Assignment gaseous state_jh_sir-2621

Topic Page No.
Theory 01 - 07
Exercise - 1 08 - 26
Answer Key 41 - 44
Contents
Gaseous State
Syllabus
Gaseous State
Gaseous state : Absolute scale of temperature, ideal gas equation; Deviation from ideality,
van der Waals equation; Kinetic theory of gases, average, root mean square and most probable
velocities and their relation with temperature; Law of partial pressures; Vapour pressure; Diffusion
of gases.
Name:____________________________ Contact No. __________________
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F-106, Road No.2 Indraprastha Industrial Area, End of Evergreen Motor, BSNL Lane,
Jhalawar Road, Kota, Rajasthan (324005)
Tel. : +91-744-242-5022, 92-14-233303

F-106, Road No.2 Indraprastha Industrial Area, End of Evergreen Motor,
BSNL Lane, Jhalawar Road, Kota, Rajasthan (324005) Tel. : +91-744-242-5022, 92-14-233303
GASEOUS STATE_ADVANCED # 1
GASEOUS STATE
Measurable properties of gases :
1. Mass :
Def. The gases do possess mass. The mass of gas is generally used in the form of number of moles
which is related as :
2. Volume :
Def. Volume of gas is nothing but volume of the container in which it is present. Relation between
different units of volume
1 m3
= 103
dm3
= 103
litre =106
cm3
= 106
ml = 109
mm3
.
3. Temperature :
Def. Degree of hotness or coldness of a body is measured by temperature
C
100 =
K 273
100

=
F 32
180

C – Celcius scale, K – Kelvin scale, F – Fahrenheit scale
Note : In all the problems of gaseous state (i.e. in all gas law equations), temperature must be
expressed in kelvin scale. i.e. , t °C + 273 = TK
4. Pressure :
Def. Force acting per unit area
P =
A
F
Units :
CGS : dyne/cm2
MKS : Newton/m2
(1N/m2
= 1Pa)
Relation : 1 N/m2
= 10 dyne/cm2
Units of pressure :
1 atm = 76 cm of Hg
= 760 mm of Hg
= 760 torr
= 1.01325×105 N/m2
= 101.325 kPa
= 1.01325 bar
= 14.7 lb/In2
(Psi)
= 10.33 meters of H2
O
DENSITY OF GASES
Absolute density Relative density
(mass per unit volume) (Relative to hydrogen turned as vapour density)
d = v
m VD =
2
massmolecular
Boyle’s law and measurement of pressure :
Statement :
For a fixed amount of gas at constant temperature, the volume occupied by the gas is inversely proportional
to the pressure applied on the gas or pressure of the gas.
V 
P
1
hence PV = constant
this constant will be dependent on the amount of the gas and temperature of the gas.
P1
V1
= P2
V2

P
v
P2
P1
V2 V1
B
A
MEASUREMENT OF PRESSURE :
Barometer : Abarometer is an instrument that is used for the measurement of pressure.The construction of
the barometer is as follows
P0
P0
P0
P = P0 atm
Mg
Perfect Vaccum
Cross sectional view of the capillary column
(‘h’ is the height to which mercury has risen in the capillary)
or, Patm
= gh
Normal atmospheric pressure which we call 1 atmosphere (1 atm), is defined as the pressure exerted by the
atmosphere at mean sea level. It comes out to be 760 mm of Hg = 76 cm of Hg. (at mean sea level the
reading shown by the barometer is 76 cm of Hg)
1 atm = (13.6 × 103
) × 9.8 × 0.76 = 1.013 × 105
Pascal.
1 torr = 1 mm of Hg.
1 bar = 105
N/m2
(Pa)
Charles’ Law :
It relates the volume and temperature of a given mass of a gas at constant pressure.
For each degree change of temperature, the volume of a sample of a gas changes by the fraction 1
273
of its volume at 0 °C.
t 0
0
V V
T T or
T
V = constant , if pressure is kept constant
Calculation of pay load : Pay load is defined as the maximum weight that can be lifted by a gas filled
balloon.
M
Buoyancy
balloon
For maximum weight that can be lifted, applying force balance
Fbuoyancy
= Mballoon
× g + Mpay load
× g
 air
v.g. = gas
v.g + Mg + mg.
mass of balloon = m net force on
volume of balloon = v balloon = 0
density of air = air
(at equilibrium / when balloon is incoming
density of gas inside the with constant speed)
balloon = gas

Gay-lussac’s law : For a fixed amount of gas at constant volume, pressure of the gas is directly
proportional to temperature of the gas on absolute scale of temperature.
P  T
T
P
= constant  dependent on amount and volume of gas
2
2
1
1
T
P
T
P
  temperature on absolute scale originally, the law was developed on the centigrade
scale, where it was found that pressure is a linear function of temperature P = P0
+ bt where ‘b’ is a constant
and P0
is pressure at zero degree centigrade.
Avogadro’s Hypothesis : For similar values of pressure & temperature equal number of molecules of
different gases will occupy equal volume.
N1
 V (volume of N1
molecules at P & T of one gas)
N1
 V (volume of N1
molecules at P & T of second gas)
 Molar volume & volume occupied by one mole of each and every gas under similar conditions will be equal.
One mole of any gas or a combination of gases occupies 22.413996 L of volume at STP.
The previous standard is still often used, and applies to all chemistry data more than decade old, in this
definition Standard Temperature and Pressure STP denotes the same temperature of 0°C (273.15K), but
a slightly higher pressure of 1 atm (101.325 kPa).
Standard Ambient Temperature and Pressure (SATP), conditions are also used in some scientific works.
SATP conditions means 298.15 K and 1 bar (i.e. exactly 105
Pa) At SATP (1 bar and 298.15 K), the molar
volume of an ideal gas is 24.789 L mol–1
Ideal Gas Equation : Combining all these gas laws , a simple equation can be derived at, which
relates P , V , n and T for a gas
PV = nRT (for n moles of gas)

1 1
1
P V
T =
2 2
2
P V
T (Combined gas law)
Relation between Molecular Mass and Gas Densities :
(A) Actual density : For an ideal gas PV = nRT or
w
PV RT
M
 , where w = mass of the gas in gms
and M = Molecular wt. in gms.

w
PM RT
V
 or PM =  RT, (where  is the density of the gas =
w
V
 d =
PM
ñ
RT
Dalton’s Law of Partial Pressures : The total pressure of a mixture of non-reacting gases is
equal to the sum of their partial pressures.
By Dalton’s Law PT
= P1
+ P2
+ ..............
Graham’s Law of Diffusion/Effusion :
Diffusion : Net spontaneous flow of gaseous molecules from region of high concentration (higher partial
pressure) to the region of lower concentration or lower partial pressure
Graham’s Law : “Under similar conditions of pressure (partial pressure) the rate of diffusion of different
gases is inversely proportional to square root of the density of different gases.”

 rate of diffusion r 
d
1
d = density of gas
2
1
r
r
=
1
2
d
d
=
1
2
M
M
=
1
2
D.V
D.V
V.D is vapour density
 The general form of the grahams law of diffusion can be stated as follows, when one or all of the
parameters are varied.
rate 
TM
P
A
P – Pressure, A – area of hole, T – Temp. , M – mol. wt.
 If partial pressure of gases are not equal.
2
1
r
r
=
2
1
P
P
1
2
M
M
Kinetic Theory of Gases :
Derivation :
m = mass of one molecule
PV =
3
1
mN 2
U Kinetic equation of gases
where 2
U is mean square speed, N = number of molecule
root mean square speed = Urms
= 2
U = 






 
N
U......UUU 2
N
2
3
2
2
2
1
Kinetic Energy of gas sample :
(i) Average kinetic energy of a single molecule =
2
3
.
N
R
. T =
2
3
KT
K = boltzman constant = 1.38 × 10–23
J/deg
(ii) Total Kinetic Energy for one mole of gas =
2
3
RT
(iii) kinetic Energy for n mol of gas = n ×
2
3
RT
Average Velocity : As per kinetic theory of gases, each molecule is moving with altogether different
velocity. Let ‘n’ molecules be present in a given mass of gas, each one moving with velocity u1
,u2
, u3,
…,un
. The average velocity or Uav = average of all such velocity terms.
Average velocity =
1 2 2 nu u u ...u
n
  
 av
8RT
U
ðM
Root Mean Square Velocity : Maxwell proposed the term rmsU as the square root of means of
square of all such velocities.
2 2 2
2 1 2 3
rms
u u u ...
U
n
  

Also rms
3RT
U
M

Most probable velocity : It is the velocity possessed by maximum no. of molecules.
mpv
2RT
U
M
Furthermore mpv av rms
2RT 8RT 3RT
U : U : U :: : :
M M M
=
8
2 : : 3
ð
= 1 : 1.128 : 1.224
Real Gases :
 Real gases do not obey the ideal gas laws exactly under all conditions of temperature and pressure.
 Real gases deviates from ideal behaviour because
 Real gas molecules have a finite volume.
{since on liquefaction real gases occupy a finite volume}
 Inter molecular attractive forces between real gas molecules is not zero.
{Real gases can be converted into liquid where as ideal gases cant be}
 Deviation of real gases from ideal behaviour can be measured by using compresibility factor : (Z)
Z =
ideal
real
)PV(
)PV(
(PV)ideal
= nRT
Z =
nRT
PV
=
RT
PVm
, VM
is volume of one mole of gas or molar volume.
Vander Waal Equation of real gases :
The ideal gas equation does not consider the effect of attractive forces and molecular volume.
vander Waal's corrected the ideal gas equation by taking the effect of
(a) Molecular volume (b) Molecular attraction
Excluded volume per molecule =
2
1






 3
)r2(
3
4
= 4






 3
r
3
4
excluded volume per mole of gas (b) = NA
4






 3
r
3
4
= 4 x NA
x Volume of individual molecule for n moles,
excluded volume = nb
Vi
= V – nb volume correction
 Pressure correction or effect of molecular attraction forces :
‘a’ is constant of proportionality
and this is dependent on force of attraction
Stronger the force of attraction greater will be ‘a’ (Constant)
Pi
= P + 2
2
v
an
Vander waal’s equation is








 2
2
v
an
P (v – nb) = nRTT
VERIFICATION OF VANDER WAAL’S EQUATIONS :








 2
mV
a
P (Vm
– b) = RT
 AT LOW PRESSURE (at separate temp.)
At low pressure Vm
will be high.
Z = 1 – RTV
a
m
Z < 1
Real gas is easily compressible as compared to an ideal gas.

 AT HIGH PRESSURE (moderate temp.)
Z =
RT
Pb
+ 1 (Z > 1)
If Z > 1, then gas is more difficult to compress as compared to an ideal gas.
 For H2
or He a ~ 0 because molecules are smaller in size or vander Wall's forces will be very weak, these are
non polar so no dipole-dipole interactions are present in the actions.
P(Vm
– b) = RT so Z = 1 +
RT
Pb
 ‘a’ factor depends on inter molecular attractive forces.
 ‘a’ factor for polar molecule > ‘a’ factor for non polar molecule.
Virial Equation of state : It is a generalised equation of gaseous state. All other equations can be written
in the form of virial equation of state.
Z = 1 +
mV
B
+ 2
mV
C
+ 3
mV
D
+ .....................
B – second virial coefficient
C – third virial coefficient
D – fourth virial coefficient
Vander waals' equation in virial form :
Z = 







 .........
V
b
V
b
V
b
1 3
m
3
2
m
2
m
–
RTV
a
m
= 1 +
mV
1







RT
a
b + 2
m
2
V
b
+ 3
m
3
V
b
+ .................
B = b –
RT
a
, C = b2
, D = b3
at low pressure : Vm
will be larger
So, at T =
Rb
a
, gas will behave as an ideal gas (or follows Boyles law)
But at constant temperature, ideal gas equation is obeying Boyles law as T =
Rb
a
, so the temperature is
called Boyles' temp.
TB
=
Rb
a
Critical constant of a gas :
TC
or critical temp : Temperature above which a gas can not be liquified
PC
or critical pressure : Minimum pressure which must be applied at critical temperature to convert the gas
into liquid.
VC
or critical volume : Volume occupied by one mole of gas at TC
& PC
Vc
= 3b
PC
= 2
)b3(3
a
= 2
b27
a
TC
= Rb27
a8

Reduced Equation of state :
Reduced Temp : Temperature in any state of gas with respect to critical temp of the gas
Tr
=
CT
T
Reduced pressure : Pr
=
CP
P
Reduced volume : Vr
=
C
m
V
V








 2
r
r
V
3
P (3Vr
– 1) = 8 Tr
(Reduced equation of state)
Above equation is independent from a, b and R, so will be followed by each and every gas, independent of its
nature.
Vapour pressure of a liquid (aqueous Tension of water) :
Vapour pressure of liquid = pressure exerted by vapours of liquid
Vapour pressure is independent of amount of liquid & surface area of liquid.
Vapour pressure of the liquid is independent of pressure of any gas in the container,
Ptotal
= Pgas
+ Pwater vapour
Eudiometry : The analysis of gaseous mixtures is called eudiometry. The gases are identified byabsorbing
them in specified and specific reagents.
Some Common Facts :
 Liquids and solutions can absorb gases.
 If a hydrocarbon is burnt, gases liberated will be CO2
& H2
O. [H2
O is seperated out by cooling the
mixture & CO2
by absorption by aqueous KOH]
 If organic compound contains S or P, then these are converted into SO2
& P4
O10
by burning the organic
compound.
 If nitrogen is present, then it is converted into N2
.
[The only exception : if organic compound contains – NO2
group then NO2
is liberated]
 If mixture contains N2
gas & this is exploded with O2
gas, do not assume any oxide formation unless
specified.
 Ozone is absorbed in turpentine oil and oxygen in alkaline pyragallol.

PART - I : OBJECTIVE QUESTIONS
Section A : Gas Laws
A-1. At constant temperature, in a given mass of an ideal gas -
(A) The ratio of pressure and volume always remains constant
(B) Volume always remains constant
(C) Pressure always remains constant
(D) The product of pressure and volume always remains constant
A-2. Three flasks of equal volumes contain CH4, CO2 and Cl2 gases respectively. They will contain equal
number of molecules if -
(A) the mass of all the gases is same
(B) the moles of all the gas is same but temperature is different
(C) temperature and pressure of all the flasks are same
(D) temperature, pressure and masses same in the flasks
A-3. A certain mass of a gas occupies a volume of 2 litres at STP. Keeping the pressure constant at what
temperature would the gas occupy a volume of 4 litres -
(A) 546ºC (B) 273ºC (C) 100ºC (D) 50ºC
A-4. At 100 ºC a gas has 1 atm. pressure and 10 L volume. Its volume at NTP would be -
(A) 10 litres (B) Less than 10 litres
(C) More than 10 litres (D) None
A-5. If 500 ml of a gas 'A' at 1000 torr and 1000 ml of gas B at 800 torr are placed in a 2L container,
the final pressure will be-
(A) 100 torr (B) 650 torr (C) 1800 torr (D) 2400 torr
A-6. Two flasks A and B of 500 ml each are respectively filled with O2 and SO2 at 300 K and 1 atm.
pressure. The flasks will contain-
(A) The same number of atoms
(B) The same number of molecules
(C) More number of moles in flask A as compared to flask B
(D) The same amount of gases
A-7. In the gas equation PV = nRT, the value of universal gas constant would depend only on -
(A) The nature of the gas (B) The pressure of the gas
(C) The temperature of the gas (D) The units of measurement
A-8. 8.2 L of an ideal gas weight 9.0 gm at 300 K and 1 atm pressure. The molecular mass of gas is-
(A) 9 (B) 27 (C) 54 (D) 81
A-9. Energy in an ideal gas is -
(A) Completely kinetic (B) Completely potential
(C) KE + PE (D) All the above.
A-10. A 0.5 dm3 flask contains gas 'A' and 1 dm3 flask contains gas 'B' at the same temperature. If density
of A = 3.0 gm dm–3 and that of B = 1.5 gm dm–3 and the molar mass of A = 1/2 of B, then the
ratio of pressure exerted by gases is-
(A) PA/PB = 2 (B) PA/PB = 1 (C) PA/PB = 4 (D) PA/PB = 3.
A-11. One litre of an unknown gas weighs 1.25 gm at N.T.P. which of the following gas pertains to the above
data -
(A) CO2 (B) NO2 (C) N2 (D) O2

A-12. If the density of a gas A is 1.5 times that of B then the molecular mass of A is M. The molecular
mass of B will be-
(A) 1.5 M (B) M/1.5 (C) 3M (D) M/3
A-13. When the pressure of 5L of N2 is doubled and its temperature is raised from 300K to 600K, the final
volume of the gas would be-
(A) 10 L (B) 5 L (C) 15 L (D) 20 L
A-14. The value of gas constant per mole is approximately-
(A) 1 cal (B) 2 cal (C) 3 cal (D) 4 cal
A-15. A gas is found to have a formula [CO]x. If its vapour density is 70 the value of x is-
(A) 2.5 (B) 3.0 (C* ) 5.0 (D) 6.0
A-16. If the pressure of a gas contained in a closed vessel is increased by 0.4 % when heated by 1ºC its initial
temperature must be :
(A) 250 K (B) 250ºC (C) 25ºC (D) 25 K
A-17. A thin balloon filled with air at 47ºC has a volume of 3 litre. If on placing it in a cooled room its volume
becomes 2.7 litre , the temperature of room is :
(A) 42ºC (B) 100ºC (C) 15ºC (D) 200ºC
A-18. If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, the
ratio of initial and final volume under the same temperature and pressure would be :
(A) 3 : 1 (B) 1 : 3 (C) 2 : 1 (D) 1 : 2
A-19. Two flasks of equal volume are connected by a narrow tube (of negligible volume) all at 27ºC and contain
0.35 mole of H2 each at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C, while the other
remains at 27º C. The final pressure in each flask is :
(A) Final pressure = 0.5714 atm (B) Final pressure = 1.5714 atm
(C) Final pressure = 0.5824 atm (D) None of these
A-20. Two flasks of equal volume are connected by a narrow tube (of negligible volume) all at 27º C and contain
0.70 moles of H2 at 0.5 atm. One of the flask is then immersed into a bath kept at 127º C , while the other
remains at 27º C. The number of moles of H2 in flask 1 and flask 2 are :
(A) Moles in flask 1 = 0.4, Moles in flask 2 = 0.3 (B) Moles in flask 1 = 0.2, Moles in flask 2 = 0.3
(C) Moles in flask 1 = 0.3, Moles in flask 2 = 0.2 (D) Moles in flask 1 = 0.4, Moles in flask 2 = 0.2
A-21. A gas is heated from 0°C to 100°C at 1.0 atm pressure. If the initial volume of the gas is 10.0  , its final
volume would be :
(A) 7.32  (B) 10.00  (C) 13.66  (D) 20.00 
A-22. Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of 1 atm but also a
concentration of 1 mol litre 1. [ R = 0.082 litre atm mol 1 K 1 ]
(A) at S.T.P. (B) when V = 22.42 L
(C) when T = 12 K (D) impossible under any condition
A-23. A and B are two identical vessels. A contains 15 g ethane at 1atm and 298 K. The vessel B contains 75 g of
a gas X2 at same temperature and pressure. The vapour density of X2 is :
(A) 75 (B) 150 (C) 37.5 (D) 45
A-24. The density of neon will be highest at :
(A) STP (B) 0°C, 2 atm (C) 273°C. 1 atm (D) 273°C. 2 atm

A-25. A 0.5 dm3 flask contains gas A and 1 dm3 flask contains gas B at the same temperature. If density of A = 3
g/dm3 and that of B = 1.5 g/dm3 and the molar mass of A = 1/2 of B, the ratio of pressure exerted by gases
is :
(A)
B
A
P
P
= 2 (B)
B
A
P
P
= 1 (C)
B
A
P
P
= 4 (D)
B
A
P
P
= 3
A-26. Which expression among the following represents Boyle's law ?
(A) (dP/dV)T = K/V (B) (dP/dV)T = –K/V2 (C) (dP/dV)T = –K/V (D) (dP/dV)T = K
A-27. For a fixed mass of a gas at constant pressure, which of the following is correct -
(A) Plot of volume versus Celsius temperature is linear with intercept zero
(B) Plot of volume versus kelvin temperature is linear with a nonzero intercept
(C) Plot of V/T versus T is linear with a positive slope
(D) Plot of V/T versus T is linear with a zero slope
A-28. The density of carbon monoxide at STP is -
(A) 0.625 g L–1 (B) 1.25 g L–1 (C) 2.5 g L–1 (D) 1.875 g L–1
A-29. At a given temperature (X) = 2(Y) and M(Y) = 3 M(X), where  and M stand respectively for
density and molar mass of the gases X and Y, then the ratio of their pressures will be -
(A) p(X) / p(Y) = 1/4 (B) p(X) / p(Y) = 4 (C) p(X) / p(Y) = 6 (D) p(X) / p(Y) = 1/6
A-30. Which of the following expression gives the variation of density of ideal gas with changes in temperature?
(A)
21
12
1
2
TP
TP
d
d
 (B)
2
11
2
T
Td
d  (C)
1
2
1
2
T
T
d
d
 (D)
11
222
2
TP
TPd
d 
A-31. The volume of ammonia obtained by the combination of 10ml of N2 and 30ml H2 is -
(A) 20ml (B) 40 ml (C) 30ml (D) 10ml
A-32. Hydrogen and Argon are kept in two separate but identical vessels at constant temperature and
pressure -
(A) Both contain same number of atoms.
(B) The number of atoms of argon is half that of hydrogen.
(C) The number of atoms of argon is double that of hydrogen
(D) None of these
A-33. Which of the following represents the avogadro number -
(A) Number of molecules present in 1 L of gas at N.T.P.
(B) Number of molecules present in 22.4 ml of gas at N.T.P.
(C) Number of molecules present in 22.4 L of gas at 298K and 1 atm. pressure
(D) Number of molecules present in one mole of gas at any temp. and pressure.
A-34. 26 c.c. of CO2 are passed over red hot coke. The volume of CO evolved is -
(A) 15 c.c (B) 10 c.c. (C) 32 c.c. (D) 52 c.c.
A-35. 10 gm of a gas at NTP occupies 5 litres. The temp. at which the volume becomes double for the same
mass of gas at the same pressure is -
(A) 273 K (B) -273ºC (C) 273ºC (D) 546ºC
A-36. An ideal gas is at a pressure (P) and temperature (T) in a box, which is kept in vacuum within a
large container. The wall of the box is punctured. What happens as the gas escape through the hole ?
(A) the temperature falls (B) its temperature rises
(C) its temperature remains the same (D) unpredictable

A-37. V versus T curves at constant pressure P1 and P2 for an ideal gas are shown in fig. Which is
correct -
(A) P1 > P2 (B) P1 < P2 (C) P1 = P2 (D) All
A-38. If pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1ºC its initial
temperature must be -
(A) 250K (B) 250ºC (C) 2500K (D) 25ºC
A-39. At a constant pressure, what should be the percentage increase in the temperature in kelvin for a
10% increase in volume -
(A) 10% (B) 20% (C) 5% (D) 50%
A-40. There is 10 litre of a gas at STP. Which of the following changes keeps the volume constant -
(A) 273 K and 2 atm (B) 273ºC and 2 atm
(C) 546ºC and 0.5 atm (D) 0ºC and 0 atm
A-41. The density of oxygen gas at 25ºC is 1.458 mg/litre at one atmosphere. At what pressure will oxygen
have the density twice the value-
(A) 0.5 atm/25ºC (B) 2 atm/25ºC (C) 4 atm/25ºC (D) None
A-42. A flask of methane (CH4) was weighed. Methane was then pushed out and the flask again weighed
when filled with oxygen at the same temperature and pressure. The mass of oxygen would be -
(A) The same as the methane (B) Half of the methane
(C) Double of that of methane (D) Negligible in comparison to that of methane
A-43. A balloon filled with methane (CH4) is pricked with a sharp point and quickly plunged into a tank of
hydrogen at the same pressure. After sometime, the balloon will have -
(A) Enlarged (B) Shrinked
(C) Remain unchanged in size (D) Ethylene (C2H4) inside it
A-43. Containers X, Y and Z of equal volume contain oxygen, neon and methane respectively at the same
temperature and pressure. The correct incereasing order of their masses is -
(A) X < Y < Z (B) Y < Z < X (C) Z < X < Y (D) Z < Y < X
A-44. Two flasks X and Y have capacity 1L and 2L respectively and each of them contains 1 mole of a gas.
The temperature of the flask are so adjusted that average speed of molecules in X is twice as those
in Y. The pressure in flask X would be -
(A) Same as that in Y (B) Half of that in Y
(C) Twice of that in Y (D) 8 times of that in Y
A-45. A gas can be liquefied by -
(A) Cooling (B) Compressing (C) Both (D) None of these.

Section B: Daltons Law of Partial Pressures
B-1. A cylinder is filled with a gaseous mixture containing equal masses of CO and N2. The ratio of their
partial pressure is-
(A) PN2
= PCO (B) PCO = 0.875 PN2 (C) PCO = 2 PN2
(D) PCO =
1
2
PN2
B-2. The total pressure of a mixture of two gases is -
(A) The sum of partial pressures of each gas
(B) The difference in partial pressures
(C) The product of partial pressures
(D) The ratio of partial pressures.
B-3. Equal masses of SO2, CH4 and O2 are mixed in empty container at 298 K, when total pressure is
2.1 atm. The partial pressures of CH4 in the mixture is -
(A) 0.5 atm (B) 0.75 atm (C) 1.2 atm (D) 0.6 atm
B-4. Air contains 79% N2 and 21% O2 by volume. If the pressure is 750 mm of Hg, the partial pressure
of O2 is -
(A) 157.5 mm of Hg (B) 175.5 mm of Hg (C) 315.0 mm of Hg (D) 257.5 mm of Hg
B-5. Equal weights of ethane & hydrogen are mixed in an empty container at 25º C, the fraction of the total
pressure exerted by hydrogen is:
(A) 1: 2 (B) 1: 1 (C) 1: 16 (D) 15: 16
B-6. A mixture of hydrogen and oxygen at one bar pressure contains 20% by weight of hydrogen. Partial pressure
of hydrogen will be
(A) 0.2 bar (B) 0.4 bar (C) 0.6 bar (D) 0.8 bar
B-7. A compound exists in the gaseous phase both as monomer (A) and dimer (A2). The atomic mass of A is 48
and molecular mass of A2 is 96. In an experiment 96 g of the compound was confined in a vessel of volume
33.6 litre and heated to 273ºC. The pressure developed if the compound exists as dimer to the extent of 50
% by weight under these conditions will be :
(A) 1 atm (B) 2 atm (C) 1.5 atm (D) 4 atm
B-8. In the below experiment, the value of P is -
P
essurePr
mm250
Bgasmol2
mm250
Agasmol1
)T(perature
temsame
atremoved
Partition

 

(A) 250 mm (B) 500 mm (C) 300 mm (D) 400 mm
B-9. A closed vessel contains equal number of oxygen and hydrogen molecules at a total pressure of 740
mm. If oxygen is removed from the system, the pressure -
(A) Becomes half of 740 mm. (B) Remains unchanged
(C) Becomes 1/9th of 740 mm. (D) Becomes double of 740 mm.
B-10. At constant temperature 200 cm3 of N2 at 720 mm and 400 cm3 of O2 at 750 mm pressure are put
together in a one litre flask. The final pressure of mixture is -
(A) 111 mm (B) 222 mm (C) 333 mm (D) 444 mm
B-11. A box of 1L capacity is divided into two equal compartments by a thin partition which are filled with
2g H2 and 16gm CH4 respectively. The pressure in each compartment is recorded as P atm. The total
pressure when partition is removed will be -
(A) P (B) 2P (C) P/2 (D) P/4

B-12. The partial pressure of hydrogen in a flask containing 2gm of H2 & 32gm of SO2 is -
(A)
1
16
of total pressure (B)
1
2
of total pressure
(C)
2
3
of total pressure (D)
1
8
of total pressure.
B-13. The mass of CO2
that must be mixed with 20 g of oxygen such that 27 ml of a sample of the
resulting mixture contains equal number of molecules of each gas –
(A) 13.75 g (B) 27.5 g (C) 41.25 g (D) 55 g
B-14. A mixture of hydrogen and oxygen (45 ml) is sparked to form liquid water. The component not in excess
reacts completely and 15 ml is left over. (All measurements are made at the same temperature and
pressure). The composition by volume in the original mixture of H2
: O2
is
(A) 4 : 5 (B) 7 : 2
(C) either 4 : 5 nor 7 : 2 (D) 2 : 1
B-15. In a gaseous mixture at 20°C the partial pressure of the components are, :
H2
: 150 Torr, CO2
: 200 Torr, CH4
: 300 Torr, C2
H4
: 100 Torr, Volume percent of H2
is :
(A) 26.67 (B) 73.33 (C) 80.00 (D) 20
B-16. At STP, a container has 1 mole of Ar, 2 moles of CO2
, 3 moles of O2
and 4 moles of N2
. Without
changing the total pressure if one mole of O2
is removed, the partial pressure of O2
:
(A) is changed by about 26 % (B) is halved
(C) is unchanged (D) changed by 33 %
B-17. Which of the following gases will have the same rate of diffusion under identical conditions?
(i) CO, (ii) CO2
, (iii) N2
O, (iv) N2
, (v) C2
H4
(vi) C3
H8
(A) CO,CO2
,C2
H4
(B) CO2
,C2
H4
,N2
O (C) C3
H8
,N2
O,CO2
(D) CO, N2
,C2
H4
,C3
H8
Section C : Grahams Law of Diffusion.
C-1. The rates of diffusion of SO3, CO2, PCl3 and SO2 are in the following order -
(A) PCl3 > SO3 > SO2 > CO2 (B) CO2 > SO2 > PCl3 > SO3
(C) SO2 > SO3 > PCl3 > CO2 (D) CO2 > SO2 > SO3 > PCl3
C-2. 20  of SO2 diffuses through a porous partition in 60 seconds. Volume of O2 diffuse under similar conditions
in 30 seconds will be :
(A) 12.14  (B) 14.14  (C) 18.14  (D) 28.14 
C-3. See the figure-1 :
The valves of X and Y are opened simultaneously. The white fumes of NH4Cl will first form at:
(A) A (B) B (C) C (D) A,B and C simultaneously
C-4. 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 identical conditions is :
(A) 10 sec. He (B) 20 sec. O2 (C) 25 sec. CO2 (D) 55 sec. CO2

C-5.* The rate of diffusion of 2 gases ‘A’ and ‘B’ are in the ratio 16: 3. If the ratio of their masses present in the
mixture is 2 : 3. Then
(A) The ratio of their molar masses is 16 : 1
(B) The ratio of their molar masses is 1 : 4
(C) The ratio of their moles present inside the container is 1 : 24
(D) The ratio of their moles present inside the container is 8 : 3
C-6. A gas 'A' having molecular weight 4 diffuses thrice as fast as the gas B. The molecular weight of gas
B is-
(A) 36 (B) 12 (C) 18 (D) 24
C-7. The increasing order of effusion among the gases, H2, O2, NH3 and CO2 is-
(A) H2, CO2, NH3, O2 (B) H2, NH3, O2, CO2
(C) H2, O2, NH3, CO2 (D) CO2, O2, NH3, H2
C-8. The rate of diffusion of methane at a given temperature is twice that of a gas X. The molecular weight
of X is -
(A) 64 (B) 32 (C) 4 (D) 8
C-9. A gas X diffuses three times faster than another gas Y the ratio of their densities i.e., Dx : Dy is-
(A)
1
3
(B)
1
9
(C)
1
6
(D)
1
12
C-10. In which of the following pairs the gaseous species diffuse through a porous plug with the same rate
of diffusion -
(A) NO, CO (B) NO, CO2 (C) NH3, PH3 (D) NO, C2H6
C-11. A balloon filled with ethylene is pricked with a sharp pointed needle and quickly placed in a tank full of
hydrogen at the same pressure. After a while the balloon would have :
(A) shrunk (B) enlarged
(C) completely collapsed (D) remain unchanged in size.
C-12. A certain gas is diffused from two different vessels A and B. The vessel A has a circular orifice while
vessel B has square orifice of length equal to the radius of the orifice of vessel A. The ratio of the
rates of diffusion of the gas form vessel A to that of in vessel B assuming same T & P is :
(A)  (B) 1/ (C) 1 : 1 (D) 2 : 1
C-13. The vapour densities of CH4 and O2 are in the ratio 1 : 2 . The ratio of rates of diffusions of O2 and
CH4 at same P and T is -
(A) 1 : 2 (B) 2 : 1 (C) 1 : 1.41 (D) 1 : 4.14
C-14. A balloon is filled with I gm of He and had a radius of 10 cm. after some time 0.27 gm of He the effused
out from the balloon. If pressure & temp. remains constant what would be the radious of balloon now–
(A) 9.5 (B) 9.0 (C) 8.0 (D) 6.5
Section D: Kinetic Theory of Gases.
D-1. Which is not correct in terms of kinetic theory of gases-
(A) Gases are made up of small particles called molecules
(B) The molecules are in random motion
(C) When molecules collide, they lose energy
(D) When the gas is heated , the molecules moves faster
D-2. The kinetic energy of 1 mole of gas is equal to -
(A)
3
2
RT (B)
3
2
KT (C)
RT
2
(D)
2
3
R

D-3. Which of the following expression does not give root mean square velocity-
(A)
3
1
2RT
M





 (B)
3
1
2P
DM





 (C)
2
1
D
P3






(D)
3
1
2PV
M






D-4. Which one of the following gases would have the highest R.M.S. velocity at 25ºC -
(A) Oxygen (B) Carbon dioxide (C) Sulphur dioxide (D) Carbon monoxide.
D-6. If the r.m.s. velocity of nitrogen molecules is 5.15 ms–1 at 298 K, then a velocity of 10.30 ms–1 will
be possessed at a temp-
(A) 149 K (B) 172.6 K (C) 596 K (D) 1192 K
D-7. The RMS velocity at NTP of the species can be calculated from the expression -
(A)
3P
d





 (B)
3PV
M





 (C)
3RT
M





 (D) All are correct.
D-8. Among the following gases which one has the lowest root mean square velocity at 25ºC-
(A) SO2 (B) N2 (C) O2 (D) Cl2
D-9. By how many folds the temp of a gas would increase when the r.m.s. velocity of gas molecules in
a closed container of fixed volume is increased from 5 x 104 cm s–1 to 10 x 104 cm s–1-
(A) 0.5 times (B) 2 times (C) 4 times (D) 16 times.
D-10. At S.T.P. the order of mean square velocity of molecules H2, N2, O2 and HBr is -
(A) H2 > N2 > O2 > HBr (B) HBr > O2 > N2 > H2
(C) HBr > H2 > O2 > N2 (D) N2 > O2 > H2 > HBr
D-11. Most probable speed, average speed and RMS speed are related as -
(A) 1 : 1.128 : 1.224 (B) 1 : 1.128 : 1.424 (C) 1 : 2.128 : 1.224 (D) 1 : 1.428 : 1.442
D-12. The root mean square velocity of an ideal gas in a closed container of fixed volume is increased from
5 x 104 cm. s–1 to 10 x 104 cm. s–1. Which of the following statements might correctly explain how
the change accomplished -
(A) By heating the gas, the temperature is doubled
(B) By heating the gas, the pressure is made four times
(C) By heating the gas, the volume is tripled
(D) By heating the gas, the pressure is doubled.
D-13. Temperature at which r.m.s. speed of O2 is equal to that of neon at 300 K is :
(A) 280 K (B) 480 K (C) 680 K (D) 180 K
D-14. The R.M.S. speed of the molecules of a gas of density 4 kg m 3 and pressure 1.2  105 N m 2 is :
(A) 120 m s 1 (B) 300 m s 1 (C) 600 m s 1 (D) 900 m s 1
D-15. The mass of moleculeAis twice that of molecule B. The root mean square velocity of moleculeAis twice that
of molecule B. If two containers of equal volume have same number of molecules, the ratio of pressure PA/PB
will be :
(A) 8 : 1 (B) 1 : 8 (C) 4 : 1 (D) 1 : 4

D-16. The average kinetic energy (in joules of) molecules in 8.0 g of methane at 27º C is :
(A) 6.21 × 10-20 J/molecule (B) 6.21 × 10-21 J/molecule
(C) 6.21 × 10-22 J/molecule (D) 3.1 × 10-22 J/molecule
D-17. According to kinetic theory of gases, for a diatomic molecule :
(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 inversely proportional to the temperature.
(D) The mean translational K.E. of the molecule is proportional to the absolute temperature.
D-18. The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity
of the gas molecules is v, at 480 K it becomes :
(A) 4v (B) 2v (C) v/2 (D) v/4
D-19. 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
D-20.* If a gas is allowed to expand at constant tempeature then which of the following does not hold true :
(A) the kinetic energy of the gas molecules decreases
(B) the kinetic energy of the gas molecules increases
(C) the kinetic energy of the gas molecules remains the same
(D) Can not be predicted
D-21. The total kinetic energy of 0.6 mol of an ideal gas at 27° C is -
(A) 1122 J (B) 1681 J (C) 2245 J (D) 2806 J
D-22. Which of the following molecule has the lowest average speed at 273 K ?
(A) CO (B) CH4 (C) CO2 (D) C2H6
D-23. Which of the following is true -
(A) urms >  > . (B) urms <  < . (C) urms >  < . (D) urms <  > .
D-24. At what temperature will be total kinetic energy (KE) of 0.30 mole of He be the same as the total
KE of 0.40 mole of Ar at 400K-
(A) 400K (B) 373 K (C) 533K (D) 300 K
D-25. Four particles have speed 2,3,4 and 5 cm/s respectively. Their rms speed is -
(A) 3.5cm/s (B) (27/2) cm/s (C) 54 cm/s (D) ( 54 /2) cm/s]
D-26. The RMS velocity of an ideal gas at 27 ºC is 0.3 m sec–1. Its RMS velocity at 927 ºC is -
(A) 0.6 m sec–1 (B) 0.9 m sec–1 (C) 2.4 m sec–1 (D) 3.0 m sec–1
D-27. Average velocity is equal to -
(A) 0.9213 RMS velocity (B) 0.9 RMS velocity
(C) 0.9602 RMS velocity (D) 0.9813 RMS velocity
D-28. The velocity possessed by most of the gaseous molecules is -
(A) Average velocity (B) Most probable velocity
(C) R.M.S. velocity (D) None of these.
D-29. A 2.24L cyclinder of oxygen at N.T.P. is found to develop a leakage. When the leakage was plugged
the pressure dropped to 570 mm of Hg. The number of moles of gas that escaped will be -
(A) 0.025 (B) 0.050 (C) 0.075 (D) 0.09

D-30. Helium atom is twice times heavier than a hydrogen molecule. At 25ºC the average K.E. of helium
atom is -
(A) Twice that of hydrogen (B) Same as that of hydrogen
(C) Four times that of hydrogen (D) Half that of hydrogen
D-31. If a gas is expanded at constant temperature-
(A) Number of molecules of the gas decreases
(B) The kinetic energy of the molecule decreases
(C) The kinetic energy of the molecules remains the same
(D) The kinetic energy of the molecules increases
D-32. Three gases of densities A(0.82), B(0.25), C(0.51) are enclosed in a vessel of 4L capacity. Pick up the
correct statement :
I. Gas A will tend to lie at the bottom
II. The number of atoms of various gases A, B, C are same
III. The gases will diffuse to form homogeneous mixture.
IV. The average kinetic energy of each gas is same.
(A) I , IV (B) only III (C) III , IV (D) II, III
D-33. Which of the following statements is not true ?
(A) The ratio of the mean speed to the rms speed is independent of the temperature.
(B) The square of the mean speed of the molecules is equal to the mean squared speed at a certain
temperature.
(C) Mean kinetic energy of the gas molecules at any given temperature is independent of the mean
speed.
(D) None of these
D-34. The temperature of an ideal gas is increased from 140 K to 560 K. If at 140 K the root-mean square
velocity of the gas molecules is V, at 560 K it becomes :
(A) 5 V (B) 2 V (C) V/2 (D) V/4
D-35. If for two gases of molecular weights MA
and MB
at temperature TA
and TB
, TA
MB
= TB
MA
, then which
property has the same magnitude for both the gases :
(A) density (B) pressure (C) K. E. per mole (D) r.m.s. speed
D-36. At what temperature will the total K. E. of 0.30 mol of He be the same as the total K.E. of 0.40 mol of Ar
at 400 K ?
(A) 533 K (B) 400 K (C) 346 K (D) 300 K
D-37. 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
D-38. For two gases, A and B with molecular weights MA
and MB
, it is observed that at a certain temperature,
T, the mean velocity of A is equal to the root mean squared velocity of B. Thus the mean velocity of A
can be made equal to the mean velocity of B, if –
(A) A is at temperature, T, and B at T1
, T > T1
(B) A is lowered to a temperature T2
< T while B is at T
(C) Both A and B are raised to a higher temperature
(D) Both A and B are lowered in temperature
Section E: Real Gases
E-1. The Vander Waals' equation explains the behaviour of -
(A) Ideal gases (B) Real gases (C) Vapours (D) Non-real gases.
E-2. The correct expression for the vander waal's equation of states is-
(A) (p + a/n2 V2) (V - nb) = nRT (B) (p + an2/V2) (V - nb) = nRT
(C) (p + an2/V2) (V - b) = nRT (D) (p + an2/V2) (V - nb) = nRT

E-3. The term that accounts for intermolecular force in vander Waal's equation for non ideal gas is -
(A) RT (B) V - b (C) (P + a / V2) (D) [RT]-1
E-4. The critical temperature of a substance is -
(A)The temperature above which the substance undergoes decomposition
(B)The temperature above which a substance can exist only as a gas
(C) Boiling point of the substance
(D) All are wrong
E-5. Critical temperature of the gas is the temperature-
(A) Below which it cannot be liquified (B) Above which it cannot be liquified
(C) At which it occupies 22.4 L of volume (D) At which one mole of it occupies volume of 22.4 L
E-6. The units of the Van der Waal’s constant ‘a’ are -
(A) atm L2 mol–2 (B) atm L–2 mol–2 (C) atm L mol–1 (D) atm mol L–2
E-7. The units of the van der Waal’s constant ‘b’ are -
(A) atmosphere (B) joules (C) L mol–1 (D) mol L–1
E-8. The Van der Waal’s parameters for gases W, X, Y and Z are -
027.0
032.0
030.0
027.0
0.12
0.6
0.8
0.4
Z
Y
X
W
)Lmol(b)molLatm(aGas 122 
Which one of these gases has the highest critical temperature ?
(A) W (B) X (C) Y (D) Z
E-9. If the Vander Waal’s constants of gas A are given as -
a (atm L2 mol2) = 6.5
b (L mol–1) 0.056
than ciritical pressure of A is
E-10. A real gas obeying Vander Waal's equation will resemble ideal gas , if the :
(A) constants a & b are small (B) a is large & b is small
(C) a is small & b is large (D) constant a & b are large
E-11. For the non-zero values of force of attraction between gas molecules, gas equation will be :
(A) PV = nRT –
V
an2
(B) PV = nRT + nbP (C) PV = nRT (D) P =
bV
nRT

E-12. Compressibility factor for H2 behaving as real gas is :
(A) 1 (B) 






RTV
a
1 (C) 






RT
Pb
1 (D)
)a1(
RTV


E-13. At low pressures (For 1 mole), the Vander Waal’s equation is written as






 2
V
a
p V = RT
The compressibility factor is then equal to :
(A) 






RTV
a
1 (B) 






a
RTV
1 (C) 






RTV
a
1 (D) 






a
RTV
1
E-14. Calculate the radius of He atoms if its Vander Waal's constant ‘b’ is 24 ml mol 1.
(Note ml = cubic centimeter)
(A) 1.355 Å (B) 1.314 Å (C) 1.255 Å (D) 0.355 Å
E-15. In vander Waal's equation of state for a non ideal gas the term that accounts for intermolecular forces is :
(A) nb (B) nRT (C) n2a/V2 (D) (nRT)-1
E-16. The values of Vander Waal's constant "a" for the gases O2, N2, NH3 & CH4 are 1.36, 1.39, 4.17, 2.253 L2 atm
mole-2 respectively. The gas which can most easily be liquified is:
(A) O2 (B) N2 (C) NH3 (D) CH4
E-17. The correct order of normal boiling points of O2, N2, NH3 and CH4, for whom the values of vander Waal's
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
E-18. NH3 gas is liquefied more easily than N2. Hence:
(A) Vander Waal’s constants 'a' and 'b' of NH3 > that of N2
(B) Vander Waal’s constants 'a' and 'b' of NH3 < that of N2
(C) a (NH3) > a (N2) but b (NH3) < b (N2)
(D) a (NH3) < a (N2) but b (NH3) > b (N2)
E-19.* The vander waal gas constant ‘a’ is given by
(A)
3
1
VC
(B) 2
CC VP3 (C)
C
C
P
RT
8
1
(D)
64
27
C
2
C
2
P
TR
E-20. At low pressure the Vander Waals equation is reduced to
(A) 1–
m
a
Z
V RT
 (B) Z
pV
RT
b
RT
bm
  1
(C) pVm
= RT (D) Z
pV
RT
a
RT
m
  1
E-21. Consider the equation Z
PV
RT
 Which of the following statements is correct ?
(A) When Z . 1, real gases are easier to compress than the ideal gas.
(B) when Z = 1, real gases get compressed easily.
(C) When Z > 1 , real gases are difficult to compress .
(D) When Z = 1 , real gases are difficult to copress.
E-22. A mixture of C3
H8
and CH4
exerts a pressure of 320 mm Hg at temperature TK in aV litre flask. On
complete combustion, gasesous contains CO2
, only and exerts a pressure of 448 mm Hg under idetical
conditions. Hence, mole fraction of C3
H8
in the mixture is :
(A) 0.2 (B) 0.8 (C) 0.25 (D) 0.75

E-23. Let the most probable velocity of hydrogen molecules at a temperature 1o
C is Vo. Suppose all the molecules
dissociate into atoms when temperature is raised to (2t + 273)o
C then the new rms velocity is :
(A)
2
3
0V (B) 3 2 273 1( ) / Vo (C) 2 3/ Vo
(D) 6Vo
E-24. The P of real gases is less than the P of an ideal gas because of -
(A) Increase in number of collisions (B) Finite size of molecule
(C) Increase in KE of molecules (D) Intermolecular forces
E-25. Average K.E. of CO2 at 27ºC is E. The average kinetic energy of N2 at the same temperature will
be-
(A) E (B) 22E (C) E/22 (D) E/ 2
E-26. The rate of diffusion of hydrogen is about -
(A) One half that of He (B) 1.4 times that of He
(C) Twice that of He (D) Four times that of He
E-27. A gas is said to behave like an ideal gas when the reaction PV/T = constant, holds. When do you
expect a real gas to behave like an ideal gas -
(A) When temperature and pressure are low
(B) When temperature and pressure are high
(C) When temperature is low and pressure is high
(D) When temperature is high and pressure is very low.
E-28. If temperature and volume are same, the pressure of a gas obeying Vander Waals equation is -
(A) Smaller than that of an ideal gas (B) Larger than that of an ideal gas
(C) Same as that of an ideal gas (D) None of these
E-29. In case of hydrogen and helium the Vander Waals forces are -
(A) Strong (B) Very strong (C) Weak (D) Very weak
E-30. Which of the following can be most readily liquefied ? Given value of 'a' for NH3 = 4.17, CO2 = 3.59,
SO2 = 6.71 , Cl2 = 6.49)
(A) NH3 (B) Cl2 (C) SO2 (D) CO2
E-31. The density of a gas at 27°C and 1 atm pressure is . Pressure remaining constant, the temperature
at which its density is 0.5  is-
(A) 200 K (B) 400 K (C) 600 K (D) 800 K
E-32. A real gas is expected to exhibit maximum deviations from ideal gas laws at -
(A) Low T and High P (B) Low T and Low P
(C) High T and High P (D) High T and Low P
E-33. Which of the following expressions of compression factor Z (= pVm / RT) of a real gas is applicable
at high pressure -
(A) Z = 1 – a / Vm RT (B) Z = 1 + a / Vm RT
(C) Z = 1 + pb / RT (D) Z = 1 – pb / RT
E-34. Which of the following expressions of compression factor Z (= pVm / RT) of a real gas is applicable
at low pressure -
(A) Z = 1 – a / Vm RT (B) Z = 1 + a / Vm RT
(C) Z = 1 + pb / RT (D) Z = 1 – pb / RT

E-35. Which of the following expressions between the van der Waals constant b and the radius r of spherical
molecules is correct -
(A) A
3
Nr
3
4
b 





 (B) 





 3
r
3
4
b (C) A
3
Nr
3
4
2b 





 (D) A
3
Nr
3
4
4b 






E-36. The value of compression factor at the critical state of a van der Waals gas is -
(A) 3/8 (B) 8/3 (C) 1 (D) 5/8
E-37. A gas with formula CnH2n+2 diffuses through the porous plug at a rate one sixth of the rate of diffusion
of hydrogen gas under similar conditions. The formula of gas is –
(A) C2H6 (B) C10H22 (C) C5H12 (D) C6H14
E-38. The values of critical temperature (TC) and critical pressure (PC) for some gases are given below. Which
of the gases can not be liquefied at 100 K and 50 atm?
Gases (i) (ii) (iii) (iv)
PC (atm) 2.2 14 35 45
TC (K) 5.1 33 127 140
(A) (iv) only (B) (i) only (C) (i) and (ii) (D) (iii) and (iv)
E-39. Let f1 and f2 be the fractions of molecules in the range c and c + dc for SO2 at 2T and O2 and T,
respectively which of the following expressions is correct -
(A) f1 > f2 (B) f1 < f2
(C) f1 = f2 (D) f1 and f2 cannot be correlated
PART - II : MISCELLANEOUS QUESTIONS
COMPREHENSION
Read the following passage carefully and answer the questions.
Comprehension # 1
One of the important approach to the study of real gases involves the analysis of a parameter Z called the
compressibility factor Z =
RT
PVm
where P is pressure, Vm
is molar volume, T is absolute temperature and R
is the universal gas constant. Such a relation can also be expressed as Z = 







idealm
realm
V
V
(where Vm ideal
and Vm real
are the molar volume for ideal and real gas respectively). Gas corresponding Z > 1 have repulsive tendencies
among constituent particles due to their size factor, whereas those corresponding to Z < 1 have attractive
forces among constituent particles. As the pressure is lowered or temperature is increased the value of Z
approaches 1. (reaching the ideal behaviour)
1. Choose the conclusions which are appropriate for the observation stated.
Observation Conclusion
I . Z = 1 I. The gas need not be showing the ideal behaviour
II. Z > 1 II. On applying pressure the gas will respond by
increasing its volume
III. Z < 1 III. The gas has the ability to be liquefied.
IV. Z  1 for low P IV. The gas is approaching the ideal behaviour.
(A) All conclusions are true (B) Conclusions I, II & IV are true
(C) Conclusions I,III & IV are true (D) Conclusions III & IV are true

2. For a real gas ‘G’ Z > 1 at STP Then for ‘G’ :
Which of the following is true :
(A) 1 mole of the gas occupies 22.4 L at NTP
(B) 1 mole of the gas occupies 22.4 L at pressure higher than that at STP (keeping temperature constant)
(C) 1 mole of the gas occupies 22.4 L at pressure lower than that at STP (keeping temperature constant)
(D) None of the above
3. Following graph represents a pressure (P) volume (V) relationship at a fixed temperature (T) for n moles of a
real gas. The graph has two regions marked (I) and (II). Which of the following options is true.
(A) Z < 1 in the region (II) (B) Z = 1 in the region (II)
(C) Z = 1 for the curve (D) Z approaches 1 as we move from region (II) to region (I)
Comprehension 2.
Real gases deviates from ideal behaviour because of the following two faulty assumptions of kinetic
theory:
(i) The actual volume occupied by molecules is negligible as compared to the total volume of the gas.
(ii) The forces of attraction and repulsion between molecules of the gas are negligible. The extent of
deviation of a real gas from ideal behaviour is expressed in terms of compressibility factor(z)
Hence suitable corrections were applied to the ideal gas equation. So that it can also explain the
behavior of real gases. The equation obtained by applying the two corrections to the usual gas equation
is known as Vander Waal equation.
1. Volume correction :
Corrected (ideal) volume = (V – nb)
where b is the effective volume of the molecules.
2. Pressure correction (Intermolecular attraction correction)
Corrected (ideal) pressure (P + P’)
However P’ = 2
2
V
an
 The Van der Waal’s equation becomes








 2
2
V
an
P (V – nb) = nRT
on the basis of the above passage, answer the following questions.
4. 0.5 value of compressibility factor (Z) indicates that the gas -
(A) shows positive deviation from ideal behaviour
(B) negative deviation from the ideal gas
(C) either of the two
(D) the factor is insufficient
5. Vander Waal equation is obeyed by the real gases -
(A) over a wide range of temperature and pressure
(B) over all temperatures
(C) over all pressures
(D) at high temperature

6. At low pressure, the Vander Wall’s equation for 1 mole gas is -
(A) PV = RT +
V
a
(B) PV = RT –
V
a
(C) PV = RT + 2
V
a
(D) PV = RT – 2
V
a
7. Identify the wrong statement related to the above graph :
(A) Between 50 K and 150 K temperature and pressure ranging from 10
atm to 20 atm matter may have liquid state.
(B) Zero is the maximum value of the slope of P-V Curve
(C) If vander wall equation of state is applicable above critical temperature
then cubic equation of Vm
will have one real and two imaginary roots.
(D) At 100 K and pressure below 20 atm it has liquid state only
MATCH THE COLUMN
8. Match the following
List I List II
(A) Urms
/Uav
(i) 1.22
(B) Uav
/Ump
(ii) 1.13
(C) Urms
/Ump
(iii) 1.08
(A) (A)-(iii), (B)-(ii), (C)-(i) (B) (A)-(i), (B)-(ii), (C)-(iii)
(C) (A)-(iii), (B)-(i), (C)-(ii) (D) (A)-(ii), (B)-(iii), (C)-(i)
9. Vander Waal’s equation for
List-I List-II
(A) High pressure (i) PV = RT + Pb
(B) Low pressure (ii) PV = RT –a/V
(C) Force of attraction is negligible (iii) PV = RT + a/V
(D) Volume of molecules is negligible (iv) 



  2V
aP (V – b) = RT
(A) (A)-(i), (B)-(ii), (C)-(i), (D)-(ii) (B) (A)-(i), (B)-(ii), (C)-(iii), (D)-(iv)
(C) (A)-(iv), (B)-(iii), (C)-ii, (D)-i (D) (A)-(iv), (B)-(ii), (C)-(iii), (D)-(i)
10. Match the column
Column I Column II
(i) Boyle’s law (A) Mass = constant
(ii) Charle’s law (B) Pressure = constant
(iii) Gaylussac’s law (C) Temperature = constant
(iv) Avogadro’s law (D) Volume = constant
(A) (i) A, C ; (ii) A,D ; (iii) A,B ; (iv) B, C (B) (i) B,D ; (ii) A,C ; (iii) A,C ; (iv) A, B, C, D
(C) (i) A,D ; (ii) D,C ; (iii) A,C ; (iv) A, C (D) (i) B,C ; (ii) C,D ; (iii) D,C ; (iv) A, D

Column I Column II
(i) T1
> T2
> T3
(A)
1/V
P T1
T2
T3
(ii) Charle’s Law (B)
V
Temperature-constant
Pressure-constant
n (no. of moles)
(iii) Boyle’s law (C)
V
Temperature-constant
Mass-constant
P
(iv) Avogadro’s law (D)
V
Pressure-constant
T
T
(A) (i) -CD; (ii)-CD; (iii)-D ; (iv) -B (B) (i) - AD; (ii) - BC; (iii)-A ; (iv) - B
(C) (i) -AC; (ii)- CD; (iii)-A ; (iv)-D (D) (i) - A; (ii) - D; (iii) - A,C ; (iv) - B
Column I Column II
(i) Z <
nRT
PV
(A) Positive deviation
(ii) Z >
nRT
PV
(B) negative deviation
(iii) H2
, He (C) Small size of atom
(iv) N2
, CO2
(D) molecular attraction
(A) (i) - A, D ; (ii) - C, D ; (iii) - A,B ; (iv) - B, C
(B) (i)- B, D ; (ii) - A, C ; (iii) - A, C ; (iv) - A, B, C, D
(C) (i)- A, D ; (ii) - D, C ; (iii) - A, C ; (iv) - A, C
(D) (i)- B, C ; (ii) - C, D ; (iii) - D, C ; (iv) - A, D

13. For a fixed amount of the gas match the two column :
Column-I Column-II
(A) (p) T1
> T2
> T3
(B) (q) P1
> P2
> P3
(C) (r) V1
> V2
> V3
(D) (s) d1
> d2
> d3
ASSERTION / REASONING
DIRECTIONS :
Each question has 5 choices (A), (B), (C), (D) and (E) out of which ONLY ONE is correct.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(C) Statement-1 is True, Statement-2 is False.
(D) Statement-1 is False, Statement-2 is True.
(E) Statement-1 and Statement-2 both are False.
14. Statement-1 : Plot of P Vs. 1/V is a straight line for constant temperature and fixed amount of ideal gas. .
Statement-2 : Pressure is directly proportional to volume.
15. Statement-1 :Absolute zero is a theoretically possible temperature at which the volume of the gas becomes
zero.
Statement-2 : The total kinetic energy of the molecules is zero at this temperature.
16. Statement-1 : In a container containing gas ‘A’ at temp 400 K, some more gasAat temp. 300 K is introduced.
The pressure of the system increases.
Statement-2 : Increase in gaseous particles increases the number of collisions among the molecules.

17. Statement-1 : Gas with lower molar mass will effuse or diffuse faster.
Statement-2 : Total Kinetic Energy of any gas depends upon its molar mass.
18. Statement-1 : Pressure exerted by a mixture of gases is equal to the sum of their partial pressures.
Statement-2 : Reacting gases react to form a new gas having pressure equal to the sum of both.
19. Statement-1 : CH4,CO2 has value of Z (compressibility factor) less than one, generally.
Statement-2 : Z < 1 is due to repulsive forces among the molecules.
20. Statement-1 : Critical temperature of the gas is the temperature at which it occupies 22.4 L of volume.
Statement-2 : Molar volume of every gas at NTP is 22.4 L.
21. Statement-1 : Excluded volume or co-volume equals to (v–nb) for n moles gas.
Statement-2 : Co-volume depends on the effective size of gas molecules.
22. Statement-1 : Gases like N2, O2 behave as ideal gases at high temperature and low pressure.
Statement-2 : Molecular interaction diminishes at high temperature and low pressure .
23. Statement-1 : Most probable velocity is the velocity possessed by maximum fraction of molecules at the
same temperature.
Statement-2 : On collision, more and more molecules acquire higher speed at the same temperature.
24. Statement-1 : Noble gases can be liquefied.
Statement-2 : Attractive forces can exist between non-polar molecules.
25. Statement-1 : The diffusion rate of oxygen is smaller than that of nitrogen under same conditions of T and P.
Statement-2 : Molecular mass of nitrogen is smaller than that of oxygen.
TRUE / FALSE
26. The volume of a gas always increases when the temperature is increased.
27. Equal volumes of helium and neon contain equal number of atoms.
28. The times of diffusion of equal volumes of two gases, under similar conditions of temperature and
pressure, are inversely proportional to their densities.
29. A gas cannot be liquified above its critical temperature.
30. Kinetic energy of a molecule is zero at 0°C.
31. The volume occupied by 32 g of oxygen is greater than that occupied by 16 g of methane, both being at the
same T and P. (assume ideal behaviour)
32. A real gas can be liquefied if its temperature is greater than its critical temperature.
33. The increase in volume per degree rise in Celsius temperature at constant pressure is V0/273.15, where V0
is the volume of gas at 0 K.
34. The rate of diffusion is directly proportional to the square root of its kelvin temperature and also inversely
proportional to the square root of its molar mass.
35. The volume of a fixed mass of gas at constant pressure varies nonlinearly with temperature expressed in
Celsius whereas it varies linearly when expressed in kelvin.
36. Kinetic energy of gaseous molecules is zero at 00C.
37. The term (Vm – b) in Vander Waals' equation represents the available volume where molecules of the gas can
move.

PART - I : MIXED OBJECTIVE
Single choice type
1. I, II, III are three isotherms respectively at T1, T2 and T3 as shown in graph. Temperature will be in order.
(A) T1 = T2 = T3 (B) T1 < T2 < T3 (C) T1 > T2 > T3 (D) T1 > T2 = T3
2. Oxygen and cyclopropane at partial pressures of 570 torr and 170 torr respectively are mixed in a gas
cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen?
(A)
740
170
= 0.23 (B)
42
170
/ 




 

32
70
42
170
= 0.19
(C)
32570
42170


= 0.39 (D)
570
170
= 0.30
3. A vessel of volume 5 litre contains 1.4 g of nitrogen at a temperature 1800 K. The pressure of the gas if 30%
of its molecules are dissociated into atoms at this temperature is :
4. One litre of a gaseous mixture of two gases effuses in 311 seconds while 2 litres of oxygen takes 20 minutes.
The vapour density of gaseous mixture containing CH4 and H2 is
(A) 4 (B) 4.3 (C) 3.4 (D) 5
5. Pure O2 diffuses through an aperture in 224 second, whereas mixture of O2 and another gas containing 80%
O2 diffuses from the same in 234 second. The molecular mass of gas will be
(A) 45.6 (B) 48.6 (C) 50 (D) 46.6
6. Three footballs are respectively filled with nitrogen, hydrogen and helium. If the leaking of the gas occurs with
time from the filling hole, then the ratio of the rate of leaking of gases )r:r:r( HeHN 22
from three footballs (in
equal time interval) is
(A)  7:14:1 (B)  1:7:14 (C)  14:1:7 (D)  14:7:1
7. A straight glass tube as shown, has 2 inlets X & Y at the two ends of 200 cm long tube. HCl gas through inlet
X and NH3 gas through inlet Y are allowed to enter in the tube at the same time and pressure at a point P
inside the tube. The distance of point P from X is :
(A) 118.9 cm (B) 81.1 cm (C) 91.1 cm (D) 108.9 cm
8. Ateacher enters a classroom from front door while a student from back door. There are 13 equidistant rows
of benches in the classroom. The teacher releases N2O, the laughing gas, from the first bench while the
student releases the weeping gas (C6H11OBr) from the last bench. At which row will the students starts
laughing and weeping simultaneously
(A) 7 (B) 10 (C) 9 (D) 8

9. A sample of a gas was heated from 300C to 600C at constant pressure. Which of the following statement(s)
is/are true.
(A) Kinetic energy of the gas is doubled (B) Boyle’s law will apply
(C) Volume of the gas will be doubled (D) None of the above
10. An amount of 1.00 g of a gaseous compound of boron and hydrogen occupies 0.820 liter at 1.00 atm and at
30C. The compound is (R = 0.0820 liter atm mole1 0K1; at. wt: H = 1.0, B = 10.8)
(A) BH3 (B) B4H10 (C) B2H6 (D) B3H12
11. A certain volume of argon gas (Mol. Wt. = 40) requires 45 s to effuse through a hole at a certain pressure and
temperature. The same volume of another gas of unknown molecular weight requires 60 s to pass through
the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is :
(A) 53 (B) 35 (C) 71 (D) 120
12. On the surface of the earth at 1 atm pressure, a balloon filled with H2 gas occupies 500 mL. This volume is
5/6 of its maximum capacity. The balloon is left in air. It starts rising. The height above which the balloon will
burst if temperature of the atmosphere remains constant and the pressure decreases 1 mm for every 100 cm
rise of height is
(A) 120 m (B) 136.67 m (C) 126.67 m (D) 100 m
13. A chemist has synthesized a greenish yellow gaseous compound of chlorine and oxygen and finds that its
density is 7.71 g/L at 36°C and 2.88 atm. Then the molecular formula of the compound will be
(A) ClO3 (B) ClO2 (C) ClO (D) Cl2O2
14. Which of the following expression correctly represents the relationship between the average kinetic energy of
CO and N2 molecules at the same temperature.
(A) E (CO) > E (N2)
(B) E (CO) < E (N2)
(C) E (CO) = E (N2)
(D) Cannot be predicted unless volumes of the gases are given
15. A 40 ml of a mixture of H2 and O2 at 18 ºC and 1 atm pressure was sparked so that the formation of water
was complete. The remaining pure gas had a volume of 10 ml at 18ºC and 1 atm pressure. If the remaining
gas was H2, the mole fraction of H2 in the 40 ml mixture is :
(A) 0.75 (B) 0.5 (C) 0.65 (D) 0.85
16. A real gas most closely approaches the behaviour of an ideal gas at -
(A) 15 atm and 200 K (B) 1 atm and 273 K
(C) 0.5 atm and 500 K (D) 15 atm and 500 K
17. Calculate the compressibility factor for CO2, if one mole of it occupies 0.4 litre at 300 K and 40 atm.
Comment on the result.
(A) 0.40, CO2 is more compressible than ideal gas
(B) 0.65, CO2 is more compressible than ideal gas
(C) 0.55, CO2 is more compressible than ideal gas
(D) 0.62, CO2 is more compressible than ideal gas
18. Which of following statement (s) is true
 – Slope of isotherm at critical point is maximum.
 – Larger is the value of TC
easier is the liquification of gas.
 – Vander waals equation of state is applicable below critical temperature at all pressure.
(A) only  (B) &  (C)& (D) only 

19. Consider the following statements:
The coefficient B in the virial equation of state
(i) is independent of temperature
(ii) is equal to zero at boyle temperature PVm = RT 







 ..........
V
C
V
B
1 2
mm
(iii) has the dimension of molar volume
Which of the above statements are correct.
(A) i and ii (B) i and iii (C) ii and iii (D) i, ii and iii
20. Consider the following statements: If the van der Waal’s parameters of two gases are given as
a (atm lit2 mol–2)b (lit mol–1)
Gas X: 6.5 0.056
Gas Y: 8.0 0.011
then (i) : VC (X) < VC (Y) (ii) : PC (X) < PC (Y) (iii) : TC (X) < TC(Y)
Select correct alternate:
(A) (i) alone (B) (i) and (ii) (C) (i), (ii) and (iii) (D) (ii) and (iii)
21. Select correct statement(s):
(A) we can condense vapours simply by applying pressure
(B) to liquify a gas one must lower the temperature below TC and also apply pressure
(C) at Tc, there is no distinction between liquid and vapour state, hence density of the liquid is nearly equal
to density of the vapour
(D) all the statements are correct statements
22. At Boyle's temperature, the value of compressibility factor Z = (PVm / RT = Vreal/Videal) has a value of 1, over
a wide range of pressure. This is due to the fact that in the van der Waal’s equation
(A) the constant 'a' is negligible and not 'b'
(B) the constant 'b' is negligible and not 'a'
(C) both the constant 'a' and 'b' are negligible
(D) the effect produced due to the molecular attraction compensates the effect produced due to the molecular
volume
23. The critical density of the gas CO2 is 0.44 g cm–3 at a certain temperature. If r is the radius of the molecule,
r3 in cm3 is approximately. (N is Avogadro number)
(A) N
25
 (B) N
100
 (C)
N
6

(D) 
25
24. The curve of pressure volume (PV) against pressure (P) of the gas at a particular temperature is as shown,
according to the graph which of the following is incorrect (in the low pressure region):
(A) H2
and He shows +ve deviation from ideal gas equation.
(B) CO, CH4
and O2
show negative deviation from ideal gas equation.
(C) H2
and He show negative deviation while CO2
, CH4
and O2
show positive deviation.
(D) H2
and He are less compressible than that of an ideal gas while CO2
, CH4
and O2
more compressible than
that of ideal gas.

25. For a real gas the P-V curve was experimentally plotted and it had the following appearance. With respect to
liquifaction. Choose the correct statement.
(A) at T = 500 K, P = 40 atm, the state will be liquid.
(B) at T = 300 K, P = 50 atm, the state will be gas
(C) at T < 300 K, P > 20 atm, the state will be gas
(D) at 300 K < T < 500 K, P > 50 atm, the state will be liquid.
26. The ratio of the root mean square velocity of H2
at 50 K and that of O2
at 800 K is
(A) 4 (B) 2 (C) 1 (D) 1/4
27. If for two gases of molecular weights MA
and MB
at temperature TA
and TB
, TA
MB
= TB
MA
, then which
property has the same magnitude for both the gases.
(A) density (B) pressure (C) KE per mole (D) Urms
28. What percent of a sample of nitrogen must be allowed to escape if its temperature, pressure and
volume are to be changed from 220°C, 3 atm and 1.65 L to 100 °C, 0.7 atm and 1 L respectively?
(A) 41.4 % (B) 8.18 % (C) 4.14 % (D) 81.8 %.
29. Assuming that air is 79 % by mole of N2
, 20 % O2
and 1 % Ar , the density of air at 25 °C and 1 atm
is :
(A) 1.18 g/lit (B) 1.08 g/lit (C) 1.28 g/lit (D) 1.0 g/lit.
30. 0.2 g of a gas X occupies a volume of 0.44 L at same pressure and temperature. Under identical
conditions of P and T, 0.1 g of CO2
gas occupies 0.32 L. Gas X can be :
(A) O2
(B) SO2
(C) NO (D) C4
H10
.
31. A flask containing 12 g of a gas of relative molecular mass 120 at a pressure of 100 atm was evacuated
by means of a pump until the pressure was 0.01 atm. Which of the following is the best estimate of the
number of molecules left in the flask
23 –1
0(N 6 10 mol )  .
(A) 6  1019
(B) 6  1018
(C) 6  107
(D) 6  1013
32. The behaviour of a real gas is usually depicted by plotting compressibility factor Z versus P at a
constant temperature. At high temperature and high pressure, Z is usually more than one. This fact can
be explained by van der Waals equation when
(A) the constant ‘a’ is negligible and not ‘b’ (B) the constant ‘b’ is negligible and not ‘a’
(C) both constant ‘a’ and ‘b’ are negligible (D) both the constant ‘a’ and ‘b’ are not negligible.
33. Under identical conditions of temperature, the density of a gas X is three times that of gas Y while
molecular mass of gas Y is twice that of X. The ratio of pressures of X and Y will be :
(A) 6 (B) 1/6 (C) 2/3 (D) 3/2.
34. X ml of H2
gas effuses through a hole in a container in 5 seconds. The time taken for the effusion
of the same volume of the gas specified below under identical conditions is :
(A) 10 seconds : He (B) 20 seconds : O2
(C) 25 seconds : CO (D) 35 seconds : CO2
.
35. One mole of N2
O4
(g) at 300 K is kept in a closed container under one atmosphere pressure. It is heated
to 600 K when 20% by mass of N2
O4
(g) decomposes to NO2
(g). The resultant pressure is :
(A) 1.2 atm (B) 2.4 atm (C) 2 atm (D) 1 atm.

More than one choice type
36. A gas cylinder containing cooking gas can withstand a pressure of 14.9 atmosphere. The pressure guaze of
cylinder indicates 12 atmosphere at 27 ºC. Due to sudden fire in the building temperature starts rising. The
temperature at which cylinder will explode is :
(A) 372.5 K (B) 99.5 ºC (C) 199 ºC (D) 472.5 k
37.
For the above graph, drawn for two different samples of gases at two different temperatures. T1
and T2
, which
of the following statements is/are necessarily true.
(A) If T2
> T1
, MB
is necessarily greater than MA
(B) If T1
> T2
, MA
is necessarily greater than MB
(C)
B
2
M
T
>
A
1
M
T
(D) Nothing can be predicted
38. Which of the following statements are correct ?
(A) Helium diffuses at a rate 8.65 times as much as CO does.
(B) Helium escapes at a rate 2.65 times as fast as CO does.
(C) Helium escapes at a rate 4 times as fast as CO2 does.
(D) Helium escapes at a rate 4 times as fast as SO2 does.
39.
In the above maxwellian plot at two different temperature which of the following statements may be true
(A) Area under the two plots is the same
(B) Fraction of molecules with speed u1 at T1 > fraction of molecules having speed u2 at T2
(C) U2 > U1 and T2 > T1
(D) UMPS at T1 < UMPS at T2 ; URMS at T1 < URMS at T2
40. Which of the following are correct statements ?
(A) vander Waals constant ‘a’ is a measure of attractive force
(B) van der Waals constant ‘b’ is also called co-volume or excluded volume
(C) ‘b’ is expressed in L mol–1
(D) ‘a’ is expressed in atm L2 mol–2
41. A gas can be easily liquefied
(A) When its inversion temperature equals the Boyle temperature
(B) under reversible adiabatic expansion
(C) under pressure when it is cooled to below the critical temperature
(D) at low pressure and above the critical temperature.
42. According to Charles’s law :
(A)
T
1
V  (B) K
dT
dV
P






(C) K
dV
dT
P






(D) 0
T
V
T
1
2







43. The temperature of ideal gas can be increased by
(A) decreasing the volume and pressure but keeping the amount constant
(B) increasing the pressure but keeping the volume and amount constant
(C) decreasing the amount but keeping the volume and pressure constant
(D) increasing the amount but keeping the volume and pressure constant

44. For a gaseous system, the pressure can be increased by
(A) increasing the volume of container but keeping the amount and temperature constant
(B) increasing the amount of gas at constant temperature and volume
(C) decreasing the volume of container but keeping the amount and temperature constant
(D) decreasing temperature but keeping amount and volume constant
45. Boyle’s law is represented by -
(A) (B) (C) (D)
46. The time taken for effusion of 32 ml of oxygen will be the same as the time taken for effusion under
identical conditions of –
(A) 64 ml of H2
(B) 50 ml of N2
(C) 27.3 mol of CO2
(D) 22.62 ml of SO2
47. Which of the following expressions is correct on the basis of the ideal gas equation?
(A) PV =
AN
N
RT (B) PV= NkB
T (C) PV =
w

RT (D) PV =
w
TMkB
48. Which of the following statements are correct?
(A) Helium diffuses at a rate 8.65 times as much as CO does.
(B) Helium escapes at a rate 2.65 times as fast as CO does.
(C) Helium escapes at a rate 4 times as fast as CO2
does.
(D) Helium escapes at a rate 4 times as fast as SO2
does.
49. Which of the following pair of gases will have same rate of diffusion under similar condition
(A) H2
& He (B) CO2
& N2
O (C) CO & C2
H4
(D) NO & CO
50. Which of the following quantities is the same for all ideal gases at the same temperature?
(A) The kinetic energy of 1 mol (B) the kinetic energy of 1 g
(C) The number of molecules in 1 mol (D) The number of molecules in 1 g
51. Four gas balloons A, B, C, D of equal volumes containing H2
, H2
O, CO, CO2
respectively were pricked
with needle and immersed in a tank containing CO2
. Which of them will shrink after some time.
(A) A (B) B (C) C (D) Both A and D
52. According to the kinetic theory of gases.
(A) the pressure exerted by a gas is proportional to the mean square speed of the molecules.
(B) the pressure exerted by a gas is proportional to the root mean square speed of the molecules
(C) the root mean square speed is inversely proportional to the temperature.
(D) the mean translational kinetic energy of the molecule is directly proportional to the absolute
temperature.
53. Indicate the correct statement for equal volumes of N2
(g) and CO2
(g) at 298 K and 1 atm.
(A) The average translational KE per molecule is the same for N2
and CO2
(B) The rms speed remains constant for both N2
and CO2
.
(C) The density of N2
is less than that of CO2
.
(D) The total translational KE of both N2
and CO2
is the same.
54. Which of the following is correct for critical temperature?
(A) It is the highest temperature at which liquid and vapour can coexist.
(B) Beyond this temperature, there is no distinction between the two phases and a gas cannot be
liquefied by compression.
(C) At this temperature, the surface tension of the system is zero.
(D) At this temperature, the gas and the liquid phases have different critical densities.

PART - II : SUBJECTIVE QUESTIONS
1. A gas is present at a pressure of 2 atm. What should be the increase in pressure so that the volume of
the gas can be decreased to 1/4th
of the initial value if the temperature is maintained constant.
2. A sample of gas occupies 10 litre under a pressure of 1 atmosphere. What will be its volume if the
pressure is increased to 2 atmospheres? Assume that the temperature of the gas sample does not
change.
3. The reading of a faulty barometer is 700 mm of Hg. When actual pressure is 750 mm of Hg. The length of the
air column trapped in this case is 10 cm .Find the actual value of the atmospheric pressure when reading of
this barometer is 750 mm of Hg.Assume that the length of the Barometer tube above mercury surface in the
container remains constant.
4. (a) In each of the following examples, find the pressure of the trapped gas.
(b)
(c)
Pg
= 75 + 10 cos .
5. 1 mole of an ideal gas at constant atmospheric pressure is heated to increase its volume by 50% of
initial volume. The change in temperature made was 300 K to T K. Than calculate final temperature.
6. A balloon of diameter 20 m weights 100 kg. Calculate its pay-load, if it is filled with He at 1.0 atm and 27ºC.
Density of air is 1.2 kg m–3
. [R = 0.0082 dm3
atm K–1
mol–1
]

7. The temperature of a certain mass of a gas is doubled. If the initially the gas is at 1 atm pressure. Find the
% increase in pressure ?
8. Pressure of gas contained in a closed vessel is increased by 0.4%, when heated by 1ºC. Calculate its
final temperature. Assume ideal nature.
9. An open vessel at 27°C is heated until 3/5th
of the air in it has been expelled. Assuming that the volume
of the vessel remains constant find
(A) the air escaped out if vessel is heated to 900K.
(B) temperature at which half of the air escapes out.
10. 5g of ethane is confined in a bulb of one litre capacity. The bulb is so weak that it will burst if the
pressure exceeds 10 atm. At what temperature will the pressure of gas reach the bursting value?
11. The density of an unknown gas at 98°C and 0.974 atm is 2.5 × 10–3
g/ml. What is the mol wt. of gas?
12. When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of
780 ml. What is the molecular formula of sulphur vapours under these conditions? Calculate the
vapour density also.
13. Calculate the mean molar mass of a mixture of gases having 7 g of Nitrogen, 22 g of CO2
and 5.6 litres of CO
at STP.
14. A gaseous mixture contains 55% N2
, 20% O2
, and 25% CO2
by mass at a total pressure of 760 mm.
Calculate the partial pressure of each gas.
15. A mixture containing 1.6 g of O2
, 1.4g of N2
and 0.4 g of He occupies a volume of 10 litre at 27°C.
Calculate the total pressure of the mixture and partial pressure of each compound.
16. In a tube of length 5 m having 2 identical holes at the opposite ends. H2
& O2
are made to effuse into the tube
from opposite ends under identical conditions. Find the point where gases will meet for the first time.
17. Assume that you have a sample of hydrogen gas containing H2
, HD and D2
that you want to separate into
pure components (H = 1
H and D = 2
H). What are the relative rates of diffusion of the three molecules
according to Graham’s law ?
18. In a container of capacity 1 litre there are 1023
molecules each of mass 10–22
gms. If root mean square speed
is 105
cm/sec then calculate pressure of the gas.
19. Arrange following in decreasing ’a’ factor ; (H2
O, CO2
,Ar)
20. Arrange following gases according to ‘a’ ; He, Ar, Ne, Kr.
21. Arrange the following according to liquification pressure; n-pentane ; iso-pentane , neo pentane.
22. Two vander waals gases have same value of b but different a values. Which of these would occupy greater
volume under identical conditions ?

23. The vander waals constant for HCI are a = 371.843 KPa.dm6
mol–2
and b = 40.8 cm3 mol–1 find the critical
constant of this substance.
24. The vander waals constant for gases A, B and C are as follows :
Gas a/dm6
KPa mol–2
b/dm3
mol–1
A 405.3 0.027
B 1215.9 0.030
C 607.95 0.032
Which gas has
(i) Highest critical temperature
(ii) The largest molecular volume
(iii) Most ideal behaviour around STP ?
25. In a container of capacity 1 litre, air and some liquid water is present in equilibrium at total pressure of 200 mm
of Hg. This container is connected to another one litre evacuated container. Find total pressure inside the
container when equilibrium is again stablised (aqueous tension or vapour pressure at this temp. is 96 mm Hg).
26. Carbon dioxide gas (CO2
) measuring 1 litre is passed over heated coke the total volume of the gases coming
out becomes 1.6 litre. Find % conversion of CO2
into carbon monoxide.
27. 100 ml of hydrocarbon is mixed with excess of oxygen and exploded. On cooling, the mixture was reported
to have a contraction of 250 ml. The remaining gas when passed through a solution of aqueous KOH, the
mixture shows a further contraction of 300 ml. Find molecular formula of the hydrocarbon.
28. 100 ml of an hydrocarbon is burnt in excess of oxygen in conditions so that water formed gets condensed out
the total contraction in volume of reaction mixture was found to be 250 ml when the reaction mixture is further
exposed to aqueous KOH a further contraction of 300 ml is observed find molecular formula of hydrocarbon.
29. Calculate the total pressure in a 10 L cylinder which contains 0.4 g of helium, 1.6g of oxygen and 1.4
g of nitrogen at 27°C. Also calculate the partial pressure of helium gas in the cylinder. Assume ideal
behaviour for gases.
30. Assuming that N2
molecules is spherical and its radius is 2×10–10
meter, calculate the empty space in
one mole of N2
gas at NTP.
31. Using Vander Waals equation calculate the pressure exerted by one mole of CO2
. Its volume at 373 K
is 0.05 dm3
. Given a = 3.592 atm L2
mol–2
and b = 0.0426 L mol–1
.
32. Density of a mixture of CO and CO2
at 303 K and 73 cm of Hg is 1.5 gram/litre. What is the mole
percent of two gases in the mixture.
33. Two grams of gas A are introduced in a evacuated flask at 25°C. The pressure of the gas is 1 atm. Now
3g of another gas B is introduced in the same flask, the total pressure becomes 1.5 atm. Calculate
(A) the ratio of molecular mass AM and BM (B) volume of the vessel, if A is O2
.
34. One litre O2
and one litre H2
are taken in a vessel of 2 litre at STP. These gases are made to react to
form water. Calculate (A) moles and weight of water formed. (B) amount of gas left in the vessel. (C)
Total pressure of the gas at 100°C.
35. At 27 °C vapour density of the mixture of NO2
and N2
O4
is 38.3. Calculate the moles of NO2
in 100
g mixture.

PART - I : IIT-JEE PROBLEMS (PREVIOUS YEARS)
Marked Questions are having more than one correct option.
1. The compressibility of a gas is less than unity at S.T.P. therefore, [JEE-2000, 1/35]
(A) Vm > 22.4 litres (B) Vm < 22.4 litres (C) Vm = 22.4 litres (D) Vm = 44.8 litres
2. The rms velocity of hydrogen is 7 times the rms velocity of nitrogen. If T is the temperature of the gas, then
[JEE-2000, 1/35]
(A) )N()H( 22
TT  (B) )N()H( 22
TT  (C) )N()H( 22
TT  (D) )N()H( 22
T7T 
3. At 100°C and 1 atm, if the density of liquid water is 1.0 g cm–3 and that of water vapour is 0.0006 g cm–3, that
the volume occupied by water molecules in 1 liter of st eam at that temperature is :[JEE-2000, 1/35]
(A) 6 cm3 (B) 60 cm3 (C) 0.6 cm3 (D) 0.06 cm3
4. The root mean square velocity of an ideal gas at constant pressure varies with density (d) as :
[JEE-2001, 1/35]
(A) d2 (B) d (C) d (D) d1
5. The compression factor (compressibility factor) for 1 mole of a van der Waals’ gas at 0ºC and100 atmosphere
pressure is found to be 0.5. Assuming that the volume of gas molecule is negligible, calculate the van der
Waals’. constant a. [JEE-2001, 5/100]
6. Which of the following volume (v)-temperature (T) plots represent the behaviour of one mole of an ideal gas at
one atmospheric pressure. [JEE-2002, 3/90]
(A) (B)
(C) (D)
7. The density of the vapours of a substance at 1 atm pressure and 500 K is 0.36 Kg m–3.The vapour effuses
through a small hole at a rate of 1.33 times faster than oxygen under the same conditions.
(a) Determine (i) molecular weight (ii) molar volume (iii) compression factor(z) of the vapours and (iv) which
forces among gas molecules are dominating, the attractive or repulsive.
(b) If the vapours behave ideally at 1000 K determine the average translational kinetic energy of a molecule.
[JEE-2002, 5/60]
8. The average velocity of gas molecules is 400 m/sec calculate its r.m.s. velocity at the same temperature.
[JEE-2003, 2/60]
9. For one mole of gas the average kinetic energy is given as E. The Urms of gas is : [JEE-2004, 3/84]
(A)
M
E2
(B)
M
E3
(C)
M3
E2
(D)
M2
E3
10. Ratio of rates of diffusion of He and CH4 (under identical conditions). [JEE-2005, 3/84]
(A)
2
1
(B) 3 (C)
3
1
(D) 2

11.* Figure displays the plot of the compression factor Z verses p for a few gases [JEE-2006, 5/184]
IV
III
I
II
Which of the following statements is/are correct for a van-der waals gas :
(A) The plot I is applicable provided the vander waals constant a is negligible.
(B) The plot II is applicable provided the vander waals constant b is negligible.
(C) The plot III is applicable provided the vander waals constants a and b are negligible.
(D) The plot IV is applicable provided the temperature of the gas is much higher than its critical temperature.
12. Match gases under specified conditions listed in Column-I with their properties / laws in Column-II.
[JEE-2007, 6/162]
Column-I Column-II
(A) Hydrogen gas (P = 200 atm, T = 273 K) (p) compressibility factor  1
(B) Hydrogen gas (P ~ 0, T = 273 K) (q) attractive forces are dominant
(C) CO2
(P = 1 atm, T = 273 K) (r) PV = nRT
(D) Real gas with very large molar volume (s) P (V – nb) = nRT
13.* A gas described by van der Waals equation [JEE-2008, 4/82]
(A) behaves similar to an ideal gas in the limit of large molar volumes
(B) behaves similar to an ideal gas is in limit of large pressures
(C) is characterised by van der Waals coefficients that are dependent on the identity of the gas but are
independent of the temperature.
(D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally
14. The term that corrects for the attractive forces present in a real gas in the vander Waals equation is :
[JEE-2009, 3/80]
(A) nb (B) 2
2
V
an
(C) – 2
2
V
an
(D) –nb
15. At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable
speed of gas Y at 60 K. The molecular weight of the gas Y is. [JEE-2009, 4/80]
Paragraph for Question Nos. 16 to 17
A fixed mass 'm' of a gas is subjected to transformation of states from K to L to M to N and back to K as
shown in the figure. [JEE-2013, P-2]
16. The pair of isochoric processes among the transformation of states is :
(A) K to L and L to M (B) L to M and N to K
(C) L to M and M to N (D) M to N and N to K
17. The succeeding operations that enable this transformation of states, are :
(A) Heating, cooling, heating, cooling (B) Cooling, heating, cooling, heating
(C) Heating, cooling, cooling, heating (D) Cooling, heating, heating, cooling

PART - II : AIEEE PROBLEMS (PREVIOUS YEARS)
1. Value of gas constant R is : [AIEEE- 2001]
(1) 0.082 litre atm. (2) 0.987 cal mol –1
K–1
(3) 8.3 J mol–1
K–1
(4) 83 erg mol–1
K–1
2. Kinetic theory of gases proves : [AIEEE- 2002]
(1) Only Boyle’s law (2) Only Charle’s law
(3) OnlyAvogardro’s law (4) All of these
3. For an ideal gas, number of moles per litre in terms of its pressure P, gas constant R and temperature T is:
[AIEEE- 2002]
(1) PT/R (2) PRT (3) P/RT (4) RT/P
4. According to kinetic theory of gases in an ideal gas between two successive collisions a gas molecule
travels: [AIEEE- 2003]
(1) In a straight line path (2) With an accelerated velocity
(3) In a circular path (4) In a wavy path
5. What volume of hydrogen gas, at 273 K and 1 atm pressure will be consumed in obtaining 21.6g of elemental
boron (atomic mass = 10.8) from the reduction of boron trichloride by hydrogen?
[AIEEE- 2003]
(1) 89.6 L (2) 67.2 L (3) 44.8 L (4) 22.4 L
6. As the temperature is raised from 20o
C to 40o
C, the average kinetic energy of neon atoms changes by a
factor : [AIEEE- 2004]
(1) 2 (2)
293
313
(3)
293
313
(4)
2
1
7. In vander Waal’s equation of state of the gas law, the constant ‘b’ is a measure of : [AIEEE- 2004]
(1) Intermolecular collisions per unit volume (2) Intermolecular attractions
(3) Volume occupied by the molecules (4) Intermolecular repulsions
8. Which one of the following statements regarding helium is incorrect ? [AIEEE- 2004]
(1) It is used to fill gas balloons instead of hydrogen because it is lighter and non-inflammable
(2) It is used as a cryogenic agent for carrying out experiments at low temperatures
(3) It is used to produce and sustain powerful superconducting magnets
(4) It is used in gas-cooled nuclear reactors
9. For gaseous state, if most probable speed is denoted by C*, average speed C and mean square speed by
C, then for a large number of molecules the ratio of these speeds are : [AIEEE- 2013]
(1) C* : C : C = 1.225 : 1.128 : 1 (2) C* : C : C = 1.128 : 1.225 : 1
(3) C* : C : C = 1 : 1.128 : 1.225 (4) C* : C : C = 1 : 1.225 : 1.128

NCERT QUESTIONS
1. What will be the minimum pressure required to compress 500 dm3
of air at 1 bar to 200 dm3
at
30 ºC ?
2. A vessel of 120 mL capacity contains a certain amount of gas at 35ºC and 1.2 bar pressure. The gas
is transferred to another vessel of volume 180 mL at 35 ºC. What would be its pressure ?
3. Using the equation of state PV = nRT; show that at a given temperature density of a gas is proportional
to gas pressure P.
4. At 0ºC; the density of a gaseous oxide at 2 bar is same as that of nitrogen 5 bar. What is the molecular
mass of the oxide?
5. Pressure of 1 g of an ideal gas A at 27ºC is found to be 2 bar when 2 g of another ideal gas B is
introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship
between their molecular masses.
6. The drain cleaner, Drainex contains small bits of aluminium which react with caustic soda to produce
hydrogen. What volume of hydrogen at 20ºC and one bar will be released when 0.15g of aluminum
reacts?
7. What will the pressure exerted by a mixture of 3.2 g of methane and 4.4g of carbon dioxide contained
in a 9 dm3
flask at 27ºC?
8. What will be the pressure of the gas mixture when 0.5L of H2
at 0.8 bar and 2.0L of oxygen at 0.7 bar
are introduced in at I L vessel at 27ºC?
9. Density of a gas is found to be 5.4g/dm3
at 27ºC at 2 bar pressure. What will be its density at STP?
10. 34.05 mL of phosphorus vapour weighs 0.0625 g at 546ºC and 0.1 bar pressure. What is the molar
mass of phosphorus ?
11. A student forgot to add the reaction mixture to the round bottomed flask at 27ºC but put it on the flame.
After a lapse of time, he realised his mistake, using a pyrometer he found the temperature of the flask
was 477ºC. What fraction of air would have been expelled out?
12. Calculate the temperature of 4.0 moles of a gas occupying 5 dm3
at 3.32 bar.
13. Calculate the total number of electrons present in 1.4 g of nitrogen gas.
14. How much time would it take to distribute one Avogadro number of wheat grains, if 1010
grains are
distributed each second ?
15. Calculate the total pressure in a mixture of 8 g of oxygen and 4 g of hydrogen confined in a vessel of
1 dm3
at 27ºC. (R = 0.083 bar dm3
K–1
mol–1
).
16. Pay load is defined as the difference between the mass of displaced air and the mass of the balloon .
Calculate the pay load when a balloon of radius 10m, mass 100kg is filled with helium at 1.66 bar at
27ºC. (density of air = 1.2 kg m–3
and R = 0.083 bar dm3
K–1
mol–1
)
17. Calculate the volume occupied by 8.8 g of CO2
at 31.1ºC and 1 bar pressure.
18. 2.9 g of a gas at 95ºC occupied the same volume as 0.184 g of hydrogen at 17ºC, at the same
pressure, What is the molar mass of the gas?

19. Through the two ends of a glass tube of length 200 cm hydrogen chlorided gas and ammonia are
allowed to enter. At what distance ammonium chloride will first appear ?
20. For 10 minutes each , at 27ºC, from two identical holes nitrogen and an unknown gas are leaked into
a common vessel of 3L capacity. The resulting pressure is 4.18 bar and the mixture contains 0.4 mol
of nitrogen. What is the molar mass of the unknown gas?
21. Equal volumes of two gases A and B diffuse through a porous pot in 20 and 10 seconds respectively. If
the molar mass of A be 80, find the molar mass of B.
22. Calculate the average kinetic energy of 32 g methane molecules at 27ºC.
23. A mixture of hydrogen and oxygen at one bar pressure contains 20 % by weight of hydrogen. Calculate
the partial pressure of hydrogen.
24. What would be the SI unit for the quantity PV2
T2
/ n.
25. In terms of Charles’law explain why – 273ºC is the lowest possible temperature.
26. Explain the physical significance of van der Waals parameters.
27. Critical temperature for carbon dioxide and methane are 31.1ºC and –81.9ºC respectively. Which of
these has stronger intermolecular forces and why?
28. A manometer is connected to a gas containing bulb. Then open arm reads 43.7 cm where as the arm
connected to the bulb reads 15.6 cm. It the barometric pressure is 743 mm mercury. What is the
pressure of gas in bar.

Assignment gaseous state_jh_sir-2621

Assignment gaseous state_jh_sir-2621

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Assignment gaseous state_jh_sir-2621