Gases and Liquids
Matter exists in three states i.e., solid, liquid and gas. Two more possible states of matter are plasma state and super cooled solid state. The state of matter depends on temperature, pressure and inter molecular forces. Matter exists as solid if its melting point (M.P.) is above room temperature, a liquid if its M.P. is below room temperature, a gas if its boiling point is below room temperature. Existence of matter in 3 states is mainly due to intermolecular forces of attraction between molecules.
Ion-dipole forces: The forces exist between ions and polar molecules like water.
e.g.: Forces between Na+, Cl - ions and H2O.
Dipole-dipole forces: The forces exist between polar molecules having permanent dipole moment.
e.g.: Forces between HCl, NH3, SO2.
Dipole induced dipole forces: The forces exist between a polar molecule (like H2O) and non polar molecules or atoms (like polar noble gas). e.g.: The forces between H2O and noble gases.
London forces: The forces exist between non-polar molecules like benzene due to momentary dipole and induced dipole.
We study some of the gas laws to know the relationship among pressure (P), volume (V), temperature (T) and number of moles (n).
Boyle's Law: At constant temperature, the volume of a gas is inversely proportional to pressure.
V ∝ 
PV = K (Constant)
P1V1 = P2V2
Charles - Gay Lussac Law: At constant P, 0ºC temperature, the volume of gas increases or decreases by
times of its volume for every one degree rise or fall in temperature.
V = V0 (1 + )
Charles Law: At constant pressure, the volume of a gas is directly proportional to absolute temperature.
V α T
Ideal gas equation:
V 
(Boyle's law) ....... (1)
V T (Charles Law) ........ (2)
V n (Avogadros' Law) ....... (3)
From (1), (2), (3)
V 
P = 
TR = C.T.R. = 
= 
Where R = Universal gas constant, constant for all gases, work done K-1 mol-1, depends upon units of P, T, V.
R = 8.314 JK-1 mol-1 = 0.0821 lit atm K-1 mol-1
= 8.314 × 107 ergs K-1 mol-1 = 1.987 Cal K-1 mol-1
= 0.083 bar dm3 K-1 mol-1 = 8.314 Kpa dm3 K-1 mol-1
Compression Factor (Z): The ratio of actual molar volume of gas to the molar volume of an ideal gas under similar conditions.
Z = 
For ideal gas Z = 1 For real gas Z ≠ 1
Z < 1 (Gas show -ve deviation, more compressible)
Z > 1 (Gas show +ve deviation, less compressible)
Ideal gas: A gas which obeys ideal gas equation under all conditions of temperature and pressure. A gas behaves ideally at high T and low pressure.
Real gas: A gas which obeys gas laws only at high P and low Temperature.
a, b are Vander Waals constants. They depend on the nature of gas, independent of T.
a: Units are: atm lit2 mol-2 & gives idea of magnitude of attractive forces.
b: Units are: lit mol-1 & gives idea of magnitude of repulsive forces, size of molecules, excluded volumes. b = 4V
Critical Pressure (Pc): The minimum pressure required to liquefy a gas at its critical temperature.
Pc = 
Critical Temperature (Tc): The temperature above which a gas can not be liquified.
Tc = 
Critical Volume (Vc): The volume occupied by a gas at Pc and Tc. Vc = 3b
Joule - Thomson Effect: The process of cooling of a real gas by allowing it, to expand adiabatically through a fine hole from high pressure into low pressure. During this effect enthalpy of system remains unchanged.
Ideal gases do not show this effect.
Inversion temperature: The temperature at which a gas shows neither cooling effect nor heating effect i.e., Joule Thomson effect is zero. A gas shows cooling effect below this temperature, heating effect above this temperature.
Graham's law of diffusion or effusion: The rate of diffusion or effusion of a gas at given pressure and temperature is inversely proportional to the square root of its density.
Applications of Graham's law: Used to separate U235, U238 isotopes, detection of methane gas by Ansil's alarm, dilution of foul smelling or poisonous gases.
Dalton's Law of partial pressures: At constant 'T' total pressure exerted by a mixture of non reacting gases is the sum of the partial pressures of individual gases present in it.
PMixture = P1 + P2 + P3
Where P1, P2, P3 are partial pressures of 1st, 2nd, 3rd gases.
Partial pressure = Mole fraction × total pressure
P1 = X1. P Where X1 = 
n1, n2, n3 are number of molecules of 1st, 2nd, 3rd gases.
Applications of Dalton's law: Pdry gas = Ptotal - PH2O
= Ptotal - Aqueous tension.
Total pressure of gaseous mixture can be determined. Gaseous mixtures do not obey Dalton's law (as they react each other) are HCl + NH3, NO+O2, CO+Cl2, H2+Cl2.
Avogadro's Law: Equal volumes of all the gases contain equal number of moles (n) or molecules under similar conditions of pressure and temperature.
V n
Kinetic molecular theory of gases: Boltzmann, Maxwell, Clasius proposed this theory to explain observed facts of the gaseous state.
Main postulates: * Tiny particles present in a gas are called 'molecules'.
* Molecules move randomly in all the directions.
* Attractions or repulsions are not observed between the molecules.
* Molecular motions are unaffected by gravitational force.
* Molecular collisions are perfectly elastic.
* Volume of individual molecule is negligible compared to the volume of the vessel.
* Pressure exerted by the gas is due to the collisions made on the walls of the vessel.
* Average kinetic energy is directly proportional to absolute temperature (T).
* Only ideal gases obey this theory.
Real gases deviate from ideal behaviour due to faulty assumptions of this theory.
Those faulty assumptions are: The volume occupied by the molecules is negligible compared to the volume of the container. The forces of attraction and repulsion between the molecules are negligible. By using the above postulates, and r.m.s. velocity, kinetic gas equation is derived as
PV = 
mnc2.
All the gas laws can be deducted from kinetic gas equation.
Deduction of Gas Laws from Kinetic Gas Equation
1. Boyle's Law: At constant temperature, the volume of a gas is inversely proportional to pressure.
PV = mnc2 PV = 
× 1/2 mnc2
1/2 mnc2 ∝ T mnc2 = KT
∴ PV = KT
At constant temperature PV = K = constant.
2. Charles Law: At constant pressure, the volume of a gas is directly proportional to absolute temperature.
PV = mnc2 PV = × 1/2 mnc2
1/2 mnc2 ∝ T mnc2 = KT
∴ PV = KT
= 
at constant pressure = K = constant.
3. Avogadro's Law: Equal volumes of all gases under same conditions of pressure and temperature contain equal number of moles (n) or molecules.
For first gas PV = m1n1c12 for second gas PV = m2n2c22
m1n1c12 = m2n2c22 ........ (1)
Average Kinetic energy per molecule is same for both the gases, as both the gases are at the same temperature.
m1c12 = m2c22
m1c12 = m2c22 .......... (2)
gives n1 = n2
4. Dalton's law of partial pressure: At constant 'T', total pressure of mixture of gases is equal to partial pressure of the component gases.
Partial pressure of first gas
.......... (1)
Partial pressure of second gas
........ (2)
Total Pressure 
∴ P = P1 + P2
5. Graham's law of diffusion: The rate of diffusion of a gas at a given pressure and temperature is inversely proportional to the square root of its density.
PV = mnc2
C2 = 
d = 
∴ C2 = 
C = 
At constant pressure C ∝ 
Maxwell's distribution of Velocities:
From these curves, one can draw conclusions:
A very small fraction of molecules has very low or very high velocities.
CP < 
< C
The fraction of the molecules with a particular velocity increases upto a maximum and then decreases.
At high temperatures, the fraction of the molecules with low velocities decreases and high velocities increases. If the fraction of molecules (f) have a narrow range of speeds between S and S + ∆ S, then
f = F(S) . ∆ S Where F(S) = 4Π 
Liquid State
Liquid state is an intermediate state between the gas and the solid. Molecules in a liquid lie in the range 10-5 to 10-7 cm. Liquids diffuse like gases, much less compressible than gases. No definite shape but definite volume is seen in liquids. Some of the important Characteristics of liquids are
1. Vapour pressure: The pressure exerted by the vapour (present in equilibrium with liquid) at a given temperature. At equilibrium rate of evaporation and condensation are equal. Factors effecting evaporation are temperature, nature of the liquid, surface area of the liquid, flow of air current over the surface of the liquid. At hill areas atmospheric pressure is less, so liquids boil at low temperature. One can overcome this problem by using pressure cookers for cooking, auto claves to sterilise instruments ( water boil at high pressure).
"The temperature at which the vapour pressure of the liquid becomes equal to the atmospheric pressure" is known as "boiling point". In Pressure cooker, pressure above the surface of the liquid increases due to steam and hence boiling point is higher.
Surface tension: The shape of mercury, rain water drops is spherical. The surface of the liquid in a tube is curved. The rise or fall of a liquid in a capillary... are some of the properties of surface tension. As water molecules have more number of hydrogen bonds, it has higher surface tension than that of ethyl alcohol or CCl4 or Acetone or diethyl ether. "The property of a liquid arising from unbalanced molecular cohesive forces at the surface, as a result of which the surface acts as stretched elastic membrane" is known as "Surface tension". Surface tension decreases with increase in temperature and becomes zero at critical temperature.
Unit of surface tension: Nm-1
Viscosity: The flow of liquids like Caster Oil, Honey, Glycerol, lubricant oil is slow and the flow of liquids like di ethyl ether, acetone, carbon tetra chloride, water is fast. More the viscosity, the more slowly the liquid flows. The main reason for high viscosity are hydrogen bonding and Vander Waals forces.
Glass behaves like a solid due to very high viscosity. Viscosity of liquids decreases with the increase in temperature. "The internal resistance of the fluid that obstructs the flow is known as viscosity". "The tangential force per unit area of the layer, required to maintain unit velocity gradient is known as Coefficient of viscosity". Unit of viscosity coefficient: NSm-2.
