state of matter gases and liquids

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4. STATES OF MATTER (GASES AND LIQUIDS)
Synopsis :
1. Anything which has mass and occupies some space is called matter.
2. Matter exists in three different physical states known as solids, liquids and gases.
3. Depending on the temperature and pressure a substance can exist in either of the 3 states and
these 3 states are inter convertible by changing P and T.
4. Both liquids and gases are termed as fluids as they have flowing ability.
5. Of these three states, gaseous state is the simplest because of uniformity in behavior.
Comparison of these 3 states:
Property Gases Liquids Solids
1. Shape No definite shape No definite shape Have definite shape
2. Volume No definite volume Have definite volume Have definite
volume
3.Randomness Complete
molecular
randomness
In between that of gases
and solids
Orderly
arrangement of
molecules
4. Density Very low Inter mediate Very high
5.Compressibility Highly
compressible
Slightly compressible Incompressible
6. Diffusion Diffuse rapidly May diffuse slowly Will not diffuse
7.Inter molecular forces Very weak Intermediate Strong
8. Inter molecular
distances
Very large Intermediate Very small
6. The standard conditions for a gas are also known as S.T.P conditions or N.T.P conditions
7. S.T.P conditions
Temperature Pressure
t = 00
C P = 1 atm
T = 273 K P = 76 cm of Hg
P = 760 mm of Hg
8. The weight of one litre of a gas is known as its density. The density of a gas depends on its
temperature and pressure.
9. The units for the density of a gas are gm/lit.
10. Mass, Volume, Pressure and temperature are the measurable properties of a gas.
11. Mass (m):
1. The mass of a gas is expressed in gms (or) kilograms.
2. The mass of 6.023 × 1023
molecules of a gas is known as gram molar mass.
3. For any gas, n = M
m
n = number of gram moles of the gas
m = mass of the gas in grams
M = gram molar mass of the gas
4. The amount of the gas is generally expressed in gram moles.

State of matter (Gases and liquids)
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5. One gram mole of a gas contains Avogadro number of molecules.
12. VOLUME (V):
1. The space occupied by the gas is known as its volume
2. The volume of a gas is expressed in litres
1 litre = 1000 ml
1 litre = 1 dm3
= 103
cm3
1 litre = 1000 cm3
1 ml = 1.000028 c.c.
1m3
= 103
dm3
= 106
cm3
= 106
ml = 103
L
3. The volume of a gas is measured with gas burette.
4. The volume occupied by one gram mole of gas under S.T.P conditions is known as gram
molar volume of a gas.
5. The density of a gas at STP = 4.22
assGrammolarm
6. The number of molecules in 22.4 lit of a gas measured under S.T.P conditions is equal to
Avogadro number.
7. The number of molecules in 1 ml of a gas measured under S.T.P. conditions is known as
Loschmidt number.
8. Loschmidt number = 2.688 × 1019
13. PRESSURE (P):
1. The pressure of a gas is defined as the force per unit area P = A
F
2. The pressure of a gas is measured with manometer.
3. The atmospheric pressure is measured with Barometer.
4. The practical unit of pressure is atmosphere.
1atm = 760mm of Hg=760torr = 76cm of Hg.
5. The absolute unit of pressure is
i) dynes/cm2
(C.G.S.system)
ii) Newtons/m2
(S.l.system)
6. The unit of high pressure is Bar.
1 Bar = 106
dynes/cm2
7. The unit of low pressure is Torr
1 Torr = 1 mm of Hg
8. The S.l. unit of pressure is Pascal (Pa). Pascal is defined as the pressure exerted when a force
of 1 Newton acts on 1square metre.
1 P = 1 N / m2
9. Units:
1atm = 1.01325×106
dynes/cm2
= 1.01325 Bar
1atm= 1.01325 × 105
N/m2
= 1.01325×105
Pa
= 101.325 K.Pa
14. Temperature:
1. The temperature of a gas is expressed in absolute scale (or) Kelvin scale.
It avoids negative values.
2. The absolute zero is at - 273.150
C
3. The temperature of a gas in absolute scale (or) Kelvin scale is given by

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1) 273CA
OO
+= 2) 273CK
O
+=
T = t + 273
4. At absolute zero,
1. Molecular motion in the gas ceases.
2. Pressure of the gas becomes zero.
3. Volume of the gas becomes zero.
4. Kinetic energy of the gas becomes zero.
15. Gas Laws: The behaviour of gases and the relation between variables like, m, V, T, P etc are
explained by certain laws known as gas laws.
BOYLE'S LAW:
1. For a given mass of a gas at constant temperature, the volume is inversely proportional to
the pressure.
2. For a given mass of a gas at constant temperature, the product of its volume and pressure is a
constant value.
3. According to Boyle's law for a given mass of a gas at constant temperature the density of the
gas is proportional to the pressure of it.
4. For a given mass of gas at constant temperature.
1. P
1
Vα
2. Pdα
PV = constant; d/P = constant
3. 2211 VPVP = 4. 2
2
1
1
d
P
d
P
=
16. CHARLES LAW:
1. For a given mass of a gas at constant pressure, the volume of the gas is directly proportional
to its absolute temperature. This is known as Charles law.
2. For a given mass of gas at constant pressure the density of the gas is inversely proportional
to its absolute temperature.
3. For a given mass of gas at constant pressure.
1) V α T 2) d α T
1
3) T
V
Constant
4) 2
2
1
1
T
V
T
V
=
 5) dT=constant 6) d1T1 = d2T2
4. For a given mass of a gas at constant pressure the volume of the gas increases or decreases
by 1/273th
part of its volume at 0°C for every 1°C raise or fall in temperature
Vt = V0 (1 + α t)
V
1/ P
PV
P
P
V
T2 > T1
T1
T2
V
T
V
t°C
P1
P2
P3
P1>P2>P3

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Vt is volume at t°C; V0 is volume at 0°C
α = 273
1
= 0.00366; α = 3.66 × 10-3
(α is volume coefficient)
17. AVOGADRO'S LAW:
At constant temperature and pressure, the volume of a gas is proportional to the number of
moles present in it. This is known as Avogadro's law V αn, 2
1
2
1
n
n
v
v
=
.
18. Under similar conditions of temperature and pressure equal volumes of all gases contain equal
number of moles (or) molecules.
19. Under similar conditions of temperature and pressure equal volumes of all gases contain equal
number of atoms. This is known as Berzilius hypothesis.
The Berzilius hypothesis leads to the conclusion that atoms are divisible, which is contrary to
the Dalton's atomic theory and therefore it is discarded.
20. At constant temperature, for a gas having constant volume, the pressure is directly proportional
to the number of moles present in it
P ∝ n; 2
1
p
p
= 2
1
n
n
21. IDEAL GAS EQUATION (OR) PERFECT GAS EQUATION (OR) EQUATION OF
STATE:
By combining Boyle's law and Charles laws we get
1. PV = nRT ; PV = RT for 1 mole
2. PV =
⎥
⎦
⎤
⎢
⎣
⎡
=
M
m
nRT
M
m
n = Number of moles of the gas
m = Mass of the gas
M = Molecular weight of the gas
3. P = 1
2
2
1
2
1
T
T
p
p
d
d
;
M
dRT
×=
d = density of the gas
4. R = nT
hdgV
(P = hdg)
d = density of mercury (13.6gm/c.c)
g = gravity (980 cm/ sec2
)
h = height of mercury column (76 cm)
22. For a given mass of a gas, "nR' is constant. So
1.
constant
T
PV
=
2. 2
22
1
11
T
VP
T
VP
=
→ Known as equation of State
3. 2
22
1
11
P
Td
P
Td
=
23. Numerical Values of R:

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R is universal gas constant or molar gas constant. R = nT
PV
The value of 'R' is independent of the nature of the gas and amount of gas but it depends on
units of expression.
1. R =
mole/k/atmitl
273
4.22
−
2. R = 0.0821 lit - atm / k / mole
3. R = 82.1 ml - atm / k / mole
4. R = 62.4 lit - mm / k/ mole
5. R = 6.24 × 104
ml - mm / k/ mole
6. R = 8.314 × 107
ergs / k/ mole
7. R = 8.314 × 107
dyne. cm. / k/ mole
8. R = 8.314 j / k/ mole
9. R = 1.987 Cals / k/ mole
10. R = 0.002 K.Cals /k / mole
11. 5.28 × 1019
ev / k/ mole
24. The gas constant for a single molecule of the gas is known as BOLTZMAN CONSTANT (K)
K = R/N (N = Avogadro’s number)
K = 1.38 × 10–16
ergs/K/molecule
K = 1.38 × 10-23
Joules /K/molecule
25. A gas which obeys gas laws (or) Ideal gas equation under all conditions of temperature and
pressure is known as ideal gas or perfect gas.
26. No gas is perfectly ideal in nature. Every gas deviates more or less from ideal nature. So all the
known gases are real gases.
27. Real gases deviate from ideal behaviour at high pressures and low temperatures.
28. Real gases will show nearer ideal behaviour at low pressures and high temperatures.
29. Real gases can be liquefied easily at high pressure and low temperature. This is due to inter
molecular attractions.
30. For ideal gases; RT
PV
=Z; Z = compressibility factor; for ideal gases, Z = 1; for real gases Z>1 or
< 1
31. GRAHAM’S LAW OF DIFFUSION:
1. The spontaneous inter mixing of gases to form a homogeneous mixture is known as the
diffusion.
2. Gases diffuse from high pressure to the low pressure.
3. The Volume of gas (V) that diffuses in unit time is known as the rate of diffusion (r) of the
gas r = t
V
; unit of rate of diffusion: c.c /sec
Graham's law:
4. At constant temperature and pressure the rate of diffusion of a gas is inversely proportional
to the square root of its density (or) molar mass (or) vapour density.
1) r α d
1
2) r α M
1
3) r α D.V
1
5. For two gases diffusing under similar conditions of temperature and pressure.

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1) 1
2
1
2
2
1
D.v
D.v
d
d
r
r
==
= 1
2
2
1
1
2
t
t
v
v
M
M
×=
6. Under similar conditions of temperature and pressure if the time of diffusion is same for two
different gases. 2
1
2
1
v
v
r
r
=
7. Under similar conditions of temperature and pressure if equal volumes of two gases diffuse.
1
2
2
1
t
t
r
r
=
8. If two gases are at different pressures and same temperature, 1
2
2
1
2
1
M
M
p
p
r
r
×=
9. Under similar conditions of P and T, 2
1
2
1
2
1
t
t
M
M
W
W
×=
10. Lighter gases diffuse rapidly than heavier gases.
11. The diffusion of a gas at high pressure into low pressure or vaccum, through a small hole is
known as Effusion.
12. Grahams law of diffusion is applicable to effusion also.
13. The separation of the component gases from a gaseous mixture based on the difference in
their rates of diffusion is known as Atmolysis.
14. Marsh gas or Ansil's apparatus alaram works on the principle of diffusion property of
gases.
Applications of diffusion
1. In the detection of marsh gas in coal mines.
2. In the separation of gas mixtures
3. In the seperation of isotopes Ex: U235
can be seperated from U238
in the form of UF6
4. In diluting poisionous and foul smelling gases.
5. In the determination of molecular weights and densities of gases.
DALTON'S LAW OF PARTIAL PRESSURES:
1. The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of
component gases present in the mixture P = P1 + P2 + P3 + .....
2. The partial pressure of a gas is the pressure exerted by that gas in the mixture of gases.
3. The partial pressure of a gas is equal to the product of its mole fraction and the total pressure of
the mixture of gases.
Pi =
P
n
ni
×
(n = total number of moles of all gases in the mixture)
Partial pressure=
pressureTotal
volumeTotal
gasofvolume
×
• If two or more gases are at different pressures and occupying different volumes are forced in to
a vessel of volume 'V' ;
then V
...vpvp
P 2211
Total
++
=
• Percentage of gas in the mixture

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=
100
pressureTotal
pressurePartial
×
• If two different gases with equal masses are present in the mixture, the gas with less molecular
weight has more partial pressure.
• If two different gases with different masses and different molecular weights but same volumes
are mixed together, their partial pressures are same.
• Dalton's law of partial pressures is applicable the mixture of non reacting gases.
Ex: CO+CO2, N2+O2 H2+N2, H2+O2, SO2+O2,
NO2+O2
• Dalton's law of partial pressures is not applicable for reacting gases
Ex: CO+O2, NO+Cl, CO+Cl2, SO2HCL2,
H2+F2, NO+O2, NH3+HCl
Aqueous Tension:
• The pressure exerted by water vapour which is in equilibrium with liquid water is called
aqueous tension.
• It is denoted by "f"
• Aqueous tension increases with temperature.
• Water insoluble gases are collected over water and they become moist gases. Pdry gas = Pmoist gas –
f
• Water insoluble gases are generally collected over water. A gas collected over water is
saturated with water vapour. Such a gas is called moist gas.
• The volume of a moist gas is generally measured at atmospheric pressure. So pressure of moist
gas is equal to atmospheric pressure.
• The pressure of water vapour in a moist gas is known as aqueous tension.
• Pmoist gas = Pdry gas + aqueous tension
• The aqueous tension increases with temperature
Temperature Aqueous tension
0 °C
25°C
26°C
27°C
28°C
29°C
30°C
100°C
4.579 mm
23.8 mm
25.2 mm
26.7 mm
28.35 mm
30.0 mm
31.8 mm
760 mm
• Dalton's law of partial pressures is not applicable to the mixture of gases like
1. CO and Cl2 2. NO and Cl2
3. NO and O2 4. H2 and Cl2
5. SO2 and Cl2 6. NH3 and HCl
• Dalton's law of partial pressures is applicable to the mixture of gases like
1.N2 and H2 2. H2 and O2
3. H2 and O2 4. SO2 and O2
5. CO2 and SO2 6. NO2 and O2
KINETIC THEORY OF GASES:
1. Kinetic molecular theory of gases was proposed by Maxwell, Boltzmen, Calssius.

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2. Kinetic molecular theory is applicable only to ideal gases.
3. Every gas contains a large number of tiny particles called molecules.
4. The actual volume of the molecules is negligible when compared with the volume occupied
gas.
5. There are no intermolecular attractions or repulsion between the gas molecules. So ideal gases
cannot be liquefied.
6. The molecules move randomly and straight in all directions with different velocities.
7. The molecules collide among themselves and also with the walls of the container.
8. The molecular collisions are perfectly elastic.
9. Molecular collisions are unaffected by gravity .
10. The pressure exerted by the gas is due to the collisions of molecules on the walls of the
container. There is no loss of energy in these collisions, ∴ collisions are said to be elastic.
11. The average kinetic energy of the gas molecules is proportional to the absolute temperature of
the gas.
Validity of kinetic theory:
• Kinetic theory holds good at low pressure and high temperatures and fails at high pressure and
low temperatures.
i) Actual volumes of gas molecules are negligible at low P and high T but considerable at high
'P' and low 'T'
ii) Gases are not liquefiable at very low P and high T but they can be liquefied at high 'P' low T.
Thus kinetic theory is applicable for ideal gases and not applicable for real gases.
Kinetic gas Equation:
Based on the assumptions of kinetic theory of gases, kinetic gas equation is derived.
Kinetic gas equation PV = 3
1
mnc2
m = mass
n = number of molecules
c = RMS velocity.
The RMS velocity is the root of mean of squares of individual velocities of gas molecules at a
given temperature.
RMS velocity is the true average velocity because it avoids the possibility of negative or zero
velocity for gas molecules.
C = n
cccc 2
n
2
3
2
2
2
1
+−−−−+++
c1, c2, c3 ...... cn are the individual velocities of 'n' molecules.
Deduction of gas laws from kinetic gas equation:
1. Boyle's law: PV = 3
2
KT (at constant 'T')
2. Charles' law: P
K
3
2
T
V
=
(at constant 'P')
3. Avogadro's law: n1 = n2 or
2
22
2
222
2
11
2
111
cm
2
1
cnm
3
1
cm
2
1
cnm
3
1
=
(at - constant P and T)
4. Dalton's law of partial pressures:

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P = v
cnm
3
1
v
cnm
3
1
2
222
2
111
+
or P = P1 + P2
5. Graham's law of diffusion:
C = d
1
ror
d
p3
α
(at constant P)
Kinetic energy:
For 'n' moles of gas, kinetic energy Ek = 2
3
nRT
For 1 mole of gas, kinetic energy Ek = 2
3
RT
For 1 molecule of gas, kinetic energy
Ek =
KT
2
3
Eor
N
RT
2
3
k =
'K' is Boltzman constant
'K' is defined as the gas constant per molecule i.e.
k = N
R
k = 1.38 × 10–16
erg.k . molecule
k = 1.38 × 10-23
Joule. k . molecule
= 3.3 × 10-24
Cal. k . molecule
• Average kinetic energy of any gas is directly proportional to the absolute temperature and
independent of nature of gas. This is called Maxwell's generalization.
• Two different gases at same temperature will posses same average K.E.
• If two different gases present at same temperature are mixed with each other there will not be
any rise in temperature.
Distribution of Molecular velocities:
• Due to frequent collisions among themselves and with the walls of the container, the velocities
of gas molecules can not remain constant.
• The velocity of a gas molecule will remain same only in very short period i.e. 10-9
seconds.
• Though the velocities change so frequently, the ratio of certain number of molecules with
certain velocity to the total number of molecules remains constant.
• The plot of fraction of molecule Vs velocity gives the following graph.
Conclusions from the above graph
• No single molecule will possess zero velocity
• Very few molecules have either very low velocities or high velocities
O
T2 > T1
T1
T2
Fractionofmolecule
Velocities

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• With increase in temperature, the number of molecules possessing higher velocities is increased
and the number of molecules possessing low velocities and the number of molecules possessing
most probable velocity is decreased.
• As the velocities of the molecules increase, the fraction of the molecules possessing a particular
velocity also increases up to maximum value and then decreases.
• Boltzman equation: It is useful to know the number of molecules having particular energy in a
given sample of gas at a given temperature.
ni = n.e–E i / KT
n = total number of molecules
T = temperature
k = Boltzuman constant
ni = number of molecules with particular energy Ei
Types of Molecular velocities:
1. Most Probable velocity (CP)
• It is the velocity possessed by the maximum number of molecules present in the gas at any
temperature
Cp = d
P2
m
PV2
M
RT2
==
M = mass of given gas
Cp = 0.8166 × RMS velocity
• The average of the velocities of all the molecules in the gas at any temperature is known as
average velocity.
It is represented by C
n
C...CCC
C n321 ++++
=
d
P8
M
PV8
M
RT8
C
π
=
π
==
m = mass of given gas
C = 0.9213 × R.M.S Velocity
• The square root of the mean of the squares of the velocities of all the molecules present in the
gas at any temperature is known as the RMS velocity. It is represented by C
C = n
C.......CCC 2
n
2
3
2
2
2
1 +++
; C = M
RT3
= d
P3
m
PV3
=
; C = 1.58
sec/cm10x
M
T 4
• For a gas at two different temperature the ratio of its RMS velocities is given by
2
1
2
1
T
T
C
C
=
• For two different gases having same RMS
velocity 2
2
1
1
M
T
M
T
=
ii) For two different gases at the same temperature,
1
2
2
1
M
M
C
C
=
• For gas at any temperature. Cp < C < C

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• At any temperature, in a given sample of gas.
pcn
> C
n
> nc
• Ratio between molecular velocities
1) Cp:
3:
8
:2C:C
π
=
2)
3:55.2:2C:C:Cp =
3)
=C:C:Cp
0.8166: 0.9213: 1 4)
=C:C:Cp
1: 1.128: 1.224

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INTERMOLECULAR FORCES:
• Inter molecular forces usually called as van der waal forces.
• Inter molecular forces are several types
1) ion - dipole 2) dipole - dipole
3) dipole- induced dipole
4) induced dipole - induced dipole and a specific inter molecular force i.e., Hydrogen bond.
• All the intermolecular forces are electrical
• Intermolecular forces generates as the result of the neutral attractions of unlike charges (or)
repulsions of like charges.
Ion - dipole interactions :
• It is attractive force between ion and dipole
Ex : In water interaction between Na+
and 2H O (dipole molecule) or Cl−
and 2H O
• The magnitude of interaction energy depends on the charge on the ion (z), its dipole moment
( )μ
and on the inverse square of the distance (r) between the ion and the dipole
2
. /E Z rμ∴ =
• Ion - dipole forces are mainly important in aqueous solutions of ionic substances
Ex: NaCl in water
Dipole - Dipole forces
• Neutral but polar molecules experience dipole-dipole forces
• These forces are due to electrical interactions among dipoles on neighbouring molecules
• These are two types
a) Attractive forces between unlike poles
b) Repulsive forces between like poles
• These forces are generally weak, are in the order of 3-4 KJ/mol. and significant only when
molecules are in close contact
• The strength of a given dipole - dipole interaction depends on the sizes of the dipole moments
involved
• As the molecule is more polar, dipole-dipole interactions are more and boiling point of
substance will be more
• a) Dipole - Dipole interactions in solids is proportional to
3
1
r
b) Dipole- Dipole interactions between rotating molecules is proportional to
6
1
r here ‘r’ is the
distance between polar molecules.
London dispersion forces:
• Instantaneous dipole on one atom can affect the electron distributions in neighbouring atoms
and induce temporary dipoles in those neighbours. As a result weak attractive forces develop
known as london forces or dispersion forces.
• London forces energies are in the range 1-10 kJ/mol.
• The magnitude of London forces depends on polarisability.
• A smaller molecule (or) atom is less polarisable and has smaller dispersion forces

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• A larger molecule or heavier atom is more polarisable and has larger disperson forces
• 2F has smaller dispersion forces hence it is gas where as 2I has larger disperson forces and it
is a solid.
• These are always attractive forces and proportional to
6
1
r , here ‘r’ is distance between the
two interactive particles.
• More spread out shapes posses higher dispersion forces than those compact molecules which
minimise molecular contact hence posses lower dispersion forces
Ex: n - pentane, b.p is 309.4k( long chain)
2,2 - dimethyl propane, b.p is 282.7k (compact chain)
Dipole - Induced forces:
• These forces are in between polar molecules and neutral molecule.
• Permanent dipole of the polar molecule induces dipole on the electrically neutral molecule by
deforming into electric cloud and attractive forces develop.
• This interaction range is proportional to
2
1
r here ‘r’ is the distance between the molecules.
• The magnitude of induced dipole moment also depends on the magnitude of the dipole
moment of permanent dipole and polarisability of neutral molecule.
• These repulsive forces between the particles (atoms, molecules or ions) are due to electron -
electron repulsions (or) nucleus - nucleus repulsions.
Thermal Energy
• The energy due to the motion of the atoms or molecules of the substance.
• Thermal energy is directly proportional to absolute temparature of the substance.
• It is a measure of average kinetic energy of the molecules of the substance.
• The movement of particles is called thermal motion.
• If thermal energy predominates over inter molecular forces the substances would change from
solid → liquid →gas
• If intermolecular forces predominate over thermal energy then substance change from
gas →liquid →solid.
Molecular collisions and mean free path :
• Mean free path(λ ) : The average distance that a molecule travels between two successive
collisions is called as “Mean free path”( λ )
• In gases the mean free paths of molecules are several hundred molecular diameters, where as
in liquids it is less than the diameter of molecules.
2. . .A
RT
N P
λ
σ
=
• Collision Freequency (Z) : The average rate of collisions made by a molecule is known as
“collisoin frequency”(Z)”
(or)
The average number of collisions one molecule makes in a time interval divided by the length
of the interval.
Time of flight :
1
Z
⎛ ⎞
⎜ ⎟
⎝ ⎠

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• The average time that molecule spends in flight between two successive collisions
1
Z
⎛ ⎞
⎜ ⎟
⎝ ⎠ .
• RMS velocity (C) =
mean free path
time of flight
C =
1
z
Z
λ
λ=
Real gases :
• In perfect gas, molecules move independently of one another here mean free path λ >>r
(the radius of the molecule).
• Perfect gas has energy only from kinetic energy but not any contribution from potential
energy.
• In real gases the intermolecular attractions are important . At large separation of molecules,
the energy lowering attractions are dominant, but at short distances the energy raising
repulsions dominate
Isotherms of 2CO and critical temperature:
• The isotherms of 2CO have shapes different from those implied by Boyle’s law particularly at
high pressure and low temperature
• Experimental isotherms of 2CO resemble the perfect gas isotherms at high temperature and
low pressure.
• At
0
31.04 C (304.19K) ( 30.98OC as per CBSE text book) the gaseous state of transforms
continuously into the condensed state and there is no stage between the liquid and gas. This
temperature is known as critical temperature ( )cT
• Critical temperature of a gas is the highest temperature at which liquefaction of gas first
occurs
• At critical temperature liquid phase passes into gaseous state imperceptibly and continuously
• A gas below the critical temperature can be liquefied by applying pressure and is called
vapour of the substance.
• A gas can not be liquefied by the application of only pressure without cooling it below the
critical temperature.
• The isotherm at critical temperature is critical isotherm.
• At critical temperature, density of vapour phase equal to density of liquid phase
• The dense fluid obtained by compressing a gas above its critical temperature is not a true
liquid but behaves as liquid in many aspects called as “super critical fluid”.
• Super critical fluid can be used as ( i) solvent
ii) It does not have a surface which separates it from vapour phase
Ex: Super critical 2CO is used to extract caffeine in the manufacture of decaffeinated coffee.
• Pressure required to liquefy a gas at its critical temperature is called critical pressure
( )cP
.
• The volume occupied by 1 mole of the gas at critical temperature and critical pressure is
critical volume
( )cV
.

15
The compression factor:(Z)
• Compression factor is the ratio of the actual molar volume of a gas to the molar volume of a
perfect gas under the same conditions.
• compression factor
( )
( )
( )
m
m
Molar volume of the gas V
molar volume of perfect gas V perfect
Z =
•
( ) real
ideal
V
V
Z =
• The molar volume of a perfect gas
( )perfect
mV
RT
P
=
. mPV
Z
RT
=
• For a perfect gas, Z = 1 at all pressures.
• If Z>1, called as positive deviation from ideal behaviour. That is molar volume of the gas is
greater than that expected for a perfect gas.
a) At low pressures some gases have Z>1
Ex: methane, ethane, ammonia
b) At high pressure all most all gases have Z>1
c) At any pressure for hydrogen gas Z>1
• If Z<1 , called as negative deviation from ideal behaviour. That is molar volume of the gas is
lower than that expected for a perfect gas
• At intermediate pressure gases have Z<1
• At very low pressure all gases have almost ideal behaviour
• Ideal behaviour depends on nature of the gas and its temparature.
• The temparature at which a real gas obeys ideal gas laws over a wide range of pressure is
called “Boyle temparature”. (or) Boyle point. ( bT )
•
bT
R
a
b
=
• Boyle point depends on nature of the gas.
• Above Boyle’s temperature real gases shows positive deviations from ideality and Z>1
• Below Boyle’s temperature of real gases first show Z<1 with increase of pressure and reaches
a minimum. On further increase of pressure ‘Z’ value continuously increases.
• At low pressure and high temperature gases shows ideal behaviour.
The vander Waals equation of state:
• For the gas molecules the available volume for free travel is not equal to the volume of the
container.
• Volume correction is = V-nb here b is proportionality constant
• At low pressure, the volume is large compared with the volume excluded by the molecules i.e.
V nb V>> ≈
• When two molecules, each of radius ‘r’ and volume
( ) 3
4/3.molV rπ=
approach each other
excluded volume is 8 molV

16
• The effect of attractive interactions between molecules is to reduce the pressure that the gas
exerts.
• Attraction experienced by a molecule is proportional to the concentration (n/v) of molecules
in the container.
Reduction in pressure
2
n
V
⎛ ⎞
∝ ⎜ ⎟
⎝ ⎠
∴ Reduction pressure =
2
2
an
v
where ‘a’ is the proportionality constant.
∴ vander Waals equation of state is
( )
2
2
an
P V nb nRT
V
⎛ ⎞
+ − =⎜ ⎟
⎝ ⎠
for ‘n’ moles . (or)
2
2
nRT n
P a
V nb V
⎛ ⎞
= − ⎜ ⎟
− ⎝ ⎠
for 1 mole
( )2
a
P V b RT
V
⎛ ⎞
+ − =⎜ ⎟
⎝ ⎠
• ‘a’ and ‘b’ are vander Waals parameters are empirical parameters.
• ‘a’ and ‘b’ depend on the nature of the gas and independent of temparature.
Vander Waal’s constants for some common gases :
Gas a(l2 atm mol-2) b.(1 mol-1)
NH3 4.17 0.0371
CO2 3.59 0.0427
CO 1.49 0.0399
Cl2 6.49 0.0562
H2 0.024 0.0266
HCl 3.67 0.0408
NO 1.34 0.0279
O2 1.36 0.0318
SO2 6.71 0.0564
He 0.034 0.0237
Water 5.46 0.0305
Relationship between critical constants and Vander Waal’s constant

17
•
2
8
, 3 ,
27 27
C C C
a a
P V b T
b Rb
= = =
• Reduced pressure is / cP P
• Reduced volume is / cV V
• Reduced temperature / cT T
Conditions of liquifaction of gases :
• A gas liquifies if it is cooled below its boiling point at a given pressure.
• Gases which have very low b.p are liquified by using Joule-Thomson efect:
Joule - Thomson effect:
• Cooling of gas by expansion from high pressure side to low pressure is called “Joule -
Thomson effect “.
• Hydrogen gas under normal conditions, it warms up in Joule- Thomson expansion. (Since
Z>1).
• Hydrogen gas also cooled by Joule - Thomson effect if it cooled first to its ‘inversion
temparature’and then allowed to expand.
LIQUID STATE
• Liquids , a) possess strong intermolecular forces
b) less compressable c) more denser
d) has definite volume e) can flow like gases
Vapour pressure:
• The pressure exerted by vapours when there is an equilibrium state between the liquid phase
and vapour phase is called equilibrium vapour pressure (or) saturated vapour presure.
• Free vapourisation through out the liquid is called boiling
• At 1 atmosphere pressure boiling temparature is called normal boiling point and at 1 bar
pressure it is called standard boiling point of the liquid.
• Standard boiling point of a liquid is slightly less than the normal boiling point since 1 bar is
less than 1 atm.
Ex: normal b.p. of water is 373k and standard b.p. of water is 372.6k
• At high altitude as the atmospheric pressure is less, the liquids boil at low temperature.
• In auto claves water is boiled under high pressure to sterilise instruments.
• In a closed vessel a liquid on heating doesn’t boil but its vapour pressure increases and at a
critical temperature, density of liquid and density of vapour is going to be equal.
Surface tension: (r):
• The force acting along the surface of a liquid at right angles to any line of 1 unit length .
• The energy required to increase the surface area of the liquid by 1 unit is called surface
energy.
• Units for surface energy is
2
Jm−
• Surface tension is numerically and dimensionally equal to surface energy.
• units for surface tension is kgs and SI unit
1
Nm−
- .

18
• The liquid has lowest energy when the surface area is minimum . Hence liquid droplets exist
in spherical shape.
• Surface tension decreases with increase of temperature because of increase in kinetic energy
of molecules and decrease in intermolecular forces.
Surface tensions of some liquids at 20 C°
(in dynes/cm )
Diethylether 16.9
Acetone 23.7
Carbon tetra chloride 26.9
Ethanol 22.3
Water 72.8
Viscosity:
• Strong intermolecular forces between the molecules of successive layers of liquid holding
them together show resistance to the flow and create friction between the layers of fluid. The
measure of this resistance to the flow of liquid is viscosity.
• The regular gradation of velocity for layers in passing from one layer to the next layer is
called “Laminar flow”.
• A force (F) is required to maintain the flow of layers is proportional to the area (A) of contact
and velocity gradient
dv
dx
⎛ ⎞
⎜ ⎟
⎝ ⎠ .
,
dv
F A F
dx
∝ ∝ .
dv
F A
dx
η∴ =
here η - proportionality constant (or) coefficient of viscosity
• Viscosity coefficient is defined as the force when velocity gradient and area of contact each is
unity.
• η is a measure of viscosity
• SI unit for η 2
Nm S− η is or PaS. C.G.S unit for is “poise”.
1 poise = 1 g
1 1
.cm s− −
=
1 1 1
10 Kgm s− − −
• As viscosity increases, liquids flow slowly.
• Hydrogen bond and vander Waals forces cause high viscosity.
• Glass is an extremely viscous liquid and properties resemble solids.
• As the temperature increases, viscosity decreases since kinetic energy of molecules that
overcome the intermolecular forces.
•
/
. E RT
Aeη = here A and E are constants for a given liquid.
Viscosities at 20 C° in milli poise
Ethyl ether 2.33
Acetone 3.29
Carbon tetrachloride 9.68
Water 10.09

19
Ethanol 12.0
Acetic acid 12.2
Ethylene glycol 19.9
glucinol 8500

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