44 GASEOUS STATE

LEVEL – IV

[ IIT-JEE FLASH BACK ]

1981
Q.1 Equal weights of methane and oxygen are mixed in an empty container at 25ºC. The fraction of
the total pressure exerted by oxygen is
1 1 2 1 273
(A) (B) (C) (D) 
3 2 3 3 298
Q.2 The temperature at which a real gas obeys the ideal gas laws over a wide range of pressure is
(A) critical temperature (B) Boyle temperature
(C) inversion temperature (D) reduced temperature
Q.3 The ratio of root mean square velocity to average velocity of a gas molecule at a particularly
temperature is
(A) 1.086 : 1 (B) 1 : 1.086 (C) 2 : 1.086 (D) 1.086 : 2
Q.4 The pressure in a bulb dropped from 2000 to 1500 mm of mercury in 47 minutes when the
contained oxygen leaked through a small hole. The bulb was then evacuated. A mixture of
oxygen and another gas of molecular weight 79 in the molar ratio of 1 : 1 at a total pressure of
4000 mm of mercury was introduced. Find the molar ratio of the two gases remaining in the
bulb after a period of 74 minutes.

1982
Q.5 Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetics
energy of a helium atom is
(A) two times that of a hydrogen molecule (B) same as that of a hydrogen molecule
(C) four times that of a hydrogen molecule (D) half that of a hydrogen molecule
Q.6 At room temperature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm
pressure are allowed to effuse through identical pin holes from opposite ends of a glass tuebe
of one metre length and of uniform cross-section. Ammonium chloride is first formed at a distance
of 60 cm from the end through which HCl gas is sent in. What is the value of P.
Q.7 Calculate the average of kinetic energy, in joules of the molecules in 8.0 g of methane at 27ºC.

1983
Q.8 Oxygen is present in 1 litre flask at a pressure 7.6 × 10–10 mm of Hg. Calculate the number of
oxygen molecules in the flask at 0ºC.
Q.9 When 2 gm of a gas A is introduced into an evaluated flask kept at 25ºC, the pressure is found
to be one atmosphere. If 3 gm of another gas B is then added to the same flask, the total
pressure becomes 1.5 atm. Assuming ideal gas behaviour, calculate the ratio of the molecular
weights MA : MB.

1984
Q.10 The total energy of one mole of an ideal monatomic gas at 27ºC is ________ calories.
Q.11 Cp - Cv for an ideal gas is ________ .
GASEOUS STATE 45

Q.12 Equal weights of methane and by hydrogen are mixed in an empty container at 25ºC. The
fraction of the total pressure exerted by hydrogen is
1 8 1 16
(A) (B) (C) (D)
2 9 9 17
Q.13 When an ideal gas undergoes unrestrained expansion, no cooling occurs because the molecules
(A) are above the inversion temperature (B) exert no attractive forces on each other
(C) do work equal to loss in kinetic energy (D) collide without loss of energy
Q.14 'Equal volumes of gases contain equal number of atoms', is true at what conditions.

1985
Q.15 Rate of diffusion of a gas is :
(A) directly proportional to its density
(B) directly proportional to its molecular weight
(C) directly proportional to the square root of its molecular weight
(D) inversely proportional to the square root of its molecular weight
Q.16 Kinetic energy of a molecule is zero at 0 ºC . [ True/False ]
Q.17 A gas in a closed container will exert much high pressure due to gravity at the bottom than at
the top. [ True/False ]
Q.18 Calculate the root mean square velocity of ozone kept in a closed vessel at 20ºC and 82 cm
mercury pressure.

1986
Q.19 The average velocity of an ideal gas molecule at 27ºC is 0.3 m/sec. The average velocity at
927ºC will be
(A) 0.6 m/sec (B) 0.3 m/sec (C) 0.9 m/sec (D) 3.0 m/sec
Q.20 The rate of diffusion of gas is ________ proportional to both ________ and square root of
molecular mass.
Q.21 If a gas is expanded at constant temperature :
(A) the pressure decreases
(B) the kinetic energy of the molecules remain the same
(C) the kinetic energy of the molecules decreases
(D) the number of molecules of the gas increases

1987
Q.22 The value of PV for 5.6 litre of an ideal gas is _________ RT at N T P.
Q.23 A spherical balloon of 21 cm diameter is to be filled up with hydrogen at NTP, from a cylinder
containing the gas at 20 atm at 270C. If the cylinder can hold 2.82 litre of water, calculate the
number of balloons that can be filled up.

1988
Q.24 In Vander Waals equation of state for a non ideal gas, term that accounts for intermolecular
forces is:
 a 
(A) (v - b) (B) RT (C)  P  2  (D) (RT)-1
 v 
 46 GASEOUS STATE

Q.25 A bottle of dry NH3 and a bottle of dry HCl connected through a long tube are opened
simultaneously at both ends, the white ammonium chloride ring first formed will be :
(A) at the centre of the tube (B) near the HCl bottle
(C) near the NH3 bottle (D) throughout the length of tube

1989
Q.26 n-butane is produced by the monobromination of ethane followed by the Wurtz reaction.
Calculate the volume of ethane at NTP required to produce 55 g n - butane, if the bromination
takes place with 90% yield and the Wurtz reaction with 85% yield.
Q.27 The values of Vander Waals constant ‘a’ for the gases O2, N2, NH3, & CH4 are 1.36, 1.39,
4.17, 2.253 2 atm mole-2 respectively. The gas which can most easily be liquified is :
(A) O2 (B) N2 (C) NH3 (D) CH4
Q.28 Eight gm each of oxygen and hydrogen at 270C will have the total kinetic energy in the ratio of
_______.

1990
Q.29 The density of neon will be highest at :
(A) S T P (B) 00 C, 2 atm (C) 2730 C, 1 atm (D) 2730 C, 2 atm
Q.30 The rate of diffusion of methane at a given temperature is twice that of gas X. The molecular
weight of X is :
(A) 64.0 (B) 32.0 (C) 4.0 (D) 8.0
Q.31 The average velocity at T1 K and the most probable velocity of T2 K of CO2 gas is 9.0 × 104 cm/s.
Calculate the value of T1 and T2.

1991
Q.32 According to kinetic theory of gases :
(A) the pressure exerted by the gas is proportional to the mean velocity of the molecule
(B) the pressure exerted by the gas is proportional to the r.m.s. velocity of the molecule
(C) the r.m.s. velocity of the molecule is inveresly proportional to the temperature
(D) the mean translational kinetic energy of the molecule is proportional to the absolute
temperature.
Q.33 Calculate the volume occupied by 5.0 g of acetylene gas at 500C and 740 mm pressure.

1992
Q.34 At constant volume, for a fixed number of moles of a gas the pressure of the gas increase with
rise in temperature due to:
(A) increase in average molecular speed
(B) increased rate of collisions amongst molecules
(C) increase in molecular attraction
(D) decrease in mean free path
Q.35 At 270C, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another
unknown gas at the same temperature and pressure as that of H2 is leaked through the same
hole for 20 minutes . After the effusion of the gases the mixture exerts a pressure of 6 atm. The
hydrogen content of the mixture is 0.7 mole . If the volume of the container is 3 litre , what is
molecular weight of unknown gas.
GASEOUS STATE 47

Q.36 A 2.0 g sample of a mixture containing sodium carbonate, sodium bicarbonate and sodium
sulphate is gently heated till the evolution of CO2 ceases. The volume of CO2 at 750 mm Hg
M HCl for
pressure and at 298 k is 123.9 ml. A 1.5 g of the same sample requires 150 ml of 10
complete neutralisation. Calculate the percentage composition of the mixture.
Q.37 At room temperature the following reactions proceed nearly to completion.
2 NO + O2  2 NO2  N2O4 .
The dimer N2O4, solidifies at 262 K. A 250 ml flask and a 100 ml flask are separated by a
stopcock . At 300 K, the NO in the larger flask exerts a pressure of 1.053 atm and smaller one
contains oxygen at 0.789 atm. The gases are mixed by opening the stopcock and after the end
of the reaction the flasks are cooled to 220 K. Neglecting the vapour pressure of the dimer,
find out the pressure and composition of the gas remaining at 220 K
[ Assuming the gases to behave ideally ]

1993
 n2 a 
Q.38 In the Vander Waals equation  P  2  (V  nb) = nRT, the constant ‘a’ reflects the actual
 V 
volume of the gas molecules. [ True/False ]
Q.39 Equal weights of ethane and hydrogen are mixed in an empty container at 250C. The fraction of
the total pressure exerted by hydrogen is :
(A) 1 : 2 (B) 1 : 1 (C) 1 : 16 (D) 15 : 16
Q.40 A gas bulb of 1 litre capacity contains 2.0 × 1021 molecules of nitrogen exerting a pressure of 7.57 ×
103 N m-2. Calculate the r.m.s speed and the temperature of the gas molecules. If the ratio of
the most probable speed to the r.m.s. speed is 0.82. Calculate the most probable speed for
these molecules at this temperature.

1994
Q.41 A 4 : 1 molar mixture of He & CH4 is contained in a vessel at 20 bar pressure . Due to a hole
in the vessel the gas mixture leaks out. What is the composition of the mixture effusing out
initially.
Q.42 An LPG cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg and shows a
pressure of 2.5 atm. In the course of use at 270C, the weight of the full cylinder reduced to
23.2 kg. Find out the volume of the gas in cubic meters used up at the normal usage conditions
and the final pressure inside the cylinder. Assume LPG to be n-butane with normal boiling
point of 0oC.
Q.43 A balloon of diameter 20 m weighs 100 kg. Calculate payload if it is filled with He at 1 atm and
270C. Density of air = 1.2 kg/m 3 .

1995
Q.44 Longest mean free path stands for :
(A) H2 (B) N2 (C) O2 (D) Cl2
Q.45 A mixture of ethane and ethene occupies 40 litre at 1 atm and 400 K. The mixture reacts
completely with 130 g of O2 to produce CO2 & H2O. Assuming ideal gas behaviour. Calculate
the mole fractions of ethane and ethene in the mixture.
 48 GASEOUS STATE

Q.46 Arrange the vander Waals constant for the gases :

(i) C6H6(g) a. 0.217
(ii) C6H5.CH3(g) b. 5.464
(iii) Ne(g) c. 18.000
(iv) H 2O d. 24.060
(A) i-a, ii-d, iii-c, iv-b (B) i-d, ii-a, iii-b, iv-c
(C) i-c, ii-d, iii-a , iv-b (D) i-b, ii-c, iii-a, iv-d
Q.47 The composition of the equilibrium mixture (Cl2  2 Cl) which is attained at 12000C is
determined by measuring the rate of effusion through a pin hole . It is observed that at 1.8 mm
Hg pressure , the mixture effuses 1.16 times as fast as Kr effuses under the same conditions.
Calculate the fraction of chlorine molecules dissociated into atoms.
Q.48 An cylinder contains helium at a pressure of 250 kPa & 300 K. The cylinder can withstand a
pressure of 1 × 106 pa. The room in which cylinder is placed catches fire. Predict weather the
cylinder will blow up before it melts or not. [ melting point of cylinder = 1800 k ]
Q.49 A 20.0 cm3 mixture of CO, CH4 and He gases is exploded by an electric discharge at room
temperature with excess of oxygen. The volume contraction is found to be 13.0 cm 3. A further
contraction of 14.0 cm3 occurs when the residual gas is treated with KOH solution. Find out
the composition of the gaseous mixture in terms of volume percentage.

1996
Q.50 A mixture of ideal gases is cooled up to liquid He temperature (4.22 K) to form an ideal
solution. Is this statement is True or False. Justify your answer in not more than two lines.
Q.51 The ratio between the r.m.s. velocity of H2 at 50 K and that of O2 at 800 K is :
(A) 4 (B) 2 (C) 1 (D) 1/4’
Q.52 X ml of H2 gas effuses through a hole in a container in 5 sec. The time taken for the effusion of
the same volume of the gas specified below under identicial conditions is :
(A) 10 sec. , He (B) 20 sec. , O2 (C) 25 sec. , CO (D) 55 sec. , CO2
Q.53 One mole of N2O4 (g) at 300 K is kept in a closed container under one atm. It is heated to 600
K when 20 % by mass of N2O4 (g) decomposes to NO2 (g) The resultant pressure is :
(A) 1.2 atm (B) 2.4 atm (C) 2.0 atm (D) 1.0 atm

1997
Q.54 The compressibility factor for an ideal gas is
(A) 1.5 (B) 1.0 (C) 2.0 (D) 
Q.55 The absolute temperature of an ideal gas is _________ to/than the average kinetic energy of
the gas molecules.
Q.56 One way of writing the equation for state for real gases is ,
 B 
P V = RT 1   ......... where B is a constant.
 V 
Derive an approximate expression for ‘B’ in terms of Vander Waals constant ‘a’ & ‘b’.
Q.57 Calculate the total pressure in a 10 litre cylinder which contains 0.4 g He, 1.6 g oxygen and
1.4g of nitrogen at 27oC. Also calculate the partial pressure of He gas in the cylinder. Assume
ideal behaviours for gases.
GASEOUS STATE 49

1998
Q.58 Read the following statement and explanation and answer as per the options given below :
(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)
(2) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(3) (A) is correct but (R) is incorrect
(4) (A) is incorrect but (R) is correct
Assertion : The value of vander Waal's constant 'a' is larger for ammonia than for nitrogen.
Reason : Hydrogen bonding is present in ammonia.
(A) 1 (B) 2 (C) 3 (D) 4

rA
Q.59 According to Graham’s law, at a given temperature the ratio of the rates of diffusion of
rB
gases A and B is given by :
12 12 12 12
P  MA  M   PA  P  MB  MA  PB 
(A) A   (B)  A    (C) A   (D)  
PB  MB   MB   PB  PB  MA  MB  PA 
Q.60 An evacuated glass vessel weighs 50.0 g when empty. 148.0 gm when filled with a liquid of
density 0.98 g/ml and 50.5 g when filled with an ideal gas at 760 mm Hg at 300 k. Determine
the molecular weight of the gas.
Q.61 Using Vander Waals equation, calculate the constant “a” when 2 moles of a gas confined in a
4 litre flask exerts a pressure of 11.0 atm at a temperature of 300 K. The value of “b” is
0.05 litre mol-1.
Q.62 The degree of dissociation is 0.4 at 400 K and 1.0 atm for the gaseous reaction ,
PCl5 PCl3 +Cl2.Assuming ideal behaviour of all gases , calculate the density of equilibrium
mixture at 400 K and 1.0 atmosphere.
Q.63 For the reaction, N2O5(g) 2NO2 (g) + 0.5O2 (g), calculate the mole fraction of N2O5(g)
decomposed at a constant volume and temperature, if the initial pressure is 600 mm Hg and the
pressure at any time is 960 mm Hg. Assume ideal gas behaviour.

1999
Q.64 The pressure exerted by 12 g of an ideal gas at temperature toC in a vessel of volume V is one
atm. When the temperature is increased by 10 degrees at the same volume , the pressure
increases by 10 %. Calculate the temperature ‘t’ and volume ‘V’.
[ molecular weight of gas = 120 ]
Q.65 One mole of N2 gas at 0.8 atm takes 38 sec to diffuse through a pin hole. Whereas one mole of
an unknown compound of Xenon with F at 1.6 atm takes 57 sec. to diffuse through the same
hole . Calculate the molecular formula of the compound.
Q.66 A gas will approach ideal behaviour at :
(A) low temperature and low pressure (B) low temperature and high pressure
(C) low pressure and high temperature (D) high temperature and high pressure

2000
Q.67 The compressibility of a gas is less than unity at STP. Therefore,
(A) Vm > 22.4 litres (B) Vm < 22.4 litres (C) Vm = 22.4 litre (D) Vm = 44.8 litres
 50 GASEOUS STATE

Q.68 Read the following statement and explanation and answer as per the options given below :
(1) Both (A) and (R) are correct and (R) is the correct explanation of (A)
(2) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(3) (A) is correct but (R) is incorrect
(4) (A) is incorrect but (R) is correct
Assertion : The pressure of a fixed amount of an ideal gas is proportional to its temperature.
Reason : Frequency of collision and their impact both increase in proportional to the
square root of temperature.
(A) 1 (B) 2 (C) 3 (D) 4

Q.69 The r.m.s. velocity of hydrogen is 7 times the r.m.s. velocity of nitrogen . If T is the
temperature of the gas :
(A) T (H2) = T (N2) (B) T (H2) > T (N2)
(C) T (H2) < T (N2) (D) T (H2) = 7 T (N2)
Q.70 The pressure of a fixed amount of an ideal gas is proportional to its temperature .
[ True/False ]
Q.71 Frequency of collision and their impact both increase in proportional to the square root of
temperature. [ True/False ]
Q.72 Calculate the pressure exerted by one mole of CO2 gas at 273 K, if the Vander Waals
constant a = 3.592 dm6 atm mol-2. Assume that the volume occupied by CO2 molecules is
negligible.

2001
Q.73 The root mean square velocity of an ideal gas at constant pressure varies with density as :
(A) d2 (B) d (C) d1/2 (D) 1/d1/2
Q.74 The compression factor (compressibility factor) for one mole of a Vander Waals gas at 0°C
and 100 atmosphere pressure is found to be 0.5. Assuming that the volume of a gas molecule is
negligible, calculate the vander waals constant ‘a’.

2002
Q.75 Which one of the following V, T plots represents the behaviour of one mole of an ideal gas at
one atm?

(A) (B) (C) (D)

Q.76 The density of the vapour of a substance at 1 atm pressure and 500 K is 0.36 Kgm–3. The
vapour effuses through a small hole at a rate of 1.33 times faster than oxygen under the same
condition.
(a) Determine :
(i) mol. wt. ; (ii) molar volume ; (iii) compression factor (z) of the vapour
(iv) which forces among the same molecules are dominating, the attractive or the repulsive
(b) If the vapour behaves ideally at 1000 K, determine the average translation K.E. of a
molecule.
GASEOUS STATE 51

2003
Q.77 The average velocity of gas molecules is 400 m/sec. Calculate its (rms) velocity at the same
temperature.
Q.78 Cv value of He is always 3R/2 but C v value of H2 is 3R/2 at low temperature and 5R/2 at
moderate temperature and more than 5R/2 at higher temperature explain in two to three lines.
Q.79 Positive deviation from ideal behaviour takes place because of –
(A) molecular interaction between atoms and nRT PV > 1

(B) PV < 1
molecular interaction between atoms and nRT

(C) PV > 1
finite size of atoms and nRT (D) PV < 1
finite size of atoms and nRT

2004
Q.80 Urms of a monoatomic gas whose molar kinetic energy is E and its molar mass is M –
3E 2E 2M
(A) 2M (B) (C) 3E (D) none of these
M
Q.81 A graph is plotted between PVm along Y-axis and P along X-axis, where Vm is the molar volume
of a real gas. Find the intercept along Y-axis.

2005
Q.82 The ratio of the rate of diffusion of helium and methane under identical condition of pressure
and temperature will be
(A) 4 (B) 2 (C) 1 (D) 0.05

2006

C
A

Z IDEAL GAS
PV
Q.83 where Z = ,
nRT
B

a = Van der Waal’s constant for pressure correction

b = Van der Waal’s constant for volume correction
Pick the only incorrect statement
(A) for gas A, if a = 0, the compressibility factor is directly proportional to pressure
(B) for gas B, if b = 0, the compressibility factor is directly proportional to pressure.
(C) for gas C, a  0, b  0, it can be used to calculate a and b by giving lowest P value and
its intercept with Z = 1
(D) slope for all three gases at high pressure is positive.