introduction to fundamental concepts of chemistry for class xi

7/31/2019 Introduction to Fundamental Concepts of Chemistry for Class XI

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Introduction to Fundamental Concepts of

Chemistry

Atom

It is the smallest particle of an element which can exist with all the properties of its own elementbut it cannot exist in atmosphere alone.

Molecule

When two or more than two atoms are combined with each other a molecule is formed. It can

exist freely in nature.

Formula Weight

It is the sum of the weights of the atoms present in the formula of a substance.

Molecular Weight

It is the sum of the atomic masses of all the atoms present in a molecule.

Chemistry

It is a branch of science which deals with the properties, composition and the structure of matter.

Empirical Formula

DefinitionIt is the simplest formula of a chemical compound which represents the element present of the

compound and also represent the simplest ratio between the elements of the compound.

ExamplesThe empirical formula of benzene is "CH". It indicates that the benzene molecule is composed of

two elements carbon and hydrogen and the ratio between these two elements is 1:1.The empirical formula of glucose is "CH2O". This formula represents that glucose molecule is

composed of three elements carbon, hydrogen and oxygen. The ratio between carbon and oxygen

is equal but hydrogen is double.


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Determination of Empirical Formula

To determine the empirical formula of a compound following steps are required.1. To detect the elements present in the compound.

2. To determine the masses of each element.

3. To calculate the percentage of each element.4. Determination of mole composition of each element.

5. Determination of simplest ratio between the element of the compound.

Illustrated Example of Empirical Formula

Consider an unknown compound whose empirical formula is to be determined is given to us.

Now we will use the above five steps in order to calculate the empirical formula.

Step I - Determination of the Elements

By performing test it is found that the compound contains magnesium and oxygen elements.

Step II - Determination of the MassesMasses of the elements are experimentally determined which are given below.

Mass of Mg = 2.4 gmMass of Oxygen = 1.6 gm

Step III - Estimation of the PercentageThe percentage of an element may be determined by using the formula.

% of element = Mass of element / Mass of compound x 100

In the given compound two elements are present which are magnesium and oxygen, therefore

mass of compound is equal to the sum of the mass of magnesium and mass of oxygen.Mass of compound = 2.4 + 1.6 = 4.0 gm

% Mg = Mass of Mg / Mass of Compound x 100

= 2.4 / 4.0 x 100= 60%

% O = Mass of Oxygen / Mass of Compound x 100

= 1.6 / 4.0 x 100= 40%

Step IV - Determination of Mole CompositionMole composition of the elements is obtained by dividing percentage of each element with itsatomic mass.

Mole ratio of Mg = Percentage of Mg / Atomic Mass of Mg

= 60 / 24

= 2.5Mole ratio of Mg = Percentage of Oxygen / Atomic Mass of Oxygen

= 40 / 16

= 2.5


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Step V - Determination of Simplest RatioTo obtain the simplest ratio of the atoms the quotients obtained in the step IV are divided by thesmallest quotients.

Mg = 2.5 / 2.5 = 1

O = 2.5 / 2.5 = 1

Thus the empirical formula of the compound is MgO

NoteIf the number obtained in the simplest ratio is not a whole number then multiply this numberwith a smallest number such that it becomes a whole number maintain their proportion.

Molecular Formula

DefinitionThe formula which shows the actual number of atoms of each element present in a molecule is

called molecular formula.

ORIt is a formula which represents the element ratio between the elements and actual number of

atoms of each type of elements present per molecule of the compound.

ExamplesThe molecular formula of benzene is "C6H6". It indicates that1. Benzene molecule is composed of two elements carbon and hydrogen.

2. The ratio between carbon and hydrogen is 1:1.

3. The number of atoms present per molecule of benzene are 6 carbon and 6 hydrogen atoms.

The molecular formula of glucose is "C6H12O6". The formula represents that1. Glucose molecule is composed of three elements carbon, hydrogen and oxygen.

2. The ratio between the atoms of carbon, hydrogen and oxygen is 1:2:1.3. The number of atoms present per molecule of glucose are 6 carbon atoms. 12 hydrogen atomsand 6 oxygen atoms.

Determination of Molecular Formula

The molecular formula of a compound is an integral multiple of its empirical formula.

Molecular formula = (Empirical formula)n

Where n is a digit = 1, 2, 3 etc.

Hence the first step in the determination of molecular formula is to calculate its empiricalformula by using the procedure as explained in empirical formula. After that the next step is to

calculate the value of n

n = Molecular Mass / Empirical Formula Mass

ExampleThe empirical formula of a compound is CH2O and its molecular mass is 180.

To calculate the molecular formula of the compound first of all we will calculate its empiricalformula mass


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Empirical formula mass of CH2O = 12 + 1 x 2 + 16

= 30n = Molecular Mass / Empirical Formula Mass

= 180 / 30

= 6

Molecular formula = (Empirical formula)n= (CH2O)6

= C6H12O6

Molecular Mass

DefinitionThe sum of masses of the atoms present in a molecule is called as molecular mass.

ORIt is the comparison that how mach a molecule of a substance is heavier than 1/12th weight or

mass of carbon atom.

ExampleThe molecular mass of CO2 may be calculated asMolecular mass of CO2 = Mass of Carbon + 2 (Mass of Oxygen)

= 12 + 2 x 16

= 44 a.m.uMolecular mass of H2O = (Mass of Hydrogen) x 2 + Mass of Oxygen

= 1 x 2 + 16

= 18 a.m.u

Molecular mass of HCl = Mass of Hydrogen + Mass of Chlorine= 1 + 35.5

= 36.5 a.m.u

Gram Molecular Mass

DefinitionThe molecular mass of a compound expressed in gram is called gram molecular mass or mole.

Examples1. The molecular mass of H2O is 18. If we take 18 gm H2O then it is called 1 gm molecular

mass of H2O or 1 mole of water.2. The molecular mass of HCl is 36.5. If we take 36.5 gm of HCl then it is called as 1 gm

molecular mass of HCl or 1 mole of HCl.

Mole

DefinitionIt is defined as atomic mass of an element, molecular mass of a compound or formula mass of a

substance expressed in grams is called as mole.


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ORThe amount of a substance that contains as many number of particles (atoms, molecules or ions)

as there are atoms contained in 12 gm of pure carbon.

Examples

1. The atomic mass of hydrogen is one. If we take 1 gm of hydrogen, it is equal to one mole ofhydrogen.

2. The atomic mass of Na is 23 if we take 23 gm of Na then it is equal to one mole of Na.

3. The atomic mass of sulphur is 32. When we take 32 gm of sulphur then it is called one mole ofsulphur.

From these examples we can say that atomic mass of an element expressed in grams is called

mole.Similarly molecular masses expressed in grams is also known as mole e.g.

The molecular mass of CO2 is 44. If we take 44 gm of CO2 it is called one mole of CO2 or the

molecular mass of H2O is 18. If we take 18 gm of H2O it is called one mole of H2O.

When atomic mass of an element expressed in grams it is called gram atom

WhileThe molecular mass of a compound expressed in grams is called gram molecule.

According to the definition of mole.One gram atom contain 6.02 x 10(23) atoms

While

One gram molecule contain 6.02 x 10(23) molecules.

Avagadro's Number

An Italian scientist, Avagadro's calculated that the number of particles (atoms, molecules) in onemole of a substance are always equal to 6.02 x 10(23). This number is known as Avogadro's

number and represented as N(A).

Example1 gm mole of Na contain 6.02 x 10(23) atoms of Na.

1 gm mole of Sulphur = 6.02 x 10(23) atoms of Sulphur.

1 gm mole of H2SO4 = 6.02 x 10(23) molecules H2SO41 gm mole of H2O = 6.02 x 10(23) molecules of H2O

On the basis of Avogadro's Number "mole" is also defined as

Mass of 6.02 x 10(23) molecules, atoms or ions in gram is called mole.

Determination Of The Number Of Atoms Or Molecules In The Given Mass Of A Substance

Example 1Calculate the number of atoms in 9.2 gm of Na.

SolutionAtomic mass of Na = 23 a.m.uIf we take 23 gm of Na, it is equal to 1 mole.

23 gm of Na contain 6.02 x 10(23) atoms


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1 gm of Na contain 6.02 x 10(23) / 23 atoms

9.2 gm of Na contain 9.2 x 6.02 x 10(23) /23= 2.408 x 10(23) atoms of Na

Determination Of The Mass Of Given Number Of Atoms Or Molecules Of A Substance

Example 2Calculate the mass in grams of 3.01 x 10(23) molecules of glucose.

SolutionMolecular mass of glucose = 180 a.m.u

So when we take 180 gm of glucose it is equal to one mole So,6.02 x 10(23) molecules of glucose = 180 gm

1 molecule of glucose = 180 / 6.02 x 10(23) gm

3.01 x 10(23) molecules of glucose = 3.01 x 10(23) x 180 / 6.02 x 10(23)

= 90 gm

Stoichiometry

(Calculation Based On Chemical Equations)

DefinitionThe study of relationship between the amount of reactant and the products in chemical reactions

as given by chemical equations is called stoichiometry.

In this study we always use a balanced chemical equation because a balanced chemical equation

tells us the exact mass ratio of the reactants and products in the chemical reaction.There are three relationships involved for the stoichiometric calculations from the balanced

chemical equations which are1. Mass - Mass Relationship2. Mass - Volume Relationship

3. Volume - Volume Relationship

Mass - Mass RelationshipIn this relationship we can determine the unknown mass of a reactant or product from a given

mass of teh substance involved in the chemical reaction by using a balanced chemical equation.

ExampleCalculate the mass of CO2 that can be obtained by heating 50 gm of limestone.

SolutionStep I - Write a Balanced Equation

CaCO3 ----> CaO + CO2

Step II - Write Down The Molecular Masses And Moles Of Reactant & ProductCaCO3 ----> CaO + CO2


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Method I - MOLE METHODNumber of moles of 50 gm of CaCO3 = 50 / 100 = 0.5 moleAccording to equation

1 mole of CaCO3 gives 1 mole of CO2

0.5 mole of CaCO3 will give 0.5 mole of CO2

Mass of CO2 = Moles x Molecular Mass= 0.5 x 44

= 22 gm

Method II - FACTOR METHODFrom equation we may write as

100 gm of CaCO3 gives 44 gm of CO21 gm of CaCO3 will give 44/100 gm of CO2

50 gm of CaCO3 will give 50 x 44 / 100 gm of CO2

= 22 gm of CO2

Mass - Volume RelationshipThe major quantities of gases can be expressed in terms of volume as well as masses. According

to Avogardro One gm mole of any gas always occupies 22.4 dm3 volume at S.T.P. So this law isapplied in mass-volume relationship.

This relationship is useful in determining the unknown mass or volume of reactant or product by

using a given mass or volume of some substance in a chemical reaction.

ExampleCalculate the volume of CO2 gas produced at S.T.P by combustion of 20 gm of CH4.


CH4 + 2 O2 ----> CO2 + 2 H2O

Step II - Write Down The Molecular Masses And Moles Of Reactant & Product

CH4 + 2 O2 ----> CO2 + 2 H2O

Method I - MOLE METHOD

Convert the given mass of CH4 in moles

Number of moles of CH4 = Given Mass of CH4 / Molar Mass of CH4From Equation

1 mole of CH4 gives 1 moles of CO2

1.25 mole of CH4 will give 1.25 mole of CO2

No. of moles of CO2 obtained = 1.25But 1 mole of CO2 at S.T.P occupies 22.4 dm3

1.25 mole of CO2 at S.T.P occupies 22.4 x 1.25

= 28 dm3

Method II - FACTOR METHOD

Molecular mass of CH4 = 16


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Molecular mass of CO2 = 44

According to the equation16 gm of CH4 gives 44 gm of CO2

1 gm of CH4 will give 44/16 gm of CO2

20 gm of CH4 will give 20 x 44/16 gm of CO2

= 55 gm of CO244 gm of CO2 at S.T.P occupy a volume 22.4 dm3

1 gm of CO2 at S.T.P occupy a volume 22.4/44 dm3

55 gm of CO2 at S.T.P occupy a volume 55 x 22.4/44= 28 dm3

Volume - Volume RelationshipThis relationship determine the unknown volumes of reactants or products from a known volume

of other gas.

This relationship is based on Gay-Lussac's law of combining volume which states that gases

react in the ratio of small whole number by volume under similar conditions of temperature &

pressure.Consider this equation

CH4 + 2 O2 ----> CO2 + 2 H2OIn this reaction one volume of CH4 gas reacts with two volumes of oxygen gas to give one

volume of CO2 and two volumes of H2O

ExamplesWhat volume of O2 at S.T.P is required to burn 500 litres (dm3) of C2H4 (ethylene)?


C2H4 + 3 O2 ----> 2 CO2 + 2 H2O

Step II - Write Down The Moles And Volume Of Reactant & ProductC2H4 + 3 O2 ----> 2 CO2 + 2 H2O

According to Equation1 dm3 of C2H4 requires 3 dm3 of O2

500 dm3 of C2H4 requires 3 x 500 dm3 of O2

= 1500 dm3 of O2

Limiting Reactant

In stoichiometry when more than one reactant is involved in a chemical reaction, it is not sosimple to get actual result of the stoichiometric problem by making relationship between any one

of the reactant and product, which are involved in the chemical reaction. As we know that when

any one of the reactant is completely used or consumed the reaction is stopped no matter the

other reactants are present in very large quantity. This reactant which is totally consumed duringthe chemical reaction due to which the reaction is stopped is called limiting reactant.

Limiting reactant help us in calculating the actual amount of product formed during the chemical


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reaction. To understand the concept the limiting reactant consider the following calculation.

ProblemWe are provided 50 gm of H2 and 50 gm of N2. Calculate how many gm of NH3 will be formed

when the reaction is irreversible.

The equation for the reaction is as follows.N2 + 3 H2 ----> 2 NH3

SolutionIn this problem moles of N2 and H2 are as follows

Moles of N2 = Mass of N2 / Mol. Mass of N2

= 50 / 28= 1.79

Moles of H2 = Mass of H2 / Mol. Mass of H2

= 50 / 2

= 25

So, the provided moles for the reaction arenitrogen = 1.79 moles and hydrogen = 25 moles

But in the equation of the process 1 mole of nitrogen require 3 mole of hydrogen. Therefore theprovided moles of nitrogen i.e. 1.79 require 1.79 x 3 moles of hydrogen i.e. 5.37 moles although

25 moles of H2 are provided but when nitrogen is consumed the reaction will be stopped and the

remaining hydrogen is useless for the reaction so in this problem N2 is a limiting reactant by

which we can calculate the actual amount of product formed during the reaction.N2 + 3 H2 ----> 2 NH3

1 mole of N2 gives 2 moles of NH31.79 mole of N2 gives 2 x 1.79 moles of NH3

= 3.58 moles of NH3

Mass of NH3 = Moles of NH3 x Mol. Mass= 3.58 x 17

= 60.86 gm of NH3

Three States Of Matter

Matter

It is defined as any thing which has mass and occupies space is called matter.Matter is composed of small and tiny particles called Atoms or molecules. It exist in threedifferent states which are gaseous, liquid & solid.

Properties of Gas


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1. It has no definite shape.

2. It has no definite volume, so it can be compressed or expanded.3. A gas may diffuse with the other gas.

4. The molecules of a gas are in continuous motion.

Properties of Liquids

1. A liquid has no definite shape.2. It has a fixed volume.

3. The diffusion of a liquid into the other liquid is possible if both of the liquids are polar or non-

polar.

4. It can be compressed to a negligible.

Properties of Solids

1. A solid has a definite shape.2. It has a fixed volume.

3. The rate of diffusion of solid with each other is very slow.

4. It cannot be compressed easily.

Kinetic Theory of Gases

It was an idea of some scientist like Maxwell & Bolzmann that the properties of gases are due to

their molecular motion. This motion of the molecules is related with the kinetic energy, so the

postulates give by the scientist about the behaviour of gases are collectively known as kinetic

molecular theory of gases.

The postulates of kinetic molecular theory are as follows.1. All gases consists of very large number of tiny particles called molecules.

2. These molecules are widely separated from each other and are so small that they are invisible.3. The size of the molecules is very small as compared to the distance between them.

4. There is no attractive or repulsive force between molecules so they can move freely.

5. The molecules are very hard and perfectly elastic so when they collide no loss of energy takes

place.6. The gas molecules are in continuous motion they move in a straight path until they collide.

The distance between two continuous collision is called Mean Free Path.

7. During their motion these molecules are collided with one another and with the walls of the

container.

8. The collision of the molecules are perfectly elastic. When molecules collide they rebound withperfect elasticity and without loss or gain of energy.

9. The pressure of the gas is the result of collision of molecules on the walls of the container.10. The average kinetic energy of gas molecules depends upon the absolute temperature. At any

given temperature the molecules of all gases have the same average kinetic energy (1/2 mv2).

Kinetic Theory of Liquids


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This theory is bases on the following assumptions.

1. The particles of a liquid are very close to each other due to which a liquid has fixed volume.2. The particles in a liquid are free to move so they have no definite shape.

3. During the motion these molecules collides with each other and with the walls of the

container.

4. These molecules possess kinetic which is directly proportional to its absolute temperature.

Kinetic Theory of Solids

The assumptions of kinetic theory for solids are as follows.

1. The particles in a solid are very closely packed due to strong attractive forces between the

molecules.2. These molecules are present at a fixed position and are unable to move.

3. They have definite shape because the particles are arranged in a fixed pattern.

4. They possess only vibrational energy.

Mean Free Path

The distance which a molecule of a gas travels before its collision with the other molecule iscalled free path. This distance between the collision of the molecules changes constantly so the

average distance which a molecule travels before its collision is called mean free path.

Boyle's Law

A relationship of volume with external pressure was given by Boyle's in the form of law. This

law is known as Boyle's Law which states,

For a given mass of a gas the volume of the gas is inversely proportional to its pressure providedthe temperature is kept constant.

Mathematically it may be written as

V 1 / POr V = K / P

Or PV = K

On the bases of the relation, Boyle's law can also be stated asThe product of the pressure and volume of a given mass of a gas is always constant at constant

temperature.

Explanation

Consider for a given mass a gas having volume V1 at pressure P1, so according to Boyle's Lawwe may write as

P1V1 = K1 (constant)If the pressure of the above system is changed from P1 to P2 then the volume of the gas will also

change from V1 to V2. For this new condition of the gas we can write as,

P2V2 = K2 (constant)But for the same mass of the gas.

K1 = K2


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P1V1 = P2V2

This equation is known as Boyle's Equation.

Charle's Law

We know that everything expand on heating and contract cooling. This change in volume issmall in liquids and solids but gases exhibit enormous changes due to the presence of large

intermolecular spaces.Change of volume of a gas with the change of temperature at constant pressure was studied by

Charles and was given in the form of a law. which states,

StatementFor a given mass of a gas the volume of the gas is directly proportional to its absolute

temperature provided the pressure is kept constant.

Mathematically this law may be written as

V TV = K TOR

V / T = KThis relation shows that the ratio of volume of a given mass of a gas to its absolute temperature

is always constant provided the pressure is kept constant. On this bases Charles Law may also be

defined as,

If the pressure remains constant for each 1C change of temperature the volume of the gas

changes to 1/273 of its original volume.

On the bases of this statement

V1 / T = K & V2 / T2 = KV1 / T1 = V2 / T2

This equation is known as Charle's equation.The volume temperature relationship can be represented graphically. When volume of a givenmass of gas is plotted against temperature, a straight line is obtained.

Graph Coming Soon

Absolute Scale Of Temperature

There are different scales for the measurement of temperature such as Celsius C and Fahrenheit

C. Similarly another scale known as absolute scale or Kelvin scale is determined on the basis of

Charle's law.On the basis of Charle's law we known that the volume of the gas changes to 1/273 times of its

original volume for each 1 C change of temperature. It suggests that the volume of a gas would

theoretically be zero at -273C. But this temperature has never been achieved for any gas becauseall the gases condense to liquid at a temperature above this point. So the minimum possible

temperature for a gaseous system is to be -273C. This temperature is referred as absolute zero or

zero degree of the absolute scale or Kelvin scale.

To form an absolute scale thermometer if the equally spaced divisions of centigrade thermometerare extended below zero and when the point -273C is maked then this point is called as absolute


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zero and the scale is called as absolute scale. It shows that for the conversion of centigrade scale

into Kelvin scale 273 is added to the degrees on the centigrade scale.K = 273 + C

Avogadro's Law

In 1811, a scientist Avogadro's established a relationship between the volume and number of

molecules of the gas, which is known as Avogadro's law.

StatementEqual volume of all gases contains equal number of molecules under the same condition of

temperature & pressure.Mathematically it may be represented as

V nOR

V = K n

On the basis of the above statement we can say that1 dm3 of O2 gas will contain the same number of molecules as 1 dm3 of H2 or N2 or any other

gas at same temperature and pressure.It was also observed that 22.4 dm3 of any gas at S.T.P contain 1 mole of that gas, so 22.4 dm3

volume at S.T.P is called as molar volume or the volume of 1 mole of the gas and the mass

present in 22.4 dm3 of any gas will be equal to its molar mass or molecular mass. It can also beexplained on the basis of following figures.

Determination of Unknown Molecular Mass of a Gas With the Help of Avogadro's Law Suppose we have two gases (i) Oxygen (ii) COThe volume of these two gases are equal which are 1 dm3.

The mass of 1 dm3 of oxygen is 1.43 gmThe mass of 1 dm3 of Co is 1.25 gmAccording to Avogadro's law we know that 1 dm3 of CO at S.T.P contain the same number of

molecules as 1 dm3 of O2 under similar condition. Hence a molecule of CO has 1.25 / 1.43 times

as much as a molecule of O2 and we know that the molecular mass of oxygen is 32 so the

molecular mass of CO would be1.25 / 1.43 x 32 = 28 g / mole

General Gas Equation (Ideal Gas Equation)To give a relation between the volume, pressure and number of moles of n gas, Boyle's law,Charle's law and Avogadro's law are used.

According to Boyle's law | V 1 / P

According to Charle's law | V TAccording to Avogadro's law | V nBy combining these laws we get

V 1 / P x T x nORV = R x 1 / P x T x P

ORP V = n R T


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This equation is known as general gas equation n is also known as equation of state because

when we specify the four variables = pressure, temperature, volume and number of moles wedefine the state for a gas.

In this equation "R" is a constant known as gas constant.

Value of R1. When Pressure is Expressed in Atmosphere and Volume in Litres or dm3According to general gas equation

P V = n R T

ORR = PV / nT

For 1 mole of a gas at S.T.P we know thatV = 22.4 dm3 or litres

T = 273 K (standard temperature)

P = 1 atm (standard pressure)

So,

R = PV / nT= 1 atm x 22.4 dm3 / 1 mole x 273 K

= 0.0821 dm3 K-1 mol0-1

2. When Pressure is Expressed in Newtons Per Square Metre and Volume in Cubic MetresFor 1 mole of a gas at S.T.P

V = 0.0224 m3 .......... ( 1 dm3 = 10-3 m3)n = 1 mole

T = 273 K

P = 101200 Nm-2So,

R = PV / nT

= 101300 Nm-2 x 0.0224 m3 / 1 mole x 273 K

= 8.3143 Nm K-1 mole-1= 8.3143 J K-1 mol-1

Derivation of Gas EquationAccording to general gas equation

P V = n R T

For 1 mole of a gas n = 1P V = R T

ORP V / T = R

Consider for a known mass of a gas the volume of the gas is V1 at a temperature T1 and pressureP1. Therefore for this gas we can write as

P1 V1 / T1 = R

If this gas is heated to a temperature T2 due to which the pressure is changed to P2 and volume is

changed to V2. For this condition we may write asP2 V2 / T2 = R

P1 V1 / T1 = P2 V2 / T2 = R


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P1 V1 / T1 = P2 V2 / T2

This equation is known as gas equation.

Graham's Law of Diffusion

We know that gas molecules are constantly moving in haphazard direction, therefore when twogases are placed separated by a porous membrane, they diffuse through the membrane and

intermix with each other. The phenomenon of mixing of molecules of different gases is calleddiffusion.

In 1881, Graham established a relationship between the rates of diffusion of gases and their

densities which is known as Graham's law of diffusion.

StatementThe rate of diffusion of any gas is inversely proportional to the square root of its density.

Mathematically it can be represented as

r 1 / d

r = K / dGraham also studied the comparative rates of diffusion of two gases. On this basis the law os

defined as

The comparative rates of diffusion of two gases under same condition of temperature and

pressure are inversely proportional to the square root of their densities.

If the rate of diffusion of gas A is r1 and its density is d1 then according to Graham's law

r1 1 / d1ORr1 = K / d1Similarly the rate of diffusion of gas B is r2 and its density is d2 then

r2 1 / d2

ORr2 = K / d2Comparing the two rates

r1 / r2 = (K / d1) / (K / d2)r1 / r2 = d2 / d1 ................... (A)But density d = mass / volumeTherefore,

For d1 we may write as

d1 = m1 / v1And for d2

d2 = m2 / v2

Substituting these values of d1 & d2 in equation (A)r1 / r2 = (m2 / v2) / (m1 / v1)But v1 = v2 because both gases are diffusing in the same volume.

Therefore,

r1 / r2 = m2 / m1Hence Graham's law can also be stated as,The comparative rates of diffusion of two gases are inversely proportional to the square root of

their masses under the same condition of temperature and pressure.


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It means that a lighter gas will diffuse faster than the heavier gas. For example compare the rate

of diffusion of hydrogen and oxygen.

Rate of diffusion of H2 / Rate of diffusion of O2 = Mass of O2 / Mass of H2 = 32/ 2 = 16 = 4It shows that H2 gas which is lighter gas than O2 will diffuse four times faster than O2.

Dalton's Law of Partial Pressures

Partial PressureIn a gaseous mixture the individual pressure oxerted by a gas is known as partial pressure.

When two or more gases which do not react chemically are mixed in the same container each gas

will exert the same pressure as it would exert if it alone occupy the same volume.

John Dalton in 1801 formulated a law which is known as Dalton's Law of partial pressure andstated as.

StatementThe total pressure of a gaseous system is equal to the sum of the partial pressures of all the

gases present in the system.Suppose in a system three gases A, B & C are present. The partial pressure of these gases are

PA = Partial pressure of gas APB = Partial pressure of gas B

PC = Partial pressure of gas C

Then Dalton's law may be mathematically written asPT = PA + PB + PC

Where PT is the total pressure of the system.

To calculate the individual pressures of gases in the above example suppose the number of moles

of A, B & C in the container are nA, nB and nC. So the total number of moles in the containerwill be

n = nA + nB + nCApply the general gas equationP V = n R T

PT = n R T / V

Since R, T and V are same for gases A, B and C, therefore the partial pressure of these gases are

as follows.Partial pressure of gas A | PA = n(A)RT / V ......... (2)

Partial pressure of gas B | PB = n(B)RT / V ......... (3)

Partial pressure of gas C | PC = n(C)RT / V ......... (4)Now divide equation (2) by (1)

PA / PT = (nA RT/V) / (nRT/V)

ORPA / PT = nA / nTTherefore,

P(gas) = P1 x n(gas) / n(total)

Application of Dalton's LawIn an inert mixture of gases the individual gas exerts its own pressure due to collision of its

molecules with the walls of the container but the total pressure produced on the container wall


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will be the sum of pressure of all the individual gases of the mixture.

On this basis the number of moles formed during a chemical reaction can be measured. For thispurpose a gas produced in a chemical reaction is collected over water. The gas also contains

some of water vapours. So the pressure exerted by the gas would be the pressure of pure gas and

the pressure of water vapours.

Therefore the pressure of the system may be represented asP(moist) = P(dry) + P(water vapour)

So,

P(dry) = P(moist) - P(water vapour)In this way we can obtain the pressure of the gas and by using general gas equation we can

calculate the number of moles of the prepared gas.

Ideal Gas

A gas which obeys all the gas laws at all temperatures and pressures is known as ideal gas.

It means that the product of pressure and volume must be constant at all pressures.

Similarly the rate of V/T will remain constant for an ideal gas.But there is no gas which is perfectly ideal because of the presence of the force of attraction or

repulsion between the molecules.

Gas Laws on the Basis of Kinetic Theory

Boyle's LawAccording to Boyle's law the volume of a given mass of a gas is inversely proportional to its

pressure at constant temperature.

It means that when the volume of the gas is decreased the pressure of the gas will increase.

According to kinetic molecular theory of gases the pressure exerted by a gas is due to thecollisions of the molecules with the walls of the container. If the volume of a gas is reduced at

constant temperature, the average velocity of the gas molecules remains constant so they collide

more frequently wit the walls which causes higher pressure.

Charle's LawAccording to Charles law the volume of a given mass of a gas is directly proportional to itsabsolute temperature at constant pressure.

According to kinetic molecular theory the average kinetic energy of gas molecules is directly

proportional to its absolute temperature so if the temperature of the gas is increased the average

kinetic energy of the gas molecules is also increased due to which the sample of the gasexpanded to keep the pressure constant. It is accordance with the law.

Graham's LawAccording to Graham's Law

r1 / r2 = m2 / m1The rate of diffusion of a gas is directly proportional to the velocity of the molecules so,

v1 / v2 = m2 / m1


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LiquefactionAccording to kinetic theory, the kinetic energy of the molecules is low for lower temperature.These slower moving molecules become subject to inter molecular attraction. At a sufficiently

low temperature these attractive forces are capable of holding the molecules with one another so

the gas is changed into liquid and the process is called liquefaction.

Liquid StateIt is one of the state of matter. In this state, the kinetic energy of the molecule is very high due to

which the molecules of the liquid are able to move but due to compact nature liquids are notcompressible. On this basis we can say that the volume of a liquid is always constant but its

shape can be changed.

Behaviour of LiquidsThe main properties of liquids are as follows.

Diffusibility

The diffusion of one liquid into another liquid is possible but its rate is slow as compared withthe rate of diffusion of gases. Example of diffusion of liquids is mixing of alcohol in water.

Explanation of Diffusion in Terms of Kinetic EnergyAs the molecular of a liquid are in cluster form they are very close to each other but these

molecules are movable so they can mix with the other molecules. Since the intermolecular

distance are smaller due to which the rate of diffusion of liquids is slow.

CompressibilityThe space between liquid molecules are very small due to strong Van der Waals forces. Whenthe pressure is applied, they can be compressed but to a very little extent.

ExpansionWhen a liquid is heated, the kinetic energy of its molecules also increases so the attractionbetween the molecules becomes weaker due to which they go further apart and hence the liquid

expands.

ContractionWhen a liquid is cooled its kinetic energy is lowered and the attraction among the molecules

becomes stronger so they comes close to each other and hence the liquid contract.

Viscosity

DefinitionThe internal resistance in the flow of a liquid is called viscosity.

Liquids have the ability to flow, but different liquids have different rates of flow. Some liquids

like honey mobil oil etc. flow slowly and are called viscous liquids while ether, gasoline etc.

which flow quickly are called less viscous.

Explanation


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The viscosity of liquid can be understood by considering a liquid in a tube, a liquid in a tube is

considered as made up of a series of molecular layer. The layer of the liquid in contact with thewalls of the tube remains stationary and the layer in the center of the tube has highest velocity as

shown.

Each layer exerts a drag on the next layer and causes resistance to flow.

Factors on Which Viscosity Depends

1. Size of MoleculesThe viscosity of a liquid depends upon the size of its molecules. If the size of the molecules is

bigger the viscosity of the liquid is high.

2. Shape of MoleculesShape of the molecules affects the viscosity. If the shapes of the molecules are spherical they can

move easily but if the shapes of the molecules are irregular such as linear or trigonal then the

molecules will move slowly and its viscosity will be high.

3. Intermolecular AttractionIf the force of attraction between the molecules of a liquid is greater the viscosity of the liquid isalso greater.

4. TemperatureViscosity of a liquid decreases with the increase of temperature.

Units of Viscosity

Viscosity of a liquid is measured in poise, centipoise or millipoise & S.I unit.1 poise = 1 N.s.m(-2)

1 centipoise = 10(-2) N.s.m(-2)

Surface Tension

DefinitionThe force acting per unit length on the surface of a liquid at right angle direction is called surface

tension.

Explanation

Consider a liquid is present in a beaker. The molecules inside the liquid are surrounded by theother molecules of the liquid. So the force of attraction on a molecule is balanced from all

direction. But the force of attraction acting on the molecules of the surface from the lower layermolecules is not balanced.

The molecules lying on the surface are attracted by the molecules present below the surface Due

to this downward pull the surface of the liquid behave as a membrane which tends to contract toa smaller area and causes a tension on the surface of the liquid known as surface tension.

Diagram Coming Soon


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Factors on Which Surface Tension Depends

1. Molecular Structure of the LiquidIf the force of attraction between the molecules is greater, the surface tension of the liquid is also

greater. Those liquids in which hydrogen bond formation take place will have more surface

tension.

2. TemperatureSurface tension of a liquid is inversely proportional to the temperature.

Units1. Dynes / cm

2. Ergs / cm2

Capillary ActionThe fall or rise of a liquid in a capillary tube is called capillary action .

When a capillary tube is dipped in a liquid which wets the wall of the tube, the liquid will rise inthe capillary tube, to decrease the surface area due to surface tension. The liquid will rise in the

capillary tube until the upward force due to surface tension is just balanced by the downward

gravitational pull. This is called capillary action.

Vapour Pressre

DefinitionThe pressure exerted by the vapours of a liquid in its equilibrium state with the pure liquid at a

given temperature is called vapour pressure.

ExplanationConsider a liquid is present in a bottle as shown.

Diagram Coming SoonIn the beginning the atmosphere above the surface of liquid is unsaturated but due to continuous

evaporation the molecule of the liquid are trapped in the bottle and the air present above the

surface of the liquid is becomes saturated and after it the molecules present in the vapour statemay hit the liquid again and rejoin it by condensing into liquid. Thus in this closed vessel two

process are going on simultaneously which are evaporation and condensation of vapours. When

the rates of these two processes becomes equal at this point the pressure exerted by vapours is

called vapour pressure.

Units of Vapour Pressure

The units for vapour pressure are1. Millimeter of Hg

2. Atmosphere

3. Torr4. Newton / m(2)


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Factors for Vapour Pressure

1. Nature of LiquidVapour pressure of a liquid depends upon the nature of the liquid. Low boiling liquid exert more

vapour pressure at a given temperature.

2. TemperatureVapour pressure of a liquid also depends upon temperature. The vapour pressure of the liquid

increases with the increase of temperature due to the increase of average of kinetic energy.

3. Intermolecular ForcesThose liquids in which the intermolecular forces are weak shows high vapour pressure.

Explanation of Evaporation on the Basis of Kinetic TheoryAccording to this theory the molecules of a liquid collide with each other during their motion.

Due to these collisions some of the molecules acquire greater energy than Van der Walls forces

which binds the molecules of the liquid together so these molecules of higher energy escapesfrom the surface into the air in the form of vapours.

Evaporation is a Cooling ProcessIn liquids, due to collision between molecules some molecules acquire higher energy and escapes

from the surface of the liquid in the form of vapours. The kinetic energy of the remaining

molecules decreases due to which the temperature of the liquid also decreases and hence we cansay that evaporation is a cooling process.

Boiling Point

DefinitionThe temperature at which the vapour pressure of a liquid becomes equal to the atmospheric

pressure is called boiling point.When a liquid is heated the rate of evaporation of the molecules also increases with the increase

in temperature. When the pressure of the vapours becomes equal to the atmospheric pressure the

liquid starts boiling and this temperature is known as boiling point.If the external pressure on a liquid is changed the boiling point of the liquid also change. The

increase in external pressure on a liquid increases the boiling point while the decreases of

external pressure decrease the boiling point.

Solid StateIt is a state of matter which posses both definite shape and definite volume. In solids the particles

are very close to each and tightly packed with a greater force of attraction.

Properties of Solids


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1. DiffusibilityDiffusion also occurs in solids but its rate is very slow. If a polished piece of zinc is clampedwith a piece of copper for a long time. After few years we will see that some particles of zinc are

penetrated into copper and some particles of copper are penetrated into zinc. It shows that the

diffusion in solids is possible but it occurs with a slow rate.

2. CompressibilityIn solids the molecules are close to each other so it is not easy to compress a solid. In other

words we can say that the effect of pressure on solids is negligible.

3. SublimationIt is a property of some solids that on heating these solids are directly converted into vapourswithout liquification. This property of solids is known as sublimation.

4. MeltingWhen solids are heated, they are changed into liquids and the property is called melting of the

solids.

5. DeformitySolids may be deformed by high pressure. When a high pressure is applied on solids due to

which some particles are dislocated the force of attraction is so strong that the rearranged atoms

are held equally well with their new neighbours and hence the solid is deformed.

Classification of Solids

Solids are classified into two main classes.1. Crystalline

2. Amorphous

1. Crystalline SolidsIn a solid if the atoms are attached with each other with a definite arrangement and it also

possesses a definite geometrical shape. This type of solid is called crystalline solid.

e.g. NaCl, NiSO4 are crystalline solids.

2. Amorphous SolidsIn these solids there is no definite arrangement of the particles so they do not have a definiteshape. The particles of such solids have a random three dimensional arrangement. Examples of

amorphous solids are glass, rubber, plastic etc.

The properties of crystalline and amorphous solids are quite different from each other. Thesedifferences in properties are given below.

Difference of Geometry

1. Crystalline SolidsIn crystalline solids particles are arranged in a definite order due to which it possesses a definitestructure.

2. Amorphous Solids


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In amorphous solids particles are present without any definite arrangement so they do not have

definite shape.

Difference of Melting Point

1. Crystalline Solids

Crystalline solids have sharp melting point due to uniform arrangement.2. Amorphous SolidsAmorphous solids melts over a wide range of temperature.

Cleavage and Cleavage Plane

1. Crystalline SolidsWhen a big crystal is broken down into smaller pieces the shape of the smaller crystals isidentical with the bigger crystal. This property of crystalline solids is called cleavage and the

plane from where a big crystal is broken is called cleavage plane.

2. Amorphous SolidsAmorphous solids do not break up into smaller pieces with an identical shape.

Anisotropy & Isotropy

1. Crystalline SolidsIt is a property of crystalline solid that they show different physical properties in different

direction. For example graphite can conduct electric current only through the plane which is

parallel to its layers. This property is called anisotropy.

2. In amorphous solids the physical properties are same in all directions. This property of

solids is called isotropy.

Symmetry in Structure

1. Crystalline solids are symmetric in their structure when they are rotated about an axis,

their appearance remains same so they are symmetric in structure.

2. Amorphous SolidsAmorphous solids are not symmetric.

Types of Crystals

There are four types of crystals.

1. Atomic crystals

2. Ionic crystals3. Covalent crystals

4. Molecular crystal

1. Atomic CrystalsMetals are composed of atoms. These atoms are combined with each other by metallic bond and

the valency electrons in metals can move freely throughout the crystal lattice. This type of solid

is called atomic crystal.

The properties of atomic crystals are1. High melting point.

2. Electrical and thermal conductivity.


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3. These are converted into sheets so these are malleable.

4. These are used as wire so these are ductile.

2. Ionic CrystalsThose solids which consists of negativity and positively charged ions held together by strong

electrostatic force of attraction are called ionic crystals. Ionic crystalline solids possesses thefollowing properties.

1. The melting and boiling point of ionic crystals is high.

2. They conduct electricity in molten state.3. Ionic crystals are very hard.

4. Indefinite growth of crystals is also a property of ionic crystals.

3. Covalent CrystalsIn covalent solids, the atoms or molecules are attached with each other by sharing of electrons.

Such type of solids are called covalent solids e.g. diamond is a covalent solid in which carbon

atoms are attached with each other by covalent bond. The other examples of covalent crystals are

sulphur, graphite etc.Covalent crystals possesses the following properties.

1. High melting point.2. High refractive index.

3. Low density.

4. Molecular CrystalsThose solid in which molecules are held together due to intermolecular forces to form a crystal

lattice are called molecular crystals e.g. iodine and solid CO2 are molecular crystals. The general

properties of molecular crystals are as follows.1. Low melting and boiling point.

2. Non - conductor of heat and electricity.

Isomorphism

When two different substance have same crystalline structure, they are said to be isomorphous

and the phenomenon is called isomorphism.e.g. ZnSO4 and NiSO4 are two different substances but both are orthorhombic similarly the

structure of CaCO3 and NaNO3 is frigonal.

Polymorphism

If a substance exist in more than one crystalline form it is called polymorphous and the

phenomenon is known as polymorphism. E.g. sulphur exist in rhombic and monoclinic formsimilarly CaCO3 exist in trigonal and orthorhombic form.

Unit Cell


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The basic structural unit of a crystalline solid which when repeated in three dimensions generates

the crystal structure is called a unit cell.A unit cell of any crystalline solid has a definite geometric shape and distinguish from other

crystals on the basis of length of the edges and angle between the edges.

Crystal Lattice

In crystalline solids atoms, ions or molecules are arranged in a definite order and form a threedimensional array of particles which is known as crystal lattice.

Atomic Structure

IntroductionAbout the structure of atom a theory was put on by John Dalton in 1808. According to this

theory matter was made from small indivisible particles called atoms.

But after several experiments many particles have been discovered with in the atom which areelectrons, protons, neutrons, positrons etc. For the discovery of these fundamental particles the

experiments are as follows.

1. Faraday's experiment indicates the existence of electron.2. Crook's tube experiment explains the discovery of electron and proton.

3. Radioactivity also confirms the presence of electrons and protons.4. Chadwick's experiment shows the presence of neutrons.

The details of these experiments are given below.

Faraday's Experiment

Passage of Electricity Through SolutionIn this experiment Faraday passed the electricity through an electrolytic solution. He observed

that when two metal plates called electrodes are placed in an electrolytic solution and electricityis passed through his solution the ions present in the solution are moves towards their respective

electrodes. In other words these ions are moves towards the oppositely charge electrodes to give

up their charge and liberated as a neutral particles.

Faraday also determined the charges of different ions and the amount of elements liberated fromthe electrolytic solution. Due to this experiment presence of charge particles in the structure of

atoms is discovered. The basic unit of electric charge was later named as electron by Stoney in

1891.

Diagram Coming Soon

Crook's Tube Or Discharge Tube Experiment

Passage of Electricity Through Gases Under Low Pressure

IntroductionThe first of the subatomic particles to be discovered was electron. The knowledge about the


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electron was derived as a result of the study of the electric discharge in the discharge tube by J.J.

Thomson in 1896. This work was later extended by W. Crooke

Working of Discharge TubeWhen a very high voltage about 10,000 volts is applied between the two electrodes, no electric

discharge occurs until the part of the air has been pumped out of the tube. When the pressure ofthe gas inside the tube is less than 1 mm, a dark space appears near the cathode and thread like

lines are observed in the rest of 0.01 mm Hg it fills the whole tube. The electric discharge passes

between the electrodes and the residual gas in the tube begins to glow. These rays which proceedfrom the cathode and move away from it at right angle in straight lines are called cathode rays.

Properties of Cathode Rays1. They travel in straight lines away from the cathode and produce shadow of the object placed in

their path.

2. The rays carry a negative charge.

3. These rays can also be easily deflected by an electrostatic field.

4. The rays can exert mechanical pressure showing that these consist of material particle whichare moving with kinetic energy.

5. The produce fluorescence when they strike the glass wall of the discharge tube.6. Cathode rays produce x-rays when they strike a metallic plate.

7. These rays consists of material particle whose e/m resembles with electron.

8. These rays emerge normally from the cathode and can be focused by using a concave cathode.

Positive RaysIn 1890 Goldstein used a discharge tube with a hole in the cathode. He observed that while

cathode rays were emitting away from the cathode, there were coloured rays producedsimultaneously which passed through the perforated cathode and caused a glow on the wall

opposite to the anode. Thomson studied these rays and showed that they consisted of particles

carrying a positive charge. He called them positive rays.

Properties of Positive Rays1. These rays travel in a straight line in a direction opposite to the cathode.

2. These are deflected by electric as well as magnetic field in the way indicating that they arepositively charged.

3. The charge to mass ratio (e/m) of positive particles varies with the nature of the gas placed in

the discharge tube.4. Positive rays are produced from the ionization of gas and not from anode electrode.

5. Positive rays are deflected in electric field. This deflection shows that these are positively

charged so these are named as protons.

The Information Obtained From Discharge Tube ExperimentThe negatively charge particles electrons and the positively charge particles protons are the

fundamental particle of every atom.

Radioactivity


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In 1895, Henry Becqueral observed that uranium and its compounds spontaneously emitted

certain type of radiation which affected a photographic plate in the dark and were able topenetrate solid matter. He called these rays as radioactivity rays and a substance which possessed

the property of emitting these radioactivity rays was said to be radioactivity element and the

phenomenon was called radioactivity.

On further investigation by Maric Curic, it was found that the radiation emitted from the elementuranium as well as its salts is independent of temperature and the source of the mineral but

depend upon the mineral but depend upon the quantity of uranium present e.g. Pitchblende U3O8

was found to be about four times more radioactive than uranium.

Radioactive RaysSoon after the discovery of radium it was suspected that the rays given out by radium and otherradioactive substance were not of one kind. Rutherford in 1902 devised an ingenious method for

separating these rays from each other by passing them between two oppositely charged plate. It

was observed that the radioactive rays were of three kinds, the one bending towards the negative

plate obviously carrying positive charge were called -rays and those deflected to the positive

plate and carrying -ve charge were named as -rays. The third type gamma rays, pass unaffectedand carry no charge.

Properties of - RAYS1. These rays consists of positively charged particles.

2. These particles are fast moving helium nuclei.

3. The velocity of -particles is approximately equal to 1/10th of the velocity of light.4. Being relatively large in size, the penetrating power of -rays is very low.5. They ionize air and their ionization power is high.

Properties of - RAYS1. These rays consists of negatively charged particles.

2. These particles are fast moving electron.

3. The velocity of -particles is approximately equal to the velocity of light.4. The penetrating power of -rays is much greater than -rays.5. These rays ionizes gases to lesser extent.

Properties of - RAYS1. Gamma rays do not consist of particles. These are electromagnetic radiations.

2. They carry no charge so they are not deflected by electric or magnetic field.3. Their speed is equal to that of light.

4. These are weak ionizer of gases.

5. Due to high speed and non-material nature they have great power of penetration.

Chadwick Experiment (Discovery of Neutron)

When a light element is bombarded by -particles, these -particles leaves the nucleus in anunstable disturbed state which on settling down to stable condition sends out radioactivity rays.The phenomenon is known as "Artificial Radioactivity".


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In 1933, Chadwick identified a new particle obtained from the bombardment of beryllium by -particles. It had a unit mass and carried no charge. It was named "Neutron".

Spectroscopic Experiment

After the discovery of fundamental particles which are electrons, protons & neutron, the nextquestion concerned with electronic structure of atom.

The electronic structure of the atom was explained by the spectroscopic studies. In thisconnection Plank's Quantum theory has great impact on the development of the theory of

structure of atom.

Planck's Quantum Theory

In 1900, Max Planck studied the spectral lines obtained from hot body radiations at different

temperatures. According to him,

When atoms or molecules absorb or emit radiant energy, they do so in separate units of wavescalled Quanta or Photons.

Thus light radiations obtained from excited atoms consists of a stream of photons and not

continuous waves.The energy E of a quantum or photon is given by the relation

E = h vWhere v is the frequency of the emitted radiation and h the Planck's constant. The value of h =

6.62 x 10(-27) erg. sec.The main point of this theory is that the amount of energy gained or lost is quantized which

means that energy change occurs in small packets or multiple of those packets, hv, 2 hv, 3 hv and

so on.

Spectra

A spectrum is an energy of waves or particles spread out according to the increasing or

decreasing of some property. E.g. when a beam of light is allowed to pass through a prism it

splits into seven colours. This phenomenon is called dispersion and the band of colours is called

spectrum. This spectrum is also known as emission spectrum. Emission spectra are of two types.1. Continuous Spectrum

2. Line Spectrum

1. Continuous Spectrum

When a beam of white light is passed through a prism, different wave lengths are refractedthrough different angles. When received on a screen these form a continuous series of colours

bands: violet, indigo, blue, green, yellow and red (VIBGYOR). The colours of this spectrum areso mixed up that there is no line of demarcation between different colours. This series of bands

that form a continuous rainbow of colours is called continuous spectrum.

Diagram Coming Soon

2. Line Spectrum


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When light emitted from a gas source passes through a prism a different kind of spectrum may

be obtained.If the emitted from the discharge tube is allowed to pass through a prism some discrete sharp

lines on a completely dark back ground are obtained. Such spectrum is known as line spectrum.

In this spectrum each line corresponds to a definite wave length.

Diagram Coming Soon

Identification of Element By SpectrumEach element produces a characteristics set of lines, so line spectra came to serve as "fingerprints" for the identification of element. It is possible because same element always emit the

same wave length of radiation. Under normal condition only certain wave lengths are emitted by

an element.

Rutherford's Atomic Model

Evidence for Nucleus and Arrangement of Particles

Having known that atom contain electrons and a positive ion, Rutherford and Marsdenperformed their historic "Alpha particle scattering experiment" in 1909 to know how and where

these fundamental particles were located in the structure of atom.Rutherford took a thin of gold with thickness 0.0004 cm and bombarded in with -particles. Heobserved that most of the -particles passed straight through the gold foil and thus produced aflash on the screen behind it. This indicated that old atoms had a structure with plenty of emptyspace but some flashes were also seen on portion of the screen. This showed that gold atoms

deflected or scattered -particles through large angles so much so that some of these bouncedback to the source.

Based on these observations Rutherford proposed a model of the atom which is known asRutherford's atomic model.

Diagram Coming Soon

Assumption Drawn From the Model1. Atom has a tiny dense central core or the nucleus which contains practically the entire mass of

the atom leaving the rest of the atom almost empty.

2. The entire positive charge of the atom is located on the nucleus. While electrons weredistributed in vacant space around it.

3. The electrons were moving in orbits or closed circular paths around the nucleus like planets

around the sun.4. The greater part of the atomic volume comprises of empty space in which electrons revolve

and spin.

Weakness of Rutherford Atomic ModelAccording to the classical electromagnetic theory if a charged particle accelerate around an

oppositely charge particle it will radiate energy. If an electron radiates energy, its speed will

decrease and it will go into spiral motion finally falling into the nucleus. Similarly if an electron

moving through orbitals of ever decreasing radii would give rise to radiations of all possiblefrequencies. In other words it would given rise to a continuous spectrum. In actual practise, atom

gives discontinuous spectrum.


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X-Rays and Atomic Number

In 1895, W.Roentgen discovered that when high energy electrons from cathode collide with theanode in the Crook's tube, very penetrating rays are produced. These rays were named as X-rays.

ExplanationWhen an electron coming from the cathode strike with the anode in the crook's tube, it can

remove an electron from the inner shell of the atom. Due to removal of t his electron the

electronic configuration of this ion is unstable and an electron from an orbital of higher energydrops into the inner orbital by emitting energy in form of a photon. This photon corresponds to

electromagnetic radiations in the x-rays region.

Relationship Between Wave Length and Nuclear Charge

In 1911, Mosley stablished a relationship between the wave length and nuclear charge. He found

that when cathode rays struck elements used as anode targets in the discharge tube, characteristicx-rays were emitted. The wave length of the x-rays emitted decreases regularly with the increase

of atomic mass. On careful examination of his data Mosely found that the number of positive

charges on the nucleus increases from atom to atom by single electronic unit. He called the

number of positive charges as the atomic number.Diagram Coming Soon

Bohr's Theory

Rutherford's model of atom fails to explain the stability of atom and appearance of the line

spectra. Bohr in 1913 was the first to present a simple model of the atom which explained the

appearance of line spectra.Some of the postulates of Bohr's theory are given below.

1. An atom has a number of stable orbits or stationary states in which an electron can reside

without emission or absorption of energy.2. An electron may pass from one of these non-radiating states to another of lower energy with

the emission of radiations whose energy equals the energy difference between the initial and

final states.3. In any of these states the electrons move in a circular path about the nucleus.

4. The motion of the electron in these states is governed by the ordinary laws of mechanics and

electrostatic provided its angular momentum is an integral multiple of h/2It can be written as

mvr = nh / 2Here mvr becomes the angular momentum of the electron. Thus Bohr's first condition defining

the stationary states could be stated as

"Only those orbits were possible in which the angular momentum of the electrons would be anintegral multiple of h/2". These stationary states correspond to energy levels in the atom.

Calculation of Radius of OrbitsConsider an electrons of charge e revolving.


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Atomic number and e the charge on a proton.

Let m be the mass of the electro, r the radius of the orbit and v the tangential velocity of therevolving electron.

The electrostatic force of attraction between the nucleus and the electron according to Coulomb's

law

= Z e x e / r2Diagram Coming Soon

The centrifugal force acting on the electron.

= mv2 / rBohr assumed that these two opposing forces must be balanced each other exactly to keep the

electron in an orbit.

ThereforeZe2 / r2 = m v2 / r

Multiply both sides by r

r x Ze2 / r2 = r x m v2 / r

Ze2 / r = m v2

ORr = Ze2 / m v2 .................. (1)

The Bohr's postulate states that only those orbits are possible in which

mvr = nh / 2Therefore,

V = nh / 2mrSubstituting the value of V in eq (1)r = Ze2 / m(nh/2mr)2or

r = Ze2 x 42 mr2/n2h2or

1/r = 42mZe2/n2h2cr

r = n2h2 / 42mZe2 ............... (2)This equation gives the radii of all the possible stationary states. The values of constants present

in this equation are as follows.

H = 6.625 x 10(-27) ergs sec OR 6.625 x 10(-37) J.sMe = 9.11 x 10(-28) gm OR 9.11 x 10(-31) kg

E = 4.802 x 10(-10) e.s.u OR 1.601 x 10(-19) C

By substituting these values we get for first shell of H atomr = 0.529 x 10(-8) m OR 0.529

The above equation may also be written as

r = n2 (h2 / 42mZe2) x n2 a0 .................... (3)For the first orbit n = 1 and r = 0.529. This is the value of the terms in the brackets sometimeswritten as a0 called Bohr's Radius. For the second shell n = 2 and for 3rd orbit n = 3 and so on.

Hydrogen Atom Spectrum

Balmer SeriesThe simplest element is hydrogen which contain only one electron in its valence shell.


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Balmer in 1885 studied the spectrum of hydrogen. For this purpose he used hydrogen gas in the

discharge tube. Balmer observed that hydrogen atom spectrum consisted of a series of linescalled Balmer Series. Balmer determined the wave number of each of the lines in the series and

found that the series could be derived by a simple formula.

Lyman SeriesLyman series is obtained when the electron returns to the ground state i.e. n = 1 from higher

energy level n(2) = 2, 3, 4, 5, etc. This series of lines belongs to the ultraviolet region of

spectrum.

Paschen SeriesPaschen series is obtained when the electron returns to the 3rd shell i.e. n = 3 from the higherenergy levels n2 = 4, 5, 6 etc. This series belongs to infrared region.

Bracket SeriesThis series is obtained when an electron jumps from higher energy levels to 4th energy level.

Heisenberg Uncertainty Principle

According to Bohr's theory an electron was considered to be a particle but electron also behaves

as a wave according to be Broglie.

Due to this dual nature of electron in 1925 Heisenberg gave a principle known as Heisenberg

Uncertainty Principle which is stated as,

It is impossible to calculate the position and momentum of a moving electron simultaneously.

It means that if one was known exactly it would be impossible to known the other exactly.Therefore if the uncertainty in the determination of momentum is px and the uncertainty in

position is x then according to this principle the product of these two uncertainties may writtenas

px . x hSo if one of these uncertainties is known exactly then the uncertainty in its determination is zero

and the other uncertainty will become infinite which is according to the principle.

Energy Levels and Sub-Levels

According to Bohr's atomic theory, electrons are revolving around the nucleus in circular orbits

which are present at definite distance from the nucleus. These orbits are associated with definiteenergy of the electron increasing outwards from the nucleus, so these orbits are referred as

Energy Levels or Shells.

These shells or energy levels are designated as 1, 2, 3, 4 etc K, L, M, N etc.The spectral lines which correspond to the transition of an electron from one energy level to

another consists of several separate close lying lines as doublets, triplets and so on. It indicates

that some of the electrons of the given energy level have different energies or the electrons

belonging to same energy level may differ in their energy. So the energy levels are accordinglydivided into sub energy levels which are denoted by letters s, p, f (sharp, principle, diffuse &


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fundamental).

The number of sub levels in a given energy level or shell is equal to its value of n.e.g. in third shell where n = 3 three sub levels s, p, d are possible.

Quantum Numbers

There are four quantum numbers which describe the electron in an atom.

1. Principle Quantum NumberIt is represented by "n" which describe the size of orbital or energy level.

The energy level K, L, M, N, O etc correspond to n = 1, 2, 3, 4, 5 etc.

Ifn = 1 the electron is in K shell

n = 2 the electron is in L shell

n = 3 the electron is in M shell

2. Azimuthal Quantum NumberThis quantum number is represented by "l" which describes the shape of the orbit. The value of

Azimuthal Quantum number may be calculated by a relation.l = 0 ----> n - 1

So for different shell the value of l are as

n = 1 K Shell l = 0n = 2 L Shell l = 0, 1

n = 3 M Shell l = 0, 1, 2

n = 4 N Shell l = 0, 1, 2, 3

when l = 0 the orbit is s

when l = 1 the orbit is pwhen l = 2 the orbit is dwhen l = 3 the orbit is f

3. Magnetic Quantum NumberIt is represented by "m" and explains the magnetic properties of an electron. The value of mdepends upon the value of l. It is given by

m = + l ----> 0 ----> l

when l = 1, m has three values (+1, 0, -1) which corresponds to p orbital. Similarly when l = 2, mhas five values which corresponds to d orbital.

4. Spin Quantum NumberIt is represented by "s" which represents spin of a moving electron. This spin may be eitherclockwise or anticlockwise so the values for s may be +1/2 or -1/2.

Pauli's Exclusion Principle


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According to this principle

No two electrons in the same atom can have the same four quantum number.Consider an electron is present in 1s orbital. For this electron n = 1, l = 0, m = 0. Suppose the

spin of this electron is s = +1/2 which will be indicated by an upward arrow . Now if anotherelectron is put in the same orbital (1s) for that electron n = 1, l = 0, m = 0. It can occupy this

orbital only if the direction of its spin is opposite to that of the first electron so s = -1/2 which issymbolized by downward arrow . From this example, we can observe the application of Pauli'sexclusion principle on the electronic structure of atom.

Electronic Configuration

The distribution of electrons in the available orbitals is proceeded according to these rules.1. Pauli Exclusion Principle

2. Aufbau Principle

3. (n + l) Rule

4. Hund's Rule

The detail of these rules and principles is given below.

1. Aufbau PrincipleIt is states as

The orbitals are filled up with electrons in the increasing order of their energy .

It means that the orbitals are fulled with the electrons according to their energy level. Theorbitals of minimum energy are filled up first and after it the orbitals of higher energy are filled.

2. Hund's RuleIf orbitals of equal energy are provided to electron then electron will go to different orbitals andhaving their parallel spin.

In other words we can say that electrons are distributed among the orbitals of a sub shell in sucha way as to give the maximum number of unpaired electrons and have the same direction of spin.

3. (n + l) RuleAccording to this rule

The orbital with the lowest value of (n + l) fills first but when the two orbitals have the same

value of (n + l) the orbital with the lower value of n fills first.

For the electronic configuration the order of the orbital is as follows.

1s, 2s, 2p, 3s, 4s, 3d, 4p, 5s, 4d, 5p, 6s etc.

Atomic Radius

For homonuclear diatomic molecules the atomic radius may be defined as

The half of the distance between the two nuclei present in a homonuclear diatomic molecules is

called atomic radius.

It may be shown as

In case of hetronuclear molecular like AB, the bond length is calculated which is (rA + rB) and ifradii of any one is known the other can be calculated.


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For the elements present in periodic table the atomic radius decreases from left to right due to the

more attraction on the valence shell but it increases down the group with the increase of numberof shells.

Ionic Radius

Ionic radius is defined as

The distance between nucleus of an ion and the point up to which nucleus has influence of its

electron cloud.

When an electron is removed from a neutral atom the atom is left with an excess of positive

charge called a cation e.g

Na ----> Na+ + c-But when an electron is added in a neutral atom a negative ion or anion is formed.

Cl + e- ----> Cl-

As the atomic radius, the ionic radii are known from x-ray analysis. The value of ionic radius

depends upon the ions that surround it.

Ionic radii of cations have smaller radii than the neutral atom because when an electron isremoved. The effective charge on the nucleus increases and pulls the remaining electrons with a

greater force.Ionic radii of anions have a large radii than the neutral atom because an excess of negative

charge results in greater electron repulsion.

Radius of Na atom = 1.57Radius of Na+ atom = 0.95 (smaller than neutral atom)

Radius of Cl atom = 0.99

Radius of Cl- atom = 1.81 (larger than neutral atom)

Ionization PotentialDefinitionThe amount of energy required to remove most loosely bounded electron from the outermostshell of an atom in its gaseous state is called is called ionization potential energy.

It is represented as

M(gas) ----> M+(gas) + e- ................... E = I.PThe energy required to remove first electron is called first I.P. The energy required to remove

2nd or 3rd electron is called 2nd I.P or 3rd I.P

M(gas) ----> M+(gas) + e- ................... E = 1st I.PM+(gas) ----> M++(gas) + e- ................E = 2nd I.PM++(gas) ----> M+++(gas) + e- ............ E = 3rd I.PThe units of I.P is kilo-Joule per mole.

Factors on which I.P Depends

1. Size of the AtomIf the size of an atom is bigger the I.P of the atom is low, but if the size of the atom is small then

the I.P will be high, due to fact if we move down the group in the periodic table. The I.P valuedecreases down the group.


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2. Magnitude of Nuclear ChargeIf the nuclear charge of atom is greater than the force of attraction on the valence electron is also

greater so the I.P value for the atom is high therefore as we move from left to right in the

periodic table the I.P is increased.

3. Screening EffectThe shell present between the nucleus and valence electrons also decreases the force of attraction

due to which I.P will be low for such elements.

Electron Affinity

DefinitionThe amount of energy liberated by an atom when an electron is added in it is called electron

affinity.

It shows that this process is an exothermic change which is represented as

Cl + e- ----> Cl- ............ H = -348 kJ / mole

Factors on which Electron Affinity Depends

1. Size of the AtomIf the size of atom is small, the force of attraction from the nucleus on the valence electron will

be high and hence the E.A for the element will also be high but if the size of the atoms is largerthe E.A for these atoms will be low.

2. Magnitude of the Nuclear ChargeDue to greater nuclear charge the force of attraction on the added electron is greater so the E.Aof the atom is also high.

3. Electronic ConfigurationThe atoms with the stable configuration has no tendency to gain an electron so the E.A of such

elements is zero. The stable configuration may exist in the following cases.

1. Inert gas configuration

2. Fully filled orbital3. Half filled orbital

Electronegativity

DefinitionThe force of attraction by which an atom attract a shared pair of electrons is called

electronegativity.

Application of Electronegativity

1. Nature of Chemical BondIf the difference of electronegativity between the two combining atoms is more than 1.7 eV, thenature of the bond between these atoms is ionic but if the difference of electronegativity is less


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than 1.7 eV then the bond will be covalent.

2. Metallic CharacterIf an element possesses high electronegativity value then this element is a non-metal but if an

element exist with less electronegativity, it will be a metal.

Factors for Electronegativity

1. Size of the AtomIf the size of the atom is greater the electronegativity of the atom is low due to the large distancebetween the nucleus and valence electron.

2. Number of Valence ElectronsIf the electrons present in the valence shell are greater in number, the electronegativity of the

element is high.

Chemical BondIntroductionAtoms of all the elements except noble gases have incomplete outermost orbits and tends to

complete them by chemical combination with the other atoms.In 1916, W Kossel described the ionic bond which is formed by the transfer of electron from one

atom to another and also in 1916 G.N Lewis described about the formation of covalent bond

which is formed by the mutual sharing of electrons between two atoms.

Both these scientists based their ideas on the fact that atoms greatest stability when they acquirean inert gas electronic configuration.

DefinitionWhen two or more than two atoms are combined with each other in order to complete their octeta link between them is produced which is known as chemical bond.

ORThe force of attraction which holds atoms together in the molecule of a compound is called

chemical bond.

Types of Chemical BondThere are three main types of chemical bond.

1. Ionic bond or electrovalent bond

2. Covalent bond

3. Co-ordinate covalent bond or Dative covalent bond

Ionic Bond OR Electrovalent Bond

DefinitionA chemical bond which is formed by the complete shifting of electron between two atoms is

called ionic bond or electrovalent bond.

OR


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The electrostatic attraction between positive and negative ions is called ionic bond.

Conditions for the Ionic Bond Formation

1. ElectronegativityIonic bond is formed between the element having a difference of electronegativity more than 1.7

or equal to 1.7 eV.Therefore ionic bond is generally formed between metals (low electronegative) and non-metal

(high electronegative) elements.

2. Ionization PotentialWe know that ionic bond is formed by the transference of electron from one atom to another, so

in the formation of ionic bond an element is required which can lose its electrons from the outermost shell. It is possible to remove electron from the outermost shell of metals because of their

low ionization potential values.

3. Electron Affinity

In the formation of ionic bond an element is also required which can gain an element is alsorequired which can gain electron, since non-metals can attract electrons with a greater force due

to high electronegativity. So a non-metal is also involved in the formation of ionic bond due tohigh electron affinity.

Example of Ionic BondIn order to understand ionic bond consider the example of NaCl. During the formation of Ionicbond between Na and Cl2, Sodium loses one electron to form Na+ ion while chlorine atom gains

this electron to form Cl- ion. When Na+ ion and Cl- ion attract to each other NaCl is formed. The

stability of NaCl is due to the decrease in the energy. These energy change which are involved inthe formation of ionic bond between Na and Cl are as follows.

i. Sodium has one valence electron. In order to complete its octet Na loses its valence electron.

The loss of the valence electron required 495 kJ/mole.

Na ----> Na+ + e- ....................... H = 495 kJ/mole

ii. Chlorine atom has seven electrons in its valence shell. It require only one electron to complete

its octet, so chlorine gains this electron of sodium and release 348 kJ/mole energy.Cl + e- ----> Cl- ...................... H = -348 kJ/moleHere the energy difference is 147 kJ/mole (495 - 348 = 147). This loss of energy is balanced

when oppositely charged ions are associated to form a crystal lattice.

iii. In third step, positively charged Na+ ion and negatively charged Cl- ion attract to each other

and a crystal lattice is formed with a definite pattern.

Na+(g) + Cl-(g) ----> Na+Cl- ........... H = - 788 kJ/moleThis energy which is released when one mole of gaseous ions arrange themselves in definite

pattern to form lattice is called lattice energy.

From this example, we can conclude that it is essential for the formation of ionic bond that the

sum of energies released in the second and third steps must be greater than the energy requiredfor the first step.

Characteristics of Ionic Compounds


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1. An ionic compounds, the oppositely charged ions are tightly packed with each other, so these

compounds exist in solid state.2. Due to strong attractive forces between ions a larger amount of energy is required to melt or to

boil the compound and hence the melting and boiling point of the ionic compound are generally

high.

3. Ionic compounds are soluble in water but insoluble in organic solvents like benzene, CCl4.etc.

4. In the aqueous solution, the ionic compounds are good electrolytes, because in water the

interionic forces are so weakened that the ions are separated and free to move under the influenceof electric current. Due to this free movement of ions, the ionic compounds conduct electricity in

their solutions.

Covalent Bond

DefinitionA link which is formed by the mutual sharing of electrons between two atoms is called covalent

bond.

ExplanationIn the formation of covalent bond, mutual sharing of electron takes place. This mutual sharing is

possible in non-metals, therefore covalent bond is generally formed between the atoms of non-

metals. For exampleIn Cl2 molecule, two atoms of chlorine are combined with each other to form Cl2 molecule.

Each atom of chlorine having seven electrons in its valencies shell. These atoms are united with

each other by sharing one of its valence electron as shown.

Cl Cl: ----> :Cl :Cl OR Cl - ClIn this molecule, one shared pair of electrons forms a single covalent bond between two chlorine

the atoms. With the formation of a covalent bond the energy of the system is also decreased.Cl + Cl ----> Cl - Cl .............. H = - 242 kJ / moleThis released energy lowered the energy of the molecule and the stability of the compound is

also increased.

Types of Covalent BondThere are three main types of covalent bond.

1. Single Covalent BondWhen a covalent bond is formed by sharing of one electron from each atom, that it is called

single covalent bond and denoted by (-) single line between the two bonded atoms e.g.

Cl - Cl, H - H, H - Br etc.

2. Double Covalent BondIn a covalent bond, if two electrons are shared from each of the bonded atom then this covalent

bond is called double covalent bond and denoted by (=) two lines e.g.

O = O, O : : O

3. Triple Covalent Bond


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When a covalent bond is formed by sharing of three electrons from each atom then this type of

covalent bond is called triple covalent bond, and denoted by () three lines between the twobonded atoms e.g.

N : : N :, N NThe bond distance of multiple bonds are shorter and the bond energies are higher.

Characteristics of Covalent CompoundsThe main characteristics properties of covalent compounds are as follows

1. The covalent compounds exist as separate covalent molecules, because the particles areelectrically neutral so they passes solid, liquid or gaseous state. This intermolecular force of

attraction among the molecules.

2. Since the covalent compound exist in all the three states of matter so their melting points andboiling point may be high or low.

3. Covalent compounds are non-electrolytes so they do not conduct electricity from their aqueous

solution.

4. Covalent compounds are generally insoluble in water and similar polar solvent but soluble in

the organic solvents.

Co-Ordinate OR Dative Covalent Bond

DefinitionIt is a type of covalent bond in which both the shared electrons are donated only be one atom,

this type is called co-ordinate covalent bond.

The ordinate covalent bond between two atoms is denoted by an arrow (). The atom whichdonates an electron pair is called as a donor of electron and the other atom involved in this bond

is called acceptor. E.g.A + B ----> A : B OR A B

Dipole Moment

DefinitionThe product of the charge and the distance present in a polar molecules is called dipole moment

and represented by .

ORThe extent of tendency of a molecule to be oriented under the influence of an electric field is

called dipole moment.

Mathematical Representation of Dipole MomentSuppose the charge present on a polar molecule is denoted by e and the s

introduction to fundamental concepts of chemistry for class xi

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