VA, PB, & VB represent
pressure and volume values at states A and B.

88. Solution:

89. Q-31: Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final
state (4 atm, 15L) in such a way that this change can be represented by a straight
line in P - V curve. The maximum temperature attained by the gas during the
above change is :
A
B
C
D
324 K
648 K
1296 K
972 K

90. Q- Two moles of an ideal gas is changed from its initial state (16 atm, 6L) to final
state (4 atm, 15L) in such a way that this change can be represented by a straight
line in P - V curve. The maximum temperature attained by the gas during the
above change is :
A
B
C
D
324 K
648 K
1296 K
972 K

91. Solution:

92. A B
C D None of these
Q-32: Which of the following graphs is not possible for a fixed amount of ideal gas
upon moving form initial state A to final state B:

93. A B
C D None of these
Q- Which of the following graphs is not possible for a fixed amount of ideal gas upon
moving form initial state A to final state B:

94. Solution:
(A) This graph is possible if temperature of gas is kept constant and pressure is
increased from A to B.
(B) This graph is possible if temperature of gas is increased continuously during the
process A to B
(C) This graph is possible if during the process :

95. Q-33: The figure shows the effect of pressure on the compressibility factor, Z of a
gas:
The wrong conclusion (s) is/are
A
B
C
D
The curve AE can be explained by PV = RT
The curve AF and CD can be
explained by PV = RT + Pb
The curve AB can be explained by
All the three curves AF, AE and AD shows the real
behaviour

96. Q- The figure shows the effect of pressure on the compressibility factor, Z of a gas:
The wrong conclusion (s) is/are
A
B
C
D
The curve AE can be explained by PV = RT
The curve AF and CD can be
explained by PV = RT + Pb
The curve AB can be explained by
All the three curves AF, AE and AD shows the real
behaviour

97. Solution:

98. Q-34: From the given plot between Z and P for a real gas the correct is:
A
B
C
D

99. Q- From the given plot between Z and P for a real gas the correct is:
A
B
C
D

100. Solution:
Graph corresponding to T2 shows ideal behaviour for a range of pressure.
Hence,

101. You can contact me
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