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c.....Three States of Matter
Definitions
Ideal gas
An ideal gas is a hypothetical (imaginary) gas, which has no existence. Ideal gas obeys all gas laws at all temperatures and pressures. There is no force of attraction or repulsion between the molecules of an ideal gas. Molecules of ideal gas occupy no space.
Real gas
Gases that exist are real gases such as Hydrogen, Nitrogen, Oxygen, He, Ne, F2, CO2, CO etc. Real gases do not obey gas laws at all temperatures and pressures. Real gases deviate from ideal behavior at high pressure and low temperature. There exists small force of attraction between the molecules of real gases.
S.T.P
S.T.P: stands for "STANDARD TEMPERATURE AND PRESSURE"
The volume of a gas changes with temperature and pressure. Therefore it is not completely defined unless temperature and pressure of the gas are specifically mentioned.
In order to compare different gases, volume of gases must be at a standard set of conditions of temperature and pressure.
The melting point of ice i.e. 0 0C or 273 K and the average pressure of atmosphere at sea level i.e. 1.00 atmosphere or 760 torr are the standard conditions of temperature and pressure.
Pressure
Force per unit area is called PRESSURE.
P = F/A
UNITS:
• Atmosphere
• cm of Hg
• Torr
• mm of Hg
• N/m2 or Pascal
• Psi or pound per square inch
Conversions of Pressure in different units:
1 atmosphere = 76 cm of Hg
1 atmosphere = 760 torr or mm of Hg
1 atmosphere = 1.01 X 105 N/m2 OR Pascal
1 atmosphere = 14.7 psi
Sublimation
Some solid substances on heating directly converted in gaseous state without passing through liquid state. This phenomenon is called as SUBLIMATION.
In the light of K.M.T the intermolecular forces in these solids (such as NH4Cl, Camphor, Naphthalene, Iodine) is less than ordinary solids. Therefore high energy molecules at solid surface overcome the attraction forces and directly pass into vapours.
Molar Volume
At S.T.P volume of one mole of any gas is 22.4dm3. This volume is referred to as "Molar Volume".
Or
A 0 0C & 1 atmosphere volume of one mole of any gas is 22.4dm3. This volume is called "Molar Volume"
Anisotropy
The crystalline substances which show variable intensity of physical properties in different directions are known ANISOTROPES and the phenomenon is called ANISOTROPY. For example:
1) Mica can be cleaved easily parallel to its plane but difficult to cut perpendicular to its plane.
2) Graphite conduct electricity parallel to its plane but it can not conduct electricity perpendicular to its plane.
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KINETIC MOLECULAR THEORY OF GASES
MAIN POSTULATES
Main postulates of kinetic molecular theory of gases are as under:
A gas consists of very small microscopic particles called 'molecules'. Depending upon the nature of gas each gas molecule may consists of an atom or group of atoms. Molecules are in a state of continuous motion.
All the molecules of a gas are in stable state and are considered identical.
Any finite volume of a gas consists of very large number of molecules.
At S.T.P. there are 3 x 1025 molecules in a cubic meter.
The molecules are wide separated from each other as compared to their own dimensions.
The diameter of a molecule is about 3 x 10-10 meter.
Gas molecules move in straight line in all possible directions (random movement) with various
speeds.
Gas molecules collide with each other and with the walls of container. There collisions are perfectly elastic in nature.
Gas molecules when collide with the walls of container, they transfer their momentum which appears as pressure of gas.
Molecules of an ideal gas exert no force of attraction or repulsion on one another except during collision.
The average kinetic energy of gas molecules is directly proportional to absolute temperature.
At a given temperature, the molecules of all gases have the same kinetic energy.
Newtonian mechanics is applicable to molecular motion.
Three States of Matter
Gas laws
Boyle’s law
Introduction
Boyle’s law is a quantitative relationship between volume and pressure of a gas at constant temperature.
Statement
"The volume of a given mass of a gas is inversely proportional to pressure if temperature remains constant ". Mathematical representation of Boyle’s law
According to Boyle’s law
V 1/P
V= (constant)(1/P)
PV=constant
At P1 pressure
P1V1 = constant ------------------(1)
At P2 pressure
P2V2 = constant ------------------(2)
Comparing (1) & ( 2)
P1V1 = P2V2
.
Second statement
"At constant temperature, the product of pressure and volume of a gas remains constant "
Graphical representation of Boyle’s law
Graph between P & V at constant temperature is a smooth curve known as "parabola"
Graph between 1/P & V at constant temperature is a straight line.
Charles law
Introduction
It is quantitative relation between volume and absolute temperature of a gas at constant pressure.
Statement
"The volume of a given mass of a gas at constant pressure is directly proportional to absolute temperature"
Second statement
"The volume of a given mass of a gas increases or decreases by 1/273 times of it’s original volume at 0 0C for every degree fall or rise of temperature at given pressure."
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Mathematical representation
Let the volume of a gas at T Kelvin is V
Then according to Charles’s law
V T
V = (constant) T
V/T = constant
At T1 k
V1/T1 = k ---------------(1)
At T2 k
V2/T2 = k ---------------(2)
Thus
V1/T1 = V2/T2
Third statement
By using above equation ,Charles’s law can also be stated as:
"The ratio of volume to absolute temperature of a gas at given pressure is always constant"
Graphical representation
Graph between Volume and absolute temperature of a gas at constant pressure is a "straight line"
Absolute scale of temperature or absolute zero
If the graph between V and T is extra plotted, it intersects T-axis at -273.16 0C At -273.16 0C volume of any gas theoretically becomes zero as indicated by the graph.
But practically volume of a gas can never become zero. Actually no gas can achieve the lowest possible temperature and before -273.16 0C all gases are condensed to liquid. This temperature is referred to as absolute scale or absolute zero. At -273.16 0C all molecular motions are ceased.
GENERAL GAS EQUATION AND EQUATION OF STATE OF A GAS
......
According to Boyle’s Law :
Volume of a given mass of a gas is inversely proportional to pressure if temperature remains constant
. V 1/P -------------------(1)
According to Charles’s law:
Volume of a given mass of a gas is directly proportional to absolute temperature if pressure remains constant.
V T ----------------------(2)
According to Avogadro’s law:
Volume of a gas is directly proportional to no of moles.
V n -----------------------(3)
Combining 1,2,and 3
V T.n1/P. V nT/P
V= (constant) nT/P
PV/nT = constant
Here constant is R
PV/nT = R
Or
PV= n RT
This is the equation of state of a gas (Ideal Gas Equation)
R= Universal gas constant
Value of R is equal to 0.0821 dm3.atmosphere/mole.k
R has different values in different systems of unit
ANOTHER FORM:
As PV/nT = constant
For initial conditions:
When temperature is T1 and pressure is P1:
P1V1/T1 = constant -----------------(a)
Similarly for final conditions:
P2V2/T2 = constant -----------------(b)
From equation (a) & (b)
P1V1/T1 = P2V2/T2
VALUE OF R
In atmp.dm3/mole.k
Consider one mole of an ideal gas at S.T.P.
As we know that at S.T.P. one mole of any gas occupies 22.4dm3 volume.
DATA
T = 0 0C + 273 = 273K P=1 atmp n =1 mole V =22.4 dm3
R = ?
Using ideal gas equation
PV = nRT
R = PV/nT
R =1atmp x 22.4 dm3/1 mole x 273K
R = 0.0821 atmp . dm3/mole .
In J/mole.k
Consider onemole of an ideal gas at S.T.P.
P=1.01 x 105 N/m2
T = 0 0C + 273 = 273K
n =1 mole
V =22.4 dm3 = 22.4/1000=0.0224 m3
R =?
Using ideal gas equation
PV = nRT
R=PV/nT
R = 1.01 x 105 x 0.0224/ 1x 273
R = 8.31 J/mole K
Explanation in the Light of Kinetic Molecular Theory
Q) explain diffusibility of gases in term of K.M.T.
According to Kinetic molecular theory:
The molecules of a gas are widely separated from each other and there are large empty spaces due to which molecules move freely. Due to this free movement gas molecules intermix with each other very quickly and diffuse very fast.
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Q) Define compressibility of a gas in the light of K.M.T.
According to Kinetic Molecular Theory there are large empty spaces between molecules of gas. When pressure is applied on a gas, molecules of gas come close to each other and the volume of gas is reduced. That’s why gases can be compressed to large extend.
Q) Explain diffusibility of liquids in terms of K.M.T.
In term of K.M.T in liquid molecules are close to each other and diffusion takes place slowly. In liquids molecules move freely. This free movement of molecules is responsible for the diffusion of liquid.
Q) Explain compressibility of liquids in terms of K.M.T.
In the light of K.M.T the liquid molecules due to their closeness roll over one and other. Due to very little space between the molecules, the liquid molecules can not be pushed close to each other by applying pressure. However at very high pressure a liquid can be compressed to very small extend.
Q) Explain compressibility of solids in terms of K.M.T.
According to K.M.T, there are very strong forces of attraction between the molecules of a solid and there is no space between two molecules. Due to this reason solids are completely incompressible. If we apply high pressure on a solid it will not compress but it will deform.
Q) Explain diffusibility of solids in terms of K.M.T.
In terms of K.M.T, there are very strong force of attraction between the molecules of a solid and there is no space among molecules. But there exists vibratory motion in the molecules of solid. This vibratory motion of molecules is responsible for the diffusion of solids. Since force of attraction are very large therefore diffusion in solids takes place with very negligible speed
Three States of Matter
Scientific Reasons
Q1) Steam produces severe burns, then boiling water, although both have same temperature.
Both steam and boiling water have the same temperature i.e. 100 oC. But heat content of steam is greater than the boiling water because latent heat of steam is 2.26 x 105 J/kg .That’s why steam produces severe burn as compared to boiling water.
Q2) evaporation causes cooling.
Temperature is the measurement of average kinetic energy of molecules. As liquid evaporates, high kinetic energy molecules escape from the liquid and lowers the average kinetic energy molecules remain in the liquid. Due to this reason temperature falls down
Q3) In mountain areas food takes longer time to cook.
Boiling point of a liquid depends on the outer atmospheric pressure.At normal atmospheric pressure boiling point of water is 100 0C. on mountain areas such as Quetta and Swat, atmospheric pressure is below 760 torr. Due to this reason B.P of water decreases and food takes longer time to cook.
Q4) Glycerin distilled at 290 0C but it decompose at this temperature, how would you distilled it?
At 760 torr, B.P of glycerin is 290 0C but at 290 0C temperature glycerine evaporates and it become difficult to distill it. In order to overcome this difficulty it is distilled at 50 torr . At 50 torr it’s B.P decreases to 210 0C. At 210 0C it does not decompose and distiledl easily.
Q5) Evaporation of a liquid is accelerated on heating?
Rate of evaporation increases with the increase in temperature because on heating kinetic energy of molecules becomes high enough to overcome intermolecular forces of attraction. Thus number of molecules leaving the liquid surface is increased. So the rate of evaporation increases on heating
Q6) Falling drop of liquid is spherical.
Falling drop of a liquid is always spherical in shape due to surface tension. The inward forces on the surface molecules of the liquid droplet tend to cause the surface to volume ratio as small as possible. Since surface to volume ratio is minimum for the spherical shape that’s why falling drop of a liquid is spherical.
Q7) Under similar conditions surface tension of water is higher than the surface tension of ether.
Surface tension depends upon the strength of intermolecular forces of attraction. Water has higher surface tension due to polar nature of its molecules. In water there exist hydrogen bond as compared to ether, which is non-polar and has no hydrogen bond. We know that hydrogen bond increases intermolecular attraction. Consequently water has high surface tension.
VAPOUR PRESSURE........
Pressure exerted by the vapour of a liquid at equilibrium is called "Vapour Pressure" of that liquid.
OR
Pressure exerted by the vapours of a liquid when rate of evaporation is and the rate of condensation becomes equal is called "Vapour Pressure".
• Under similar conditions of temperature and pressure, different liquids have different vapor pressures .
• Vapour pressure varies with temperature.
• At elevated temperature, vapor pressure also increases
Q) Evaporation is a cooling process, explain.
We know that evaporation takes place at all temperatures and pressure. But only those molecules escape from the liquid having high kinetic energies. As a result only those molecules remain in the liquid which have low kinetic energy. Since K.E is directly related to temperature, we feel a cooling effect due to evaporation.
BOILING POINT
The temperature at which the vapour pressure of a liquid becomes equal to atmospheric pressure is called BOILING POINT. At this temperature a liquid starts boiling.
Boiling point of liquid varies with atmospheric pressure. If atmospheric pressure is less then 760 torr then the boiling point of a liquid will decrease from its standard boiling point.
Boiling point of a liquid decreases with the decrease in pressure and vice versa
Normal boiling point
Boiling point of a liquid when atmospheric pressure is 1.00 atmp or 760 torr is referred to as NORMAL BOILING POINT.
VISCOSITY.........
Viscosity is characteristic property of liquid, viscosity describes the flow of a liquid.
Definition:
Viscosity is defined as the resistance in the flow of a liquid Or
Internal friction present between two layers of a liquid
which resists the flow of liquid is commonly known as Viscosity.
• A liquid with high viscosity is thick and flows slowly.
• A liquid with low viscosity is thin and flows quickly.
• Different liquids have different viscosities.
FACTORS AFFECTING VISCOSITY
Size of molecules
Viscosity of a liquid having large molecules is high whereas the viscosity of those liquids that have small molecules is low.
Shape of molecules
Spherical molecules provide resistance but oval shaped or disc like molecules provide greater resistance in the flow of liquid. That’s why viscosity of liquids having spherical molecules is low.
Inter molecular forces
Liquids having large inter molecular forces have greater viscosity.
Temperature
Viscosity of liquid decreases with increase in temperature. Because an increase in temperature, reduces the forces of attraction between molecules.
Units:
• Most common unit is "POISE"
• Small unit is "CENTI POISE"
• In S.I system unit is N.S/m2
Conversion factors
1Centipoise = 10-3 NS/m2 or 0.001 NS/m2
SURFACE TENSION
Surface tension is a characteristic property of a liquid.
Definition:
"Perpendicular force acting on the unit length of the surace of a liquid is called SURFACE TENSION".
Surface tension = force/length
g = F/L
2nd definition:
"Energy per unit area on the surface of a liquid is called SURFACE TENSION"
s = energy /area
Unit of surface tension
• N/m (in S.I system)
• Dyne/cm (in C.G.S system)
• Joule/m2 (in S.I system)
• Erg/cm2 (in C.G.S system)
FACTORS AFFECTING SURFACE TENSION
Inter molecular forces
If force of attraction between molecules is high then surface tension will also be high.
Hydrogen bonding
Liquids that have H-bond such as water, have high values of surface tension.
Temperature
Surface tension of a liquid decreases with the increase in temperature because an increase in temperature, reduces force of attraction between molecules.
Properties of Solid..........
LATENT HEAT OF FUSION
Latent heat of fusion is defined as:
The amount of heat required to melt unit mass of solid substance at its melting point.
It is denoted by Hf.
Unit:
Its unit is
J/Kg ,
erg/gm
Formula: Q=m x Hf
Where
m= mass of solid
Q= amount of heat
UNIT CELL Crystals made of very small basic patterns or arrangements of atoms or molecules or
ions.These basic patterns are joined together to form a crystal.Theses basic patterns are known
as "UNIT CELL". All the unit cell of a crystal are identical.
Characteristics of unit cell
A unit cell has a definite shape.
Length of edges of a unit cell are definite.
Angle between the edges are definite.
All unit cells of a substance always contain equal numbers of atoms or molecules or ions.
Cell parameters
Length of edges (axes) and the angle between the edges are collectively known as "Cell Parameters".
CRYSTAL SYSTEM
There are seven types of crystals
1) Cubic Crystal System:
• In cubical crystal system, all the edges are equal
a = b = c
angle between the edges are equal i.e. 90
a = b = g = 90
Examples:
1. Sodium chloride (NaCl)
2. Zinc sulphide (ZnS)
3. Diamond
2) Tetragonal Crystal System:
• In tetragonal crystal system, two sides are equal but third side is different.
a = b ¹c
• Angles between the edges are equal i.e 90
a = b = g = 90
Examples:
1. SnO2
2. BaSO4.4H2O
3) Orthorhombic Crystal System:
• In orthorhombic crystal system, all the edges are different.
a ¹ b¹c
• Angle between the edges are equal i.e 90o
a = b = g = 90
Example:
1. FeSO4.7H2O
2. ZnSO4.7H2O
3. KNO3
4) Trigonal Or Rhombohedral Crystal System:
• In this system, all the edges are equal
a = b = c
• angles are equal but not equal to 90o. angles are between 90 and 120
a = b = g ¹ 90
Examples:
1. KNO3
2. AgNO3
5) Hexagonal Crystal System:
In this system, two sides are equal but third side is different.
a = b ¹ c
Two angles between the edges are equal to 90o but third angle is equal to 120.
a = b = 90, g = 120
Examples:
Graphite
6) Monoclinic Crystal System:
• In monoclinic crystal system, all the edges are different
a ¹ b ¹ c
• two angles are equal to 90 but third angle is not equal to 90
a = g = 90
b ¹ 90
Examples:
1. CuSO4. 5H2O
2. Sugar
7) Triclinic Crystal System:
in this system, all the edges are different
a ¹ b ¹ c
angles between the edges are not equal to 90
a ¹ b ¹ g ¹ 90
Examples:
1. CuSO4. 5H2O
2. K2Cr2O7
POLYMORPHISM-ALLOTROPY-ISOMORPHISM
POLYMORPHISM
Existence of substance into more than one crystalline forms is known as "POLYMORPHISM".
In other words: Under different conditions of temperature and pressure, a substance can form more than one type of crystals. This phenomenon is called Polymorphism and different crystalline forms are known as ‘POLYMORPHICS’
Example:
1) Mercuric iodide (HgI2) forms two types of crystals.
a. Orthorhombic
b. Trigonal
2) Calcium carbonate (CaCO3) exists in two types of crystalline forms.
a. Orthorhombic (Aragonite)
b. Trigonal
Polymorphous substances have similar chemical properties but different physical properties.
ALLOTROPY
"Existence of an element into more than one physical forms is known as ALLOTROPY "
Under different conditions of temperature and pressure an element can exist in more than one
physical forms. This phenomenon is known as Allotropy and different forms are known as "Allotropes"
Example:
Coal, lamp black, coke, Diamond, graphite etc. are all allotropic forms of carbon.
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ISOMORPHISM
Existence of different substances in one crystalline form is known as "ISOMORPHISM"
Or
Different substances may exist in identical crystalline forms. This phenomenon is called as
Isomorphism and these substances are known as ‘Isomorphous’.
Examples:
1) Na2SO4 & Ag2SO4 both exist in Hexagonal crystalline form.
2) KBF4 & BaSO4 both exist in Orthorhombic
3) ZnSO4 & NiSO4 both exist in Orthorhombic
4) CaCO3 & NaNO3 both exist in Trigonal
Properties of Isomorphic Substances
1) Isomorphic substances have same atomic ratio
2) Empirical formula of isomorphic substances is same
For example
CaCO3 NaNO3
1:1:3 1:1:3
NaF MgO
1:1 1:1
3) They have different chemical & physical properties.
4) When their solutions are mixed, they form mixed type of crystals.
5) They show property over growth.
TYPES OF SOLIDS
TYPES OF SOLIDS
Solids can be divided in to two distinct classes.
1) Crystalline solids
2) Amorphous solids
CRYSTALLINE SOLIDS
Crystalline solids have the following fundamentals properties.
1. They have characteristic geometrical shape.
2. They have highly ordered three-dimensional arrangements of particles.
3. They are bounded by PLANES or FACES
4. Planes of a crystal intersect at particular angles.
5. They have sharp melting and boiling points.
Examples:
Copper Sulphate (CuSO4), NiSO4, Diamond, Graphite, NaCl, Sugar etc
AMORPHOUS SOLIDS
Solids that don’t have a definite geometrical shape are known as Amorphous Solids.
1. In these solids particles are randomly arranged in three dimension.
2. They don’t have sharp melting points.
3. Amorphous solids are formed due to sudden cooling of liquid.
4. Amorphous solids melt over a wide range of temperature
5. Examples:
Coal, Coke, Glass, Plastic, rubber etc
Types of Crystals
Types of Crystals
Solid crystals can be divided into four categories.
1) Metallic crystals
2) Ionic crystals
3) Covalent crystals
4) Molecular crystals
1) Metallic Crystals
In metallic crystals, atoms are joined together by metallic bond. Metallic crystals are very hard.
• They have high melting point and boiling point
• They have shiny surface
• They conduct electricity and heat
• They are ductile
They are malleable
2) Ionic Crystals
• Solids that contain ionic bond in their structure consist of ionic crystals.
• In ionic crystals, oppositively charged ions are joined together by strong electrostatic forces
• They are hard substances
• They have high melting and boiling point.
• They posses ionic bond
• They conduct electricity in molten state and in the form of solution.
• They are brittle
• They are not ductile
• They can not be drawn into sheets
3) Covalent Crystals
• Solid substances in which atoms are held together by covalent bond are known as covalent crystals.
• These crystals are very stable
For example:
Diamond
Graphite
4) Molecular Crystals:
In molecular crystals, molecules are joined together by weak Vander Wall forces.
These substances have low melting point and boiling point.
Generally they are volatile (evaporates)
Difference between Amprphous Solids and Crystalline Solids
Amprphous Solids Crystalline Solids
1. Solids that don't have definite geometrical shape. They have characteristic geometrical shape
2. Amorphous solids don't have particular melting point. They melt over a wide range of temperature. T hey have sharp melting point
3. Physical properties of amorphous solids are same in different direction,i.e. amorphous solids are isotropic Physical properties of crystalline solids are different in different directions. This phenomenon is known as Anisotropy.
4. Amorphous solids are unsymmetrical When crystalline solids are rotated about an axis, their appearance does not change. This shows that thay are symmetrical
5. Amorphous solids don't break at fixed cleavage planes. Crystalline solids cleavage along particular direction at fixed cleavage planes.
DALTON'S LAW OF PARTIAL PRESSURE
PARTIAL PRESSURE
In a mixture of different gases which do not react chemically each gas behaves independently of the other gases and exerts its own pressure. This individual pressure that a gas exerts in a mixture of gases is called it's partial pressure.
DALTON'S LAW OF PARTIAL PRESSURE
Based on this behaviour of gases, JOHN DALTON formulated a basic law which is known as "The Dalton's law of partial pressure" .
The law states that:
"If two or more gases (which do not react with each other) are enclosed in a vessel,
the total pressure exerted by them is equal to the sum of their partial pressure".
MATHEMATICAL REPRESENTATION
Consider a mixture of three non-reacting gases a , b and c .Partial pressures of these gases are Pa ,Pb and Pc .According to Dalton's law of partial pressure, their total pressure is given by:
Ptotal = Pa + Pb + Pc
DALTON'S LAW IN THE LIGHT OF KINETIC MOLECULAR THEORY
According to kinetic molecular theory of gases there is no force of attraction or repulsion among the gas molecules. Thus each gas behaves independently in a mixture and exerts it's own pressure.
In terms of KINETIC MOLECULAR THEORY, Dalton's law of partial pressure can be explained as:
"In a non-reacting mixture of gases, each gas exerts separate pressure on the container in which it is confined due to collision of it's molecules with the walls of container.
The total pressure exerted by the gaseous mixture is equal to
the sum of collisions of the molecules of individual gas ."
EXPRESSION FOR PARTIAL PRESSURE
Consider a gaseous mixture of three different gases a , b and c enclosed in a container of volume Vdm3 at T Kelvin. Let the partial pressures of these gases are Pa ,Pb and Pc respectively and total pressure of mixture is Pt. Let there are na ,nb and nc moles of each gas respectively and the total number of
moles are nt.
Three gases confined in a cylinder under similar conditions:
Using equation of state of gas:
PV = nRT
OR
P = nRT/V
For gas a
Pa = naRT/V--------------- (i)
For gas b
Pb = naRT/V--------------- (ii)
For gas c
Pc = ncRT/V--------------- (iii)
For any gas
Pgas = ngasRT/V
OR
---------(a)
Adding equation (i) , (ii) and (iii), we get,
Pt = naRT/V + nbRT/V + ncRT/V
Pt = (na + nb + nc)RT/V
OR
But nt = na + nb + nc
Pt = nt RT/V
Comparing equation (a) and (b), we get,
This expression indicates that the pressure of a gas is proportional to number of moles if confined under similar conditions.
DIFFUSION--GRAHAM'S LAW OF DIFFUSION
DIFFUSION OF GASES
Inter mixing of two or more gases to form a homogeneous mixture without any chemical change is called "DIFFUSION OF GASES" . Diffusion is purely a physical phenomenon. Gases diffuse very quickly due to large empty spaces among molecules. Different gases diffuse with different rates (velocities).
GRAHAM'S LAW OF DIFFUSION
Graham's law is a quantitative relation between the density and rate of diffusion of gases.
STATEMENT
The rate of diffusion of a gas is inversely proportional to the square root of its density.
The comparative rates of diffusion of two gases are inversely proportional to the square root of their densities.
MATHEMATICAL REPRESENTATION OF THE LAW
Consider two gases A and B having mass densities d1 and d2 and their rates of diffusions are r1 and r2 respectively.
According to Graham's law of diffusion:
For gas A:
OR
..................(i)
For gas B:
OR
..................(ii)
Dividing equation (i) by equation (ii)
Since density molecular mass, therefore, we can replace density d by Molecular mass M.
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