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States of Matter
GASEOUS STATE
Generally four parameters are used to characterise gases : They are
1
...
It is expressed in litre (L), millilitres (ml) or cubic
centimeter (cm3) or cubic meter (m3)
...
The Pressure
It is the force exerted by the gas per unit area of the wall of the container
...

Units :
1 atm
...
I
...
325 × 105 Nm–2 = 101
...

It is also expressed in ‘bar’ 1 bar = 105 Pa
...
The temperature
The temperature is measured either in degree centigrade (°C) or in kelvin (K) with the help of thermometer
...
I
...
The Mass
Mass of gas is expressed in gm or kg or in moles
...


GAS LAWS
(A) Boyle’s Law
At constant temperature the volume of the given mass of gas is inversely proportional to its pressure
...
e
...

Graphical Representation

(i)

(ii)
P

P

V

1/V

(iii)

(iv)
PV

log P

P

logV

(v)

(vi)

T1
T2

P

P

T3

T1
T2
T3
V

1/V
T1
T2

(vii)
PV

P
(B) Charle’s law
This law is based on the observation that for each degree change in temperature, the volume of the gas is
changed by 1/273rd times the initial volume of gas at 0°C
...
If
temperature is increased by t°C the new volume becomes, Vt
...
”
Mathematically
VT

V

or

(if P and ‘n’ are constants)

 constant if pressure and ‘n’ are constants
...



p t
pt  p0  0
273
t 

pt  p0  1 273 

273

of its pressure at 0°C per degree change



where 273 + t = T

273  t
T
pt  p0   273   p0  273



or
P  T
...
e
...





P1
T1



P2
T2

(D) Avogadro’s Law
The volume of same number of moles of all gases measured at constant temperature and pressure are the same
...


V  n at constant T and p

Mathematically

V = k
...
At 0°C and 1 atm the value of k for 1 mole of gas is 22
...

Ideal Gas Law Equation of State
Combination of Boyle’s law, Charle’s law and Avogadro’s law gives the ideal gas equation
...


Charle’s law



V  T if P is constant
...


Thus, V 

nT

i
...
PV  nT
P
Where R is molar gas constant
or



or

PV  nRT

PV  RT for 1 mole of gas

Numerical values of R
(i)

PV
(For one mole of gas)
T
Since one mole of a gas at one atm pressure and 0°C (273 K) occupies a volume of 22
...

R

Then R 
(ii)

1 22
...
0821 litre atm
...


273
If pressure is taken in dyne/cm2 and volume in ml
...
67  981 22400
= 8
...
314 J mole–1 k–1
...
184 × 107 erg
...
314 10 
 calorie mol k
1
...
184 107
If pressure is taken in bar so that volume is 22
...
7
 0
...

where P is the total pressure and PA, PB, PC
...

respectively
...

Let n1 and n2 be the no
...
T
...
e
...

Effusion : A process in which gas is allowed to escape under pressure through a fine orifice or small aperture
made in the vessel or wall of a closed container is called effusion
...

If r1 and r2 are the rates of diffusion of two gases having densities d1 and d2 respectively
...

r1
r2



vapour
vapour

density2

 M2
density1
M1

Again if m1 and m2 are the number of moles of two gases or t1 and t2 are the time of flow for equal volumes of
the gases, we have
r1 m1 V1 t2
d


  2 
r2 m2 V2 t1
d1

M2
M1

When the pressure is not constant then rate of effusion may be taken proportional to pressure

r  p and

Then,

r P

r 

1
M





or

M

p
 1
r 2 p2
r1

M2
M1



m1
m2

Kinetic Theory of Gases
The kinetic theory was presented by Bernoulli (in 1738) and developed by Clausius and Maxwell (in 1860)
...
Gases are made up of small structural units called atoms or molecules
...

2
...

3
...
e
...

4
...

5
...

6
...

Kinetic energy  absolute temperature
7
...

Kinetic Gas Equation


On the basis of the postulates of kinetic theory of gases, it is possible to derive the mathematical expression,
commonly known as kinetic gas equation, i
...

PV 

1

mnc2

3
where P = pressure of the gas, m = Mass of a molecule, n = number of molecules present in the given amount of
a gas and c = Root mean square speed
...

RMS speed =


c12  c22  c23 
...
E
...
It may not be possible to find
the speeds of individual molecules but from probability considerations it has become possible to work out the
distribution of molecule between different speeds
...

 The distribution of speeds remain constant at a given temperature although individual speeds of molecules
may go on changing
...

This speed corresponding to the speak in the curve is referred to as most probable speed   
...

 As the temperature is increased, the molecules possessing higher speeds increase
...
This is because of the
increase in the value of most probable speed 
...
However, area under the curve will remain the same
...


DIFFERENT TYPES OF MOLECULAR SPEEDS
1
...
It is the speed possessed by maximum fraction of molecules at particular temperature
...
Average Speed v 
...
It
is given by following expressions
v v v
 8RT
v  1 2 3
...
Root Mean Square Speed (u or urms)
...
It is given by following expressions
urms 

3RT
3PV
3P
v12  v22  v32
...
The
deviation is observed at low temperatures and high pressures
...

It refers to ideal behaviour
 If Z = 1, i
...
, PV = nRT

If Z > 1 i
...
, PV > nRT
Positive deviation, i
...
, the gas is less compressible than expected from ideal behaviour
...
e
...
e
...

 At low temperature and high pressure, neither the volume of molecules is negligible nor the attractive forces
among the molecules
...
The value of constant ‘a’ gives the idea of the magnitude of attractive forces between the
molecules of the gas
...
Larger the value of a, larger will be the intermolecular attraction
among the gas molecules
...
Its units
are L mol–1
...
The value of b is four times the actual volume of
the molecules

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