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4.1


Kinetic
Molecular Theory:
This
Theory describes the behavior of different stats of matter. However it is a
best model for an ideal gas. So, it is also called kinetic molecular theory
of gases.
The main postulates of this theory are
as given below:
Postulates:
1)
Gases are composed of a large number of particles
that behave like hard, spherical
objects in a state of constant, random motion.
2)
These particles move in a straight line until they
collide with another particle or the walls of the container.
3)
These particles are much smaller than the distance
between particles. Most of the volume of a gas is therefore empty space.
4)
There is no force of attraction between gas
particles or between the particles and the walls of the container.
5)
Collisions between gas particles or collisions
with the walls of the container are perfectly elastic. None of the energy of
a gas particle is lost when it collides with another particle or with the
walls of the container.
6)
The average kinetic energy of a collection of gas
particles depends on the temperature of the gas and nothing else.
7)
Gases exert pressure which the result of collision of molecule
of gas to the walls of container




4.1.2

GAS
LAW:
The gases have volume,
pressure, temperature etc. All these quantity are related to one and another
according to some statement, called “The gas laws”.. some of the important
gas laws are as follow:
ü Boyle’s law.
ü Charle’s law.
ü Avogadro’s
law.
ü Graham’s law
of diffusion.
ü Dalton’s law
of partial pressure.
Boyle’s
Law:
Robert
Boyle, in 1662, showed the relationship between the pressure and the volume
of a gas at constant temperature. This is called “BOYLE’S LAW.”
Statement
1:
According
to the Boyle’s law
“At
constant temperature, the volume of a given mass of gas is inversely
proportional to the pressure applied on it.”
Explanation:
It
means that the increase in pressure would result in a decrease of volume of a
gas, similarly the decrease in pressured result in the increase in the
volume.
Simply we can say, if the
pressure is doubled, the volume becomes half and if the pressure is reduce to
half, the volume becomes double.
Mathematic
Expression:
Mathematically, Boyle’s law can
be expressed
as (at constant
temperature)
ð P x V =K
Where K = proportionality constant.
This equation gives another
statement Boyle’s law, which is as under:
Statement
2:
“At
constant temperature, the product of pressure and a volume of a given mass of
a gas is always constant.”
Therefore; if
P_{1 }& V_{1}
are initial pressure & volume, &
P_{2} & V_{2}
are changed pressure & volume,
Then P_{1}V_{1}=P_{2}V_{2 }This
is called “Boyle’s law equation
Graphical
Representation:
When
pressure’ P’ of a given mass of a gas is plotted against it’s volume ‘V’, a
parabolic curve is obtained, showing the decrease in volume in increasing
temperature. On the contrary, when
pressure ‘P’ of a given mass oa a gas is plotted against reciprocal pf volume
i.e. a straight line is
obtained. This confirms the direct relationship between ‘P’ and ‘’.
Limitations of Boyle’s law: This law is
not obeyed by gases under conditions of high pressure & law temperature.
CHARLE’S
LAW:
In
1787, a French physicist, Charles’s showed the relationship between the
volume of a given mass of a gas and it’s temperature at a constant pressure.
This law is called Charles’s law
STATEMENT # 1:
According
to this law:
“At constant pressure, the
volume of a given mass of a gas is directly proportional to the absolute temperature.”
EXPLAINATION:
It
means, if the pressure is kept constant, the increase in temperature would
result also in increase the volume of a given mass of a gas. Similarly, the
decrease in temperature results also in decrease in the volume of a gas.
MATHEMATICAL
EXPRESSION:
Mathematically, Charle’s law can be
expressed as:
VaT (At. Constant Pressure)
OR V=KT OR
This expression gives another
statement of Charle’s law, which is as under.
STATEMENT#2:
“At
constant pressure, the ratio of volume to the absolute temperature of given
mass of a gas is always constant.”
Therefore; if
V_{1}&T_{1}
are initial volume & temperature & V_{2 }&T_{2}
are changed volume & temperature.
Then
This is called “CHARLES’S law
equation.”
EXPERIMENTAL
VERIFICATION:
Consider
a gas cylinder fitted with a move able piston. The volume of the gas enclosed
in the cylinder is V_{1} at temp. T_{1} . When the gas is
heated to T_{2}, its volume is increase to V_{2} by moving
the piston upward. It the pressure on the piston is kept constant, then it is
observed that the ratio between V_{1} andT_{1} is equal to
the ratio V_{2} and T_{2}.i.e.
This verifies the Charle’s law.
300
200 100 0 100
200 300
GRAHAM’S LAW
OF DIFFUSION:
Diffusion
is the natural process by which gases intermix with one another to form a
homogenous mixture.
In
1833, Graham established a relation ship between the rate of diffusion of
gases and their densities which is terms as “Gaham’s law of diffusion”.
STATEMENT:
According
to this law,
“The rates of
diffusion of gases are inversely proportional to the square root of their
densities under same condition of temperature and pressure”.
MATHEMATICAL Expression:
Mathematically,
graham’s law can be expressed as:
OR
Where r = rate of diffusion of gas,
d= density of gas,
K= Proportionality
constant.
Suppose two gases with densities d_{1}
& d_{2}, diffuse into each other. If the rate of diffusion of the
gases are r_{1} & r_{2} respectively, then according to
graham’s law:
For gas 1,
& For gas 2,
By
combining the two equations, we get
Since the density of a gas is
proportional to its molecular mass, so Graham’s law may also be expressed as:
Experimental Verification:
Take
a 100 cm long glass tube. Plug one end of it with a piece of cotton soaked in
NH_{3} solution and the other with a piece of cotton soaked in HCl
solution as shown in the diagram.
The
vapours of NH_{3} and HCl escape into the glass tube simultaneously.
A white ring of NH_{4}Cl appears at the meeting point of the two gases.
Measure out the distance of te white ring from two ends.
Suppose,
the distance covered by NH_{3} = 60 cm
&
the distance covered by HCl = 40 cm
Since
the time ‘t’ is the same, therefore The rate of diffusion of NH_{3}
gas =
&
the rate of diffusion of HCl gas =
\ Molecular Mass of NH_{3}
= = 17
&
Molecular Mass of HCl = = 36.5
\ According to Graham’s law of
diffusion,
1.5 = 1.5
Since
L.H.S. = R.H.S., therefore Graham’s law of diffusion of gases is verified.
Dalton’s Law of Partial Pressure:
The
behavior observed, when two or more gases are placed in same container is
summarize in Dalton’s Law of Partial Pressure.
Statement: In 1801, Dalton’s found that
“The total pressure of a gaseous
mixture is the sum of the
partial pressure, exerted by each of the
gases present in
the mixture”.
Mathematical
Expression:
Mathematically
this law can be expressed as,
P
= P_{1} + P_{2} + P_{3} + ………………
Where
P =
Total pressure of gaseous mixture
P_{1} = Partial Pressure of gas 1.
P_{2} = Partial Pressure of gas 2.
P_{3} = Partial Pressure of gas 3.
Explanation:
When
two or more gases which do not react chemically, are mixed in the same container,
then each gas will exert the same pressure as it would exert if it alone
occupied the volume containing the mixed gases, under the same condition.
This portion of the total pressure of a mixture is known as PARTIAL PRESSURE.
Dalton observed that the total pressure of a mixture of different gases is
always equal to the sum of individual or partial pressure of each gas present
in a mixture.
Experimental
Verification:
Let
us suppose that two different gases A & B are confined in two separate
compartments as shown, in the figure. Both the compartments are of same size
with a pressure measuring device.
Now
suppose that the pressure of a gas is ‘A’ is 800 torr and that of gas ‘B’ is
900 torr in their separate compartments. If gas ‘A’ was transferred into the
compartment ‘B’ with the help of a movable piston through the total pressure
in this compartment would be the sum of the original pressure in the two
compartments when the gases were occupying same volume separately.
i.e. P_{total} = P_{A} + P_{B}
1700 = 800 + 900
1700 = 1700
Hence,
law is verified.




4.1.3

KMT
EXPLAINATION FOR BOYLE’S LAW
Boyle’s
law can easily be explained on the basis of the kinetic theory of gases, when
the volume of a given amount of a gas is decrease, there is more crowding of
the molecules in that space. This result in more frequent collision between
the molecules and the walls of the container and thus the pressure of the gas
is increased and viseversa.
Limitations of Boyle’s law: This law is
not obeyed by gases under conditions of high pressure & law temperature.
KMT
EXPLAINATION FOR CHARLES’ LAW
This
law can be easily explained with the help of Kinetic molecular theory as:
An
increase in temperature increases the K.E. of gas molecules which results in
their more collision per second against the walls of the container. But if
the pressure is kept constant the extra force of the colliding molecules is
utilized for the expansion of gas, i.e. increase in volume.
KMT
EXPLAINATION FOR AVOGADRO ‘S LAW
It
means that, if we take different sample of different gases at same
temperature and pressure, then if the volume of each gas sample is equal, the
no. of molecules of each sample will be also equal evidently, if we increase
the volume of gas sample, the no, of molecules will be also increase.
Avogadro’s
also found that at the some condition of temperature and pressure, the one
mole of any gas occupies always 22.4dm^{3}
volume, this volume is called molar gas volume. Also, this volume contain
always constant no. of particles of gas, and its value is 6.02 x 10^{23}.
This value is called Avagadro’s number.




4.2.1

Charles’s
law can also be explained by graphical method, if the volume of the given
mass of a gas is plotted against its absolute temperature values at a
constant pressure, a straight line is obtained, showing the direct
relationship between ‘V’ and ’T’.
If
the straight line is extra plotted it intercepts the temperature axis at
273.16^{o}C. This temperature is called “ABSOLUTE ZERO”.
ABSOLUTE ZERO:
It
is a hypothetical temperature, at which the volume of all gases become zero.
Its value is 273.16^{o}C.This temperature can never be achieved.
The
scale on which 273.16^{o}C is taken as zero is called “KELVIN SCALE”
and is indicated by K. Centigrade is related to Kelvin scale as;
^{o}K = ^{o}C
+ 273



4.2.2

NUMBERICAL




4.3.1

AVAGADRO’S LAW:
In
1811, Amadeo Avagadro stated the relation ship between the volume and the no.
of molecules of the gas. This is called “AVAGADRO’S LAW”.
Statement:
According
to Avogadro’s law;“The Volume of a gas is directly proportional to the number
of molecules of the gas at constant temperature & pressure”.
Explanation:
It
means that, if we take different sample of different gases at same
temperature and pressure, then if the volume of each gas sample is equal, the
no. of molecules of each sample will be also equal evidently, if we increase
the volume of gas sample, the no, of molecules will be also increase.
Avogadro’s
also found that at the some condition of temperature and pressure, the one
mole of any gas occupies always 22.4dm^{3}
volume, this volume is called molar gas volume. Also, this volume contain
always constant no. of particles of gas, and its value is 6.02 x 10^{23}.
This value is called Avagadro’s number.
Mathematical
Expression:
Mathematically,
Avogadro’s law can be written as,
V
µ
n
OR
V = K n
Where
n= no. of molecules of gas




4.4.1

General Gas
Equation:
Boyle’s
law, Charles law and Avogadro’s law may be combined together to give a
general relation between the pressure, volume, temperature and no. of moles
of a gas. This relationship is called “General
Gas Equation”
According to Boyle’s law
According to Charle’s law V µ T
On
combining these three laws. We get
OR
OR PV= nRT
This expression is called ‘GENERAL
GAS EQUATION’. Where ‘R’ is a proportionally constant and is called gas
constant.
For
1mole of a gas, n=1.
\PV=RT



4.4.2

When
the temperature of a gas changes from T_{1} to T_{2}, then
its volume as well as pressure changes from V_{1} to V_{2}
and P_{1} to P_{2}.
\ For initial
state:
& For final state:
Combine
these two, we have
This
relationship is used to solve problems regarding changes of volume of gases,
due to the changes in the pressure & temperature.
VALUES &
UNIT’S OF ‘R’:
(a)
According to Avagadro’s law, at S.T.P the one mole
of any gas occupies a volume of 22.4dm^{3}.
i.e. T=0˚C=273^{o}K , P=1atm., n=1mole and V=22.4dm^{3}
Then the value and unit of gas
constant will be;
(b)
When ‘P’ is expressed in and volume ‘V’ in m^{3},then at S.T.P,
P=101300 ,V=0.0224m^{3 } , n=1mol. And T=273^{o}K.
Then the value and
unit of gas constant will be.
\
R
= 8.314 N.m / mole x K
R
= 8.314 J/mole x K




4.4.3


U



4.4.4


A


4.5

4.5.1

Deviations
from ideal behavior
Ideal gas : a gas which obeys the general gas
equation and other gas laws under all conditions of temperature and pressure
is known as Ideal gas or perfect gas.
The molecules of an ideal gas :
(i)
Occupy negligible or no volume
(ii)
Have no intermolecular
attractive forces.
Real gas : a gas
which does not obeys general gas
equation and all other gas laws strictly but tends towards ideality at low
pressure and high temperature is knonw as real gas .
Cause
of deviations from ideal behavior
In order to explain deviations from ideal behavior
,Vander waal pointed out that the following two assumptions in kinetic theory
are faulty.
(i)
The volume occupied by the gas
molecules themselves is negligible as compared to total volume of the gas
The above assumption
is nearly valid if the pressure is low .At low pressure ,the gas molecules
are widely separated and the free
space between the molecules is very large in comparison to the actual volume
of molecules of the gas. Under such condition, the volume of the gas
molecules can be neglected in comparison to the total volume. At the high
pressure, the molecules of gas are relatively closed together and the total
volume is significantly less . However
the actual volume of the gas
molecules remains unchanged because the gas molecules are
incompressible. Under these conditions, the volume of a real gas is larger than that for an ideal
gas.
(ii)
The molecules of a gas exert no
appreciable attraction upon each other .
This assumption is
nearly valid when the pressure is low and the temperature is high so
that the molecules are far away from
each other . if the pressure is high and the temperature is low , the volume
of the gas decrease .Gas molecules come closer to each other .The attractive
force between the gas molecules under
these conditions are quite appreciable and can not neglected .

U


4.5.2

Numerical for
ideal equation



4.6

4.6.1
































Sunday, December 11, 2011
Notes of AKUEB
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Wow sir thats great aap nay bohat achay notes dalay hai aj pehli dafa may nay aap ki website visit ki thank you very much...
ReplyDeleteSurface tension
ReplyDeleteSurface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects (e.g. water striders) to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids.
Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.
In materials science, surface tension is used for either surface stress or surface free energy.
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