Xi-chemistry 1,2,3.docx

Chemistry: Definition: Chemistry is the branch of natural science which deals with the study of matter and the changes it undergoes. Chemistry is often called the “central science” because of its divers applications Matter: Matter is any thing that occupies space and has mass. Example: iron, Nacl, water, O2 etc. Atom: Atom is the smallest unit or building block of matter which take part in chemical reaction. All matters are made up by atoms. Element: Element is the simplest form of matter which cannot be further simplified by any physical or chemical process. Example:

C, H, S, N, Na etc

Molecule: A molecule is a combination of two or more atoms, which can exist free in nature. Example: H2, O2, NH3, Cl2 etc Substance: A substance is mater that has constant composition and unique properties. Example:

H2O, Fe, CO2, H2 SO4

Valency: atom. Example:

Valency is the combining power of an atom or number of unpaired electrons in an N Na S

: : :

etc

Valency = 3 Valency =1 Valency =2

Significant figures: Definition: The reliable digits in a number that are known with certainty are called significant figure. Explanation: In measurement there is always uncertainty or doubt in accuracy in the last digit. For example the mass of a ball is 10.3g. The mass is still uncertain by +1 in the last digit. This can be expressed as 10.3 or 10.4. The greater the number of significant figure, the smaller the uncertainty (and hence the greater precision) of the measurement. Example: 68.35 has 4 Significant figure 127 has 3 Significant figure 0.041 has 2 Significant figure

Rules for determining significant figures: There are five rules to determine the number of significant figures. 1) Any digit that is not zero is significant. Example:

653cm has three significant figure. 9.9867kg has five significant figures

2) Zeros between non-zero digits are significant. Example: 4005m has four significant figures. 6.3007kg has five significant figures. 3) Zeros to the left of the first nonzero digit in a number less than one are not significant. Example:

0.007g has one significant figure. 0.00016mm has two significant figures.

4) In a number greater than one, all the zeros written to the right of the decimal point are significant. Example:

7.500cm has four significant figures. 4.00g has three significant figures.

5) Zeros after a non zero digit in a number greater than one are not significant. Example:

7000mg has one significant figure. 602000mm has three significant figures.

Rounding off Data: Definition: To reduce a number to the desired significant figures is called rounding off data or to round off. Explanation: It is the procedure of dropping non significant digits in a measurement and adjusting the last digit reported. A number is rounded off to the desired significant figures by dropping one or more digits to the extreme right according to certain rules. Rules: 1) If the dropping digit is greater than 5, drop it and add 1 (one) to the adjacent digit. Example: 5.768 has 4 significant figures 5.77 has 3 significant figures 5.8 has 2 significant figures 2) If the dropping digit less than 5, drop it and the adjacent digit is unchanged. Example: 6.434 has 4 significant figures 6.43 has 3 significant figures 6.4 has 2 significant figures 3) If the dropping digit is exactly 5, two possible solution arise due to even or odd nature of the last digit to be retained.

(a) If it is odd, then add “1” to the digit to be retained. Example: 6.55 is rounded off to 6.6 5.75 is rounded off to 5.8 (b) If it is even or zero then the digit to be retained is unchanged. Example: 6.85 is rounded off to 6.8 7.05 is rounded off to 7.0 Exponential Notation OR Exponential terms: Definition: The short hand expression of very large or very small number in the form of exponent (Power of 10) is called exponential notation or terms. Explanation: It is a convenient method to deal with very large and very small quantities. It is helpful in simplifying many types of arithmetical problems and minimize errors. In order to write such quantities without writing a large number of zeros, exponential notation is used. For example 3050000000 may be written as 3.05x109. Logarithms: Definition: A logarithm is an exponent where the base usually 10. The logarithm is divided into two parts. i) Characteristic: It is the integral part of logarithm and may be positive or negative. It is may be determined by just looking at the numbers. ii) Mantissa: It is the decimal fraction part of logarithm. It is always positive and may be find out with the help of logarithm table. Explanation: The logarithm greatly helps in the simplification of expression involving multiplication, division, taking of power. Example: Log of 273= 2.4362 Where characteristic = 2 And mantissa = 0.4362 PROBLEMS: (i) Log (3742x931) Log 3742+ log 931 3.5731 + 2.9689 Log = 6.5420 Antilog of 6.5420 = 3483000 Answer (ii)

Log (3762  213)

Log 3762 – log 213 3.5754 – 2.3284 Log = 1.247 Antilog of 1.247 = 17.66 Answer (iii)

Log(68)1/8 = 1/8 x log 68 = 1/8 x 1.8325 Log = 0.2290 Antilog of 0.2290 = 1.694 Answer

Atomic Mass: Definition: The mass of one atom of an element compared with the mass of one atom of C12 (the stable light isotope of carbon). Explanation: One atom of hydrogen which weighs approximately 1/12 the mass of one atom of carbon (12) has an atomic mass of 1 (

1 x 12 = 1). 12

Unit: It is a ratio and has no unit. It may be expressed in atomic mass unit (a.m.u.) it can also be expressed in grams, pounds, ounces etc. Example: Atomic mass of H = 1 a.m.u, Atomic mass of C = 12 a.m.u. Gram atomic mass: Atomic mass expressed in grams is called gram atom or gram atomic mass. Example: Gram atomic mass of H = 1g, Gram atomic mass of C = 12g. Molecular Mass: Definition: The sum of atomic mass of the atoms present in a molecule as shown by its molecular formula. It is based on molecular formula of a substance. It is written for the covalent substance or elements present in molecular state. formula.

Example: i. Molecular mass of water H2O = 2 x 1 + 16 = 18 a.m.u ii. Molecular mass of Benzene C6H6=6 x 12 + 6 x 1 = 72 + 6 = 78 a.m.u Unit: It has no unit but in may be expressed in a.m.u. It can also be expressed in gram, pounds etc. Gram molecular mass:

Molecular mass expressed in gram is called gram molecule or gram molecular mass. Example: Gram molecular mass of H2O = 18g. Gram molecular mass of C6H6 = 78g Formula Mass: Definitions: Sum of atomic mass as given in the simplest (empirical) formula of ionic compound. OR It is the sum of atomic mass of all the atoms present in one molecule of compound as shown by its simplest or empirical formula. Explanation: In many substances the atoms are not organized into discrete molecules, but form a net work structure in which all the atoms are bonded to one another. Hence the molecular formula can not be assigned to such substances. They are instead represented by an empirical formula, which gives the ratio of atoms of different kinds in a molecule. Example: Formula mass of NaCl = 23+35.5=58.5 a.m.u Formula mass of CaO = 40+16 =56 a.m.u Gram-formula mass: Formula mass expressed in grams is called gram formula mass or gram formula. Example: Gram formula mass of NaCl = 58.5g Gram formula mass of CaO = 56g Empirical Formula: Definition: The simplest formula of a compound which tells us the simplest ratio between the atoms of different elements, present in a compound. Explanation: This formula expresses the relative number of atoms of each element present in a molecule of a compound. It does not indicate the actual number of atoms in a compound but shows only the ratio of atoms. Examples: The empirical formula of benzene (C6H6) is C-H in the ratio of 1:1.The empirical formula of glucose (C6H12 O6) is CH2O in the ratio of 1:2:1. There are many compounds, which have empirical and molecular formula. For example Methane has same empirical and molecular formula. To work out (Determining) empirical formula: The empirical formula is determined by applying the following steps. i. Detect the elements present in compounds. ii. To determine the mass of the element. iii. To calculate the percentages of the element. iv. To calculate the mole ratio of the elements.

Mole ratio=

Given percentage Atomic mass

v. To calculate the simple mole ratio of atoms Simple mole ratio =

mole ratio smallest mole ratio

vi. If the result is not in whole number, then convert it by simple multiplication. Problem: 2.0 grams of organic compound containing C, H, and O combustion produce 4.8 gm of CO2 and 1.0 grams of H2O. Find out empirical formula. Solution Step No. 1:

Find out  of elements.

At. Mass of C  Mass of CO 2 100 Mol mass of CO 2  Mass of organic compound 12  4.8g 100 = 44  2

a)  of carbon (C) =

C = 65.46  b)  of hydrogen (H) =

Mol. mass of H  Mass of H 2 O 100 Mol. Mass of H 2 O  mass of organic compound 2 1 = 18  2

H = 5.53 c)  of oxygen by differential method  of oxygen (O) = 100 – ( of C +  of H) = 100 – (65.46 + 5.53) = 100 -71 O = 29  Step No. 2 find out mole ratio

65.46  5.455 12 5.53  5.53 H= 1 29  1.812 O= 16 C=

Step No. 3 find out simplest mole ratio

5.455 3 1.812 5.53 3 H= 1.812 1.812 1 O= 1.812 C=

Result

Empirical formula is C3H3O

Molecular Formula: Definition: The actual formula of compound, which shows the exact number of atoms presents in a compound, is called molecular formula. Explanation: Empirical formula of benzene is CH. The molecular formula is C6H6. This shows that Benzene molecule composed of 6 atoms of carbon and 6 atoms of hydrogen. This indicates that the molecular formula is an integral multiple (n) when n= 1.2.3…) of the empirical formula. Molecular formula = (empirical formula)x n Where n = 1.2.3…. To work out (Determining) Molecular formula: The molecular formula is determined by applying the following steps. i. Find out the empirical formula. ii. Find out the empirical formula mass from empirical formula iii. Find out or calculate the value of integer “n” n= iv.

Molecular Mass Empirical formula mass

Multiply the empirical formula with “n” this gives the molecular formula. Molecular formula = (empirical formula) x n

Problem: A compound has empirical formula C H2O, if its molecular mass is 180. Find out molecular formula. Data

Empirical formula = C H2O Molecular mass of compound = 180 Molecular formula = ??

Solution Empirical formula mass of C H2O = 12 + 2 + 16 = 30 Value of integer “n” n = Molecular formula

Result:

Molecular formula

Molecular Mass 180  6 Empirical formula 30

= (empirical formula) x n = (C H2O) x 6 = C6H12O6

= C6H12O6

Mole: Definition: Gram atomic mass or gram molecular mass or gram formula mass of any substance (atoms, molecule, ions) which contain 6.02x1023 particles. Explanation: In chemical problems, it is necessary to consider quantities of substance in terms of the number of atoms or ions or molecule present. The unit to express numbers of atoms or ions or molecules is called the mole.

Examples: 1 Mole of C = 12g 1 Mole of Na = 23g 1 Mole of H2O = 18g 1 Mole of C6H12O6 = 180g Calculations: NO: of moles =

Given Mass Atomic mass or Molecular mass

OR Given mass in gram = No of moles x Molar mass or Atomic Mass.

Given number of particles 6.02  10 23 Given volu me of gas in dm 3 No: of moles = 22.4dm 3 NO: of moles =

OR No. of particles =No of mole x NA Mass in gram =

At/Mol. Mass  given particles 6.02  10 23

Problem No: 1 Calculate number of moles in 230 gram in Na. Data

Given mass of Na = 230g Atomic mass of Na = 23 No, of moles of Na = ??

Solution: No. of moles of Na = Result:

Given mass of Na 230   10Moles Atomic mass of Na 23

No. of moles of Na = 10 moles

Problem No:2 Calculate mass in gram of 3.01x1023 molecules of C6H6 . Data

Given no: of molecules = 3.01x1023 Molecular mass of C6H6 = 78 a.m.u. Mass in grams of C6H6 = ??

Solution: Mass in grams of C6H6 = Result:

Molecular mass of C6H6  given molecules 78a.m.u.  3.02  1023   39 g 6.02  1023 6.02  1023

Mass of C6H6 is 39 g

Problem No: 3 Calculates the number of atoms in 9.2 g of Na. Data

Mass of Na = 9.2g At. mass of Na = 23 a.m.u. No. of atoms of Na = ??

Solution: No. of atoms of Na =

6.02 10 23  Mass of Na 6.02  10 23  9.2  At. Mass of Na 23a.m.u. 23 6.02  10  9.2 = 23 a.m.u. = 2.408 x 1023 atoms

Result:

No. of atoms of Na are 2.408 x 1023

Avogadro’s Number: Definition: One mole of any substance contain 6.02x1023 particles (atoms, ions, molecules). This number is fixed and called Avogadro’s Numbers. Representation: It is given in the honor of Amadeo Avogadro’s it is expressed by NA. Explanation: The numbers of particles (atoms, ions, or molecules) present in one mole of any substance (gram atomic mass, gram formula mass or gram molecular mass) is called Avogadro’s Numbers.

Examples: One mole of hydrogen atom (H=1g) contains 6.02 x 1023 H atoms One moles of oxygen atom (O=16g) contains 6.02 x 1023 O atoms One mole of oxygen gas (O2=32g) contains 6.02 x 1023 O2 molecules One mole of water (H2O=18g) contains 6.02x1023 H2O molecules Calculation Based on Chemical equation: OR STOICHIOMETRY: It is derived from Greek work “stoicheon”= element and “metron” = measure. Definition: The branch of chemistry, which deals with the quantitative relation ship between the amount of reactants and the products in a balanced chemical equation, is called Stoichiometry. Explanation: A balance chemical equation gives us the exact mole ratio of reactants and products during a chemical reaction. From balance equation we can calculate the mass or volume (amount) of any reactant or product. This quantitative relation ship is called Stoichiometry. Relationships: There are three relationships involved in Stoichiometry Calculation. i. Mass-Mass relationship ii. Mass- Volume relationship iii. Volume- Volume relationship i. Mass-Mass relationship: In this relationship the mass of reactants and products is calculated from the given mass of reactant and product with the help of balanced chemical equation. ii. Mass volume relationship All gases can be expressed by amount in terms of masses or volumes. This relationship is used to interchange mass and volume of a gas in chemical equation. This relationship is governed by Avogadro’s law. According to Avogadro’s law one-gram mole of any gas at standard temperature (0°C = 273 K), pressure (1 atmosphere = 760mmHg) occupies a volume of 22.4 dm3. This volume is called MOLAR – VOLUME. If the mass is expressed in ounces (1 pound = 16 ounces) then one ounces mole of any gas at standard temperature and pressure (STP) occupies a volume of 22.4 cubic feet this volume is called ounce molar volume. This relationship allows us to interchange mass and volume units of a gas through mass volume relationship in a chemical equation. iii. Volume-Volume Relationship This relationship is for reaction tacking place in gaseous state. This relationship is governed by Gay-Lussac’s law of combining volumes. This states that the “Gases react in the ratio of small whole numbers by volume under similar conditions of temperature and pressure”.

In this relationship, the volume of any substance (gas) present In the balance chemical equation is to be calculated from given volume of any gas present in the same reaction. Example: Consider the following reaction 2H2S(g) + 3O2  2H2O(g) + 2SO2 Two volumes of H2S react with the three volumes of O2 to produce two volume of H2O and two volumes of SO2. OR Two dm3 of H2S react with three dm3 of O2 to produce two dm3 of H2O and two dm3 of SO2. The ratio of whole numbers would be 2:3:2:2 Limiting Reactant Definition: The reactant present in smaller amount and produce minimum amount of product called limiting reactant. EXPLANATION: If in a chemical reaction the reactants are not present in exactly the correct ratio, the reaction continues until one of the reactant is completely consumed and the reaction stops. The reactant which is consumed is called Limiting Reactant. The other reactants which are relatively in large amount are called Excess Reactants. The calculations are made on the bases of Limiting Reactant.

THE THREE STATES OF MATTER GASES, LIQUIDS AND SOLIDS STATES OF MATTER: There are three states of matter, Gas, Liquid and Solid. GAS: A gas consists of molecules, has no definite shape and volume. The molecules are free to move about through out the container. LIQUID: A liquid has no definite shape but occupies definite volume. SOLID: A solid has both definite shape and volume. KINETIC MOLECULAR THEORY OF GASES: In 1859 Maxwell and Boltzmann put for word this theory, which explains the behavior of particles of gases in motion. It is based on the fundamental concepts that a gas is made of a large number of molecules in continuous motion. Hence the theory is called the kinetic molecular theory. The kinetic molecular theory makes the following assumptions. 1) PARTICLES: All the gases are composed of a large number of invisibly very small particles called atoms or molecules. 2) VOLUME: The volume of gas molecules is negligible in comparison to the total volume of the gas. 3) COMPRESSION: The gas molecules are widely spread. They are easy to compress due to large empty spaces between them. 4) MOTION: The gas molecules are in state of continues random motion. 5) COLLISION: During collision gas molecules do not loss or gain kinetic energy because collisions are elastic. 6) PRESSURE: Pressure of the gases is due to the collision of the gas molecules with the walls of the container. 7) FORCE: In an ideal gas, there are no attractive or repulsive forces between molecules. Thus the gas molecules can move freely. 8) KINETIC ENERGY: The average kinetic energy of gas molecules is directly proportional to the absolute temperature. GASES STATE BEHAVIOR OF GASES: The assumptions of kinetic molecular theory better explain the properties and behavior of gases. 1) DIFFOUSIBILITY: DEFINITION: The mixing or spreading of one gas molecule into the spaces of the other gas molecule is called diffusion. EXAMPLE: Drop of perfume diffuses rapidly with air. According to kinetic molecular theory, molecules of the gases are widely spread and separated having large empty spaces among them, hence they

are free to move. Free movement of the molecules causes intermixing of two gases more easily and rapidly.

EFFUSION: It is opposite to diffusion and is defined as the continuous escape of gas molecules from small hole of container is called effusion. EXAMPLE: Effusion of air from the small hole of the Tyre tube. 2) COMPRESSIBILITY: All the gases have property to compress when pressure is applied. According to kinetic molecular theory the gases have large empty spaces among their molecules, so when pressure is applied the molecules come closer to one another and thus volume is reduced and compression takes place. EXAMPLE: Pumping of air into tyre tube. EXPANSION: The expansibility is opposite to compressibility. The gases expand when pressure is decreased or temperature is increased which causes increase in the volume. EXAMPLE: Rushing of air out of punctured tyre. 3) PRESSURE: DEFINITION: The force exert by gas molecules on a unit area is called pressure. INSTRUMENT: Mercury Manometer. UNITS: In SI (international system) the unit of pressure is ‘Pascal’ (pa). It is the pressure of a force of one Newton (N) per square meter (m2) area. Pa = N/m2 = Kg.m/s2 = kg/m.s2 m2 ATMOSPHERIC PRESSURE: The pressure of air that can support 760mm Hg column at sea level, is called one atmospheric pressure. RELATION SHIP BETWEEN UNITS: 1atm = 76cm of Hg = 760mm of Hg = 760 torr = 1.01300 x 105 Pa = 101300 N/m2 = 14.7psi = 20 tons. Since these units are more useful therefore we will use these units. VOLUME:

DEFINITION: The space occupied by matter is called volume. UNITS: Milliliter (ml), liter (L), cubic centimeter (cm3), cubic decimeter (dm3) and cubic meter (m3) 1m3 = 1 x 102 dm3 = 1 x 106 cm3 Standard volume = 0.0224m3 = 22.4dm3 = 22400cm3 TEMPERATURE: The average kinetic energy of a substance is called temperature. The S.I. unit of temperature is Kelvin (K). K = OC + 273 or oC = K –273 GAS LAWS: The volume of the given sample of gas depends on the temperature, mass and pressure applied to it. Any change in temperature, mass or pressure will affect the volume of the gas. As a result of several experiments, scientists derived the relationships among the pressure, mass, temperature and volume of the given gas. These relationships, which describe the general behavior of gases, called the gas laws. BOYLE’S LAW (PRESSURE – VOLUME LAW): INTRODUCTION: An English chemist Robert Boyle was introduced this law in the year 1660. STATEMENT: “The volume of fixed amount of gas is inversely proportional to the pressure applied at constant temperature”. OR “The product of pressure and volume of fixed amount of gas is always constant at constant temperature”. MATHEMATICAL DERIVATION: Let volume is ‘v’ and pressure is ‘p’ therefore according to Boyle’s law V

1 (T is P

constant)

1 (K is proportionality constant) P PV =K –––––––––––– eq: (i)

V=Kx

For two states of the system the eq: (i) will be, P1V1 =P2V2

––––––––

eq: (ii)

Boyle’s law

GRAPHICAL REPRESENTATION: If volume of the gas is plotted against the total pressure a parabolic curve is obtained showing the decrease in volume with increasing pressure. Similarly 1 graph between V and 1/p is in straight line shows that V P

P1V1 P2V2

1 P

V V1 Volume V2

Verification of law: Robert Boyle took ‘J’ shaped glass vessel in which the shorter graduated limb is closed and its larger limb is opened. He poured the mercury from open limb till the level of mercury in both limbs become same, it showed that the gas is subjected to atmospheric pressure. A more mercury is poured from open limb and observed that the level of mercury in open limb is raised which caused the increase of pressure and decrease of the volume, thus law was verified. P total =P atm +Ph (where ‘h’ is difference in heights of mercury in both limbs) P1 atm

P2 atm

h

V1

V2

Mercury

BOYLE’S LAW IN TERMS OF KINETIC MOLECULAR THEORY: In terms of Kinetic molecular theory of gases, the pressure of gases is due to collision of the gas molecules. At constant temperature when the volume is decreased the molecules come closer to each other as a result collision increases which results increase of pressure, i.e, V 1/p at constant ‘T’ Thus it is in accordance with Boyle’s Law. PROBLEM: What volume does 300 dm3of a gas at 700 torr occupy when the pressure is changed to 2 atmospheres.

Data: V1 =300dm3

SOLUTION: P1V1=P2V2

P1 = 700 torr = 700  760 = 0.92 atm P2 = 2 atm V2 = ??

0.92atm 300dm 3 P1V1  P2 2atm. 3 = 138dm

V2 =

Result: V2 =138 dm3 CHARLE’S LAW (TEMPERATURE – VOLUME LAW): INTRODUCTION: French physicist Jacques Charles introduced this Law in the year 1787. STATEMENT: “The volume of a fixed amount of gas is directly proportional to absolute temperature at constant pressure.” OR “At constant pressure, for each 1OC change (rise or fall) of temperature the volume of the gas changes (increases or decreases) to 1/273 of its initial volume at 0OC”. MATHEMATICAL DERIVATION: According to Charle’s law, V T (P is constant) V= K x T (where k is proportionality constant)

V T

=K  Ratio between V and T is constant

Then,

V2 V1 = K and T2 T1

= K

V1 V 2  Charle’s law T1 T2

V GRAPHICAL REPRESENTATION: When volume of gas is plotted against absolute temperature at constant pressure the straight line is obtained which shows the direct relationship between volume V and absolute temperature of the gas.

T

CHARLE’S LAW IN TERMS OF KINETIC MOLECULAR THEORY: In terms of kinetic molecular theory, the average kinetic energy of gas molecules decreases as the temperature is decreased. With the decrease of kinetic energy, velocity of molecules decreases. At constant pressure, the decreased velocity causes the sample of gas to shrink and occupy smaller volume. i.e. V  T at Constant Pressure. This is in accordance with Charle’s Law ABSOLUTE ZERO: Plot a graph between volume (V) and temperature (T) gives straight line in accordance with Charles law. When this line is extra plotted then it cuts the temperature axis at- 273.16 OC and zero volume. It suggests that the volume of gas would theoretical be zero at –273oC. In fact all the gases convert into Liquid above this temperature, so that gas behavior no longer be observed. In 1848 Lord Kelvin realized the significance of this behavior and set up an absolute temperature scale, now called the “Kelvin temperature scale.”

–300 –200 –100 0 100 200 300 OC

“Thus the temperature of –273OC is referred to as the absolute zero or zero Kelvin at which volume of gases is considered to be zero.”

PROBLEM: A gas under 546 K temperatures occupies 100cm 3 volume. What will be its volume if temperature is changed to 100OC. Pressure remain constants. DATA: T1 = 546K T2 = 100OC + 273 = 373K

SOLUTION: V1 V2  T1 T2 273K VT V2 = 1 2 = 100cm3 x 546 K T1

V1 = 100cm3 V2 = 68.31cm3 V2 = ?? Result: Volume of gas will be 68.31cm3 AVOGADRO’S LAW (VOLUME – AMOUNT LAW) OR AVOGADRO’S HYPOTHESIS: INTRODUCTION: Italian physicist Amadeo Avogadro introduced this law in 1811. STATEMENT: “Equal volumes of different gases under similar condition of temperature and pressure contain the same number of gas molecules”. OR “The Volume of a gas is directly proportional to the number of molecules of the gas at constant temperature and pressure”. V n (P and T constants) Where V = volume and n = no. of molecules of a gas”. EXPLANATION: This law can be explained with the help of molar volume. “The volume of one mole of any gas at S.T.P. is 22.4dm3 is called molar volume.” At S.T.P one mole of any gas possesses 6.02 x 1023 molecules. If two gases H2 and O2 are available in two vessels of same volume at constant Pressure and Temperature then they possesses same number of molecules. EXAMPLE: i) 1 mole of CO2 (44gm) has volume = 22.4dm3 = 6.02x 1023 molecules. ii) 22.4 dm3 of any gas have molecules 6.02x 1023 molecules . 

1 dm3 of any gas has molecules =

6.02  10 23  1dm3 2.687  10 22

= 2.687x1022 molecules AVOGADRO’S LAW IN TERMS OF KINETIC MOLECULAR THEORY: In terms of kinetic molecular theory the average Kinetic energy of one molecule of one gas will be equal to the average Kinetic energy of one molecule of other gas at the same temperature and pressure. Hence equal volume of different gases has the same kinetic energy when they have same number of molecules. Thus it is in accordance with Avogadros’law.

IDEAL GAS OR PERFECT GAS: The gas, which obeys gas law and all postulates of kinetic molecular theory of gases under all the conditions of temperature and pressure, is called ideal gas. The ideal gas is imaginary (not known), so it does not exist. PROPERTIES OF IDEAL GAS: i) The molecules of ideal gas do not attract or repel each other. ii) The molecules of Ideal gas do not occupy space thus the volume is negligible. REAL GAS OR NON – IDEAL GAS: The gas, which obeys gas law and all the postulates of Kinetic molecular theory of gases under moderate conditions of temperature and pressure, is called non- ideal gas. The non ideal gas is real (Known) so it exists. DEVIATION OF NON – IDEAL GAS: The real gas shows deviation from ideal gas behavior, which is due to two properties of ideal gas at (i) high pressure and (ii) low temperature. The deviation of real gas is due to the presence of intermolecular forces like Vander Waals force between their molecules. GENERAL GAS EQUATION OR IDEAL GAS EQUATION OR EQUATION OF STATE INTRODUCTION: The relationship between volume, pressure, temperature and no. of molecules or moles of a gas is called Gas Equation. MATHEMATICAL VERIFICATION: The combination of Boyle’s law, Charles law and Avogadro’s law is called gas equation as, V

1 (T is constant) P

VT

(P is constant)

V  n (P and T are constant)

 Boyle’s law  Charle’s law  Avogadro’s law

By combining these three laws we have

1 Tn P 1 V=R x T x n (where R is gas constant) P nRT V= P V

PV = nRT  Gas Equation For 1 mole of gas n = 1 Hence PV = RT

OR

PV = R (R depends upon P, V, T and n) T If P1V1 and T1 are initial values and P2 V2 and T 2 are final values then,

PV P1V1  R Similarly 2 2  R T2 T1 OR

P1V1 P2V2  T1 T2 This is called general gas equation and useful for solving the problems . APPLICATIONS OF IDEAL GAS EQUATION: 1) Molecular mass of gas is calculated as . PV = nRT

Given mass Molecular mass m n = equation (i) M

Moles of gas (n) =

PV = nRT By substituting the value of ‘n’ from eq: (i) we get PV =

m RT equation (ii) M M=

mRT PV

2) Density may be calculated as, PV = nRT From eq. (i) we get the value of “n”

mRT VM m RT  P= equation (ii) V M P=

We know that d = Put the value of P=

dRT M

m v

m in equation (ii) we get v

d=

PM RT

The Value of ‘R’ (Gas constant)

Part – I

Part – II

Data:

Data: n = 1 mole T =273 K P = 1 atm V= 22.4dm3 R = ??

n = 1 mole, T = 273K P = 101300 Nm–2 V = 0.0224m3 (1dm3 = 10-3 m3) R = ??

Solution: According to general gas equation PV = nRT PV R= nT 1atm.  22.4dm 3 R= 1mole  273K 0.0821atmdm3 R= mole.K R = 0.0821atm. dm3 mole-1 K-1

Solution: According to general gas equation. PV = nRT PV R= nT

101300 Nm 2  0.0224m 3 1mole  273K R = 8.3143 Nm. mole-1 K-1 Since 1J = 1Nm R = 8.3143J.mole-1 K-1 R=

This is constant value

This is constant value

DIFFUSION: “The mixing of molecules of different gases to produce homogenous mixture is called diffusion.” RATES OF DIFFUSION: The distance covered by a gas for the purpose of diffusion is called rate of diffusion. GRAHAM’S LAW OF DIFFUSION: INTRODUCTION: Scottish scientist Thomas Graham introduced this law in 1881. STATEMENT: “Rate of diffusion of a gas is inversely proportional to the square root of its density under similar condition of temperature and pressure for two gases.” MATHEMATICAL DERIVATION: if ‘r’ is the rate of diffusion and ‘d’ is density of gas then mathematically this is derived as,

1 d K r=K d r

Where ‘K’ is proportionality constant.

equation (i)

Let us consider two gases having densities d1 and d2 and the rate of diffusion r1 and r2, then the equation for two gases will be,

GAS – I

r1 

1 d1

r1 

K d1

GAS – II

1 d2 K r2  d2

r2 

By comparing rates of diffusion of two gases we get,

d2 r r1 K K K or 1      r2 r2 K d1 d2 d1

d2 d1

eq: (ii)

MOLECULAR MASS: Density is related with molecular mass i.e., density is directly proportional to molecular mass (d  M) Thus, d1  M1 and d2  M2, then eq: (ii) will be as

r1 M2  r2 M1

eq: (iii)

GRAHAM’S LAW OF DIFFUSION IN TERMS OF KINETIC MOLECULAR THEORY: According to kinetic theory average kinetic energy is proportional to absolute temperature. If temperature is kept constant the kinetic energy is of one gas will be equal to kinetic energy of other gas. Thus it is in accordance with Graham’s law of diffusion. PROBLEM: The ratio of rates of diffusion of two gases is 3:1. If molecular mass of first gas is 9 gm. Find out molecular mass of 2nd gas. DATA: r1 = 3 r2 = 1 m1 = 9 m2 = ?? SOLUTION: By applying formula,

r1 m2  r2 m1 m2 m1 3  3  3  3  m2 1 9 3

9  m2

By squaring on both sides, m2   9  2

2

m2  81gm RESULT: Molecular mass of 2nd gas will be 81gm. PARTIAL PRESSURE When two or more non-reacting gases are mixed together each gas will exert its own pressure. The part of pressure exerted by a single gas in a mixture is called partial pressure. DALTON’S LAW OF PARTIAL PRESSURE: INTRODUCTION: English scientist John Dalton introduced this law in the year 1801. STATEMENT: The total pressure of the mixture of gasses is the sum of the partial pressure of different gasses present in a mixture. PT = P1 + P2 + P3 + ………………. Where PT is the total pressure and P1 + P2 + P3 +………………. are the partial pressure of different gasses. EXPLANATION: Partial pressure means the individual pressure for example atmospheric pressure is equal to 1atm this pressure includes the pressure of all gasses which are present in the air. 1 atm = P(N2) + P(O2) + P(H2)+ …………… + P (Remaining gasses) According to Dalton’s law the sum of the partial pressure the pressure of gasses before mixing and after mixing remains same and constant. DIAGRAM

PA = 0.2atm + PB = 0.3atm =

PT = 0.5atm

FORMULA FOR PARTIAL PRESSURE: Pi =

ni  Pt nt

APPLICATIONS: This law applies most commonly to the gas collected over water or aqueous. The pressure of moist gas = Pressure of dry gas + pressure of water vapour P (MOIST GAS) = P(DRY GAS) +( PH2O VAPOUR) P (DRY GAS) = P (MOIST GAS) - (PH2O VAPOUR)

DALTON’S LAW OF PARTIAL PERSSURE IN TREMS OF KINETIC MOLECULAR THEORY In terms of kinetic molecular theory the there are no attractive and repulsive forces between gas particles at ordinary temperature and pressure., there fore each gas behaves independent of the presence of other gases in the gaseous mixture. The pressure of each gas in the mixture depends up on the number of its particles colliding against the wall of the container. This pressure of each gas in the mixture is called the partial pressure of the gas. Therefore, the total pressure on the walls of the container would be the sum of the partial pressure of the gases in the mixture. It is an accordance with Dalton’s law of partial pressure. PROBLEM: A gaseous mixture containing 8 moles of H2 and 12 moles of N2, is enclosed in a cylinder under a pressure of 30 atm. Calculate the partial pressure of H2 and N2. DATA:

nH 2 = 8 mole,

n N 2 = 12 moles

nt = nH + n N 2 = 8 + 12 = 20 moles 2

Pt = 30atm (a) PH 2 = ?? SOLUTION: (a) PH 2 = (b) PN 2 =

(b) PN 2 = ??

Pt  nH 2 nt Pt  n N 2 nt



30atm.  8moles  12atm 20moles



30atm. 12moles  18atm 20moles

RESULT: (a) PH 2 = 12atm CHECK: Total Pressure Pt 30atm 30 atm

(b) PH 2 = 18atm

= = = =

Sum of Partial Pressure PH 2 + PH 2 12atm + 18atm 30atm

CHANGE OF STATE OR (LIQUIFICATION): When gases are cooled, they convert into liquid state, thus is called change of states or Liquefaction .In fact at absolute zero (–273OC) all gases are converted into liquids. LIQUIDS: The physical state of matter in which it has definite volume but no definite shape is called liquids. LIQUID STATE: The intermediate state between gases and solids is liquid state. The liquid molecules are close to each other having low kinetic energy.

KINETIC THEORY OF LIQUIDS: (1) All the liquids are composed of tiny molecules. (2) The molecules are randomly arranged. (3) The molecules have cluster due to which they are close to one another. (4) Liquid molecules have moderate inter molecular attraction. (5) The kinetic energy of liquid molecules is directly proportional to the absolute temperature. BEHAVIOR OF LIQUIDS: . 1: DIFFUSIBILITY: Liquid are diffusible into one another. Example: Drop of ink diffuses in a glass of water. According to kinetic molecular theory the free movement of liquid molecules permits diffusion to take place but the closeness of molecules makes it slower as compared to gases. 2: COMPRESSIBILITY: Generally liquids cannot be compressed under normal conditions but at a very high pressure compression occurs to a very low extent. In terms of kinetic theory the liquid molecules are close to one another so when pressure is highly increased, the molecules roll over one another and liquids are squeezed. 3: EXPANSION AND CONTRACTION: Liquids expand on heating and contract on cooling i.e, Mercury (Hg) in thermometer. According to kinetic molecular theory with the increase of temperature the kinetic energy of molecules increases and molecules become away from one another thus volume increase and expansion take place. Similarly lowering the temperature causes the decreases in kinetic energy and molecules come closer in the result volume decreases and contraction takes place. VISCOSITY DEFINITION: “The internal resistance to the flow of liquids is called viscosity” OR “The resistance or friction of the liquids to its flow is called viscosity”. REPRESENTATION: It is represented by Greek letter ‘’ (eata). UNITS: The CGS unit of viscosity after the name of its investigator poiseulle is poise centipoises, millipoise (1 poise = 1gm / cm .sec) S.I UNITS: N.s/m2 1 Poise = 10-1 N.s/m2, 1 centipoise = 10-3 N.s/m2, 1 millipoise = 10-4 N. s/ m2 APPARATUS: Ostwald’s viscometer EXPLANATION:

Liquids have the ability to flow (hence these are called fluids) some liquids flow slowly and some fastly. Those flow slowly are said to be more viscous. Example: Glycerin is more viscous than water. FACTOR ON WHICH VISCOSITY DEPENDS: 1: INTERMOLECULAR ATTRACTIVE FORCES: Higher the intermolecular attraction greater will be the resistance, so higher will be the viscosity. Example: Honey > water (viscosity  intermolecular attraction). 2: MOLECULAR SIZE: Viscosity increases with the increase of molecular size. Example: Glycerine > water (viscosity  molecular size). 3: MOLECULAR SHAPE: Irregular shaped molecules increase viscosity. Example: Glycerin > Ether (viscosity  Irregular shape). 4: DENSITY: Denser molecules have higher viscosity, while less denser have less viscosity. Example: Milk > water (viscosity  density) 5: TEMPERATURE: With the increase of temperature the viscosity decreases because intermolecular attraction decreases. (Viscosity 1/temperature) SURFACE TENSION: DEFINITION: “The amount of energy required to stretch or increase the surface of a liquid by unit area. OR The force per unit length (1cm) or energy per unit area (1cm2) of the surface of liquid is called surface tension.” REPRESENTATION: It is represented by Greek letter “” gamma. UNITS: CGS unit is dynes / cm or ergs /cm2 and S.I unit is N/m or J/m2 APPRATUS: STALAGMOMETER OR

DROP PIPETTE

EXPLANATION: The liquid molecules have intermolecular attraction forces, means each molecule is attraction by neighboring molecule in all the direction, but the surface molecules are only attracted by inner molecules that causes the inward pull or tension to the surface. As a result of this inward pull, the surface of the liquid behaves as a membrane tending to contract to smallest area and causing a tension on the surface of liquid.

Intermolecular attraction at a liquid surface occur only with in the

surface and below FACTOR ON WHICH SURFACE TENSION DEPENDS: 1) INTERMOLECULAR ATTRACTION: Greater the inter molecular attraction greater will be the surface tension. H – bonded liquids have more surface tension. THE INTERMOLECULAR FORCES MAY BE (i) (ii)

COHESIVE FORCE ADHESIVE FORCE

i) COHESIVE FORCE: The attractive force between similar molecules. Example: The attractive force among water molecules. ii) ADHESIVE FORCE: The attractive force between dissimilar molecules. Example: The attractive force among water and glass of the container. 3) Temperature: Surface tension decreases with the increase of temperature. i.e. S.T  1/T 4) DENSITY: Higher the density greater will be the surface tension, more will be the attraction between molecules. 5) SURFACE AREA: Surface tension tends to pull the surface molecules inside, hence the surface area of liquid decrease. i.e. surface area  1/surface tension. CAPILLARY ACTION: DEFINITION: The rise or fall of liquid in the capillary tube is called capillary action. EXPLANATION: If the adhesive force is greater than cohesive force, the liquids rises up the sides of capillary tube when tube is dipped in the liquid say water, it wets the glass due to surface tension, which minimizes surface area. The liquid like water rise in capillary tube until the upward force due to surface tension is just balanced by down ward gravitational pull then concave meniscus is formed. The level of non- wetting liquid in the capillary tube will fall below the level of liquid in surrounding space. Example: “Hg” which forms convex meniscus, there is less adhesive force or greater cohesive force.

EVAPORATION: The conversion of a liquid into its vapours without external heating is called “evaporation”. CONDENSATION: The process in which the vapours are converted into the liquid state on cooling. VAPOUR PRESSURE:

(A STATES OF DYNAMIC EQUILIBRIUM)

DEFINITION: The pressure exerted by the vapour over the surface of liquid in closed container, when vapours are in equilibrium with the liquid state is called vapour pressure. APPARATUS: Manometer UNITS: m m Hg, cm Hg, torr, atm, Pascal, N.m-2, lbs/ inch2 EXPLANATION IN TERMES OF KINETIC MOLECULAR THEORY: Evaporation occurs when high-energy molecules at the surface of liquid break away from their neighbors and escape into the gas phase. During evaporation, the escape of high-energy molecules lowers the average kinetic energy of the remaining molecules; consequently the temperature of the remaining liquid falls down. Thus it is said that evaporation is a cooling process. When liquid is placed in closed container two continuous processes are occurring one is evaporation and other is condensation. The process of conversion of vapors into liquids is called condensation. In the beginning the rate of evaporation is greater than the rate of condensation but at last a stage is occurred, the two processes will take place with exactly the same rate, this stage is called equilibrium, state. Evaporation  condensation At this equilibrium, there are some vapors presents above the surface of liquid. The vapors of these molecules strikes the surface of the liquid as well as the walls of the container, thus a pressure is created and this pressure is called vapour pressure.

Vapour pressure

Open container

closed container

FACTORS ON WHICH VAPOUR PRESSURE DEPENDS 1) TEMPERATURE: The vapour pressure increases with the rise of temperature. For instance at 15OC the vapour pressure of H2O is 13.0 torr. 25OC the vapour pressure of H2O is 24.0 torr.

100OC the vapour pressure of H2O is 760.0 torr. The vapour pressure is constant at constant temperature. (Vapour pressure  temperature) 2) FORCE OF ATTRACTION: Greater the force of attraction between liquid molecules, less will be the vapour pressure, hence less vapors are formed. (Vapour pressure  1/Force of attraction) 3) DENSITY: Greater the density more will be the attraction; hence less will be the vapour pressure. (Vapour pressure  1/Density) 4) NATURE OF LIQUID: Low boiling point liquids exert more vapour pressure and high boiling point liquids exert less vapour pressure at a given temperature. BOILING POINT OR (CHANGE OF STATE): The temperature at which the vapour pressure of liquids becomes equal to the atmospheric pressure is called boiling point. OR The temperature at which the vapour pressure of liquid is equal to 760torr (1atm) is called normal boiling point. Example: The boiling point of H2O at 1atm = 100oC but at Mount Everest boiling point of H2O = 71oC and pressure 244 torr. APPLICATIONS: (i) PRESSURE COOKER: At high attitude places the food takes time to cook because water that dissolves food evaporates or boil at low temperature. Thus to cook food, pressure cooker is used, the heat is supplied to the pressure cooker which produce more vapour pressure, then boiling point of water increase, hence food is cooked in less time. (ii) VACUUM DISTILLATION: The liquids, which are decomposed at their boiling point, cannot be distilled; such liquids are distilled at low temperature under reduced pressure (vacuum distillation). Example: Glycerin boils at 290OC and 760torr but it decomposes. However, when pressure is reduced to 50torr, glycerin starts boiling at 210C and can be distilled with out decomposition. SOLIDS: The physical state of matter in which it has definite volume as well as definite shape is called solid. KINETIC THEORY OF SOLIDS: (1) All solid are composed of tiny particles, which only vibrate on their mean position. (2) The particles are strongly packed with each other. (3) The inter particles forces are very high. (4) The particles have very low kinetic energy. (5) The average kinetic energy of particles is directly proportional to absolute temperature. BEHAVIOUR OF SOLIDS: 1) COMPRESSIBILITY:

Normally the solids do not compress, but under high pressure the compression takes place up to little extent. In terms of kinetic molecular theory the particles of solids are so tightly packed together that only very small unfilled space is left, so they can withstand considerable external stress. 2) DEFORMITY: Under very high pressure solid are deformed. In terms of kinetic molecular theory when very high pressure is applied then some particles are dislocated and rearranged with neighboring particles with equal force of attraction. 3) DIFFUSIBILITY: There is no remarkable diffusion in solid but in rare cases the diffusion takes place to a very low extent. In terms of kinetic molecular theory there is no translational movement of particles in solid but particles are vibrating at their mean positions. The vibrational motion of the particles is responsible for diffusion in solids. 4) MELTING: Solids on heating melt at a particular temperature. In terms of kinetic molecular theory when solids are heated vibrational energy of their particles increases; until at melting point some particles are vibrating with sufficient energy to overcome the forces holding them, hence they become melt. 5) SUBLIMATION: The process in which volatile solids, when are heated they directly convert into vapours without going into liquid state is called sublimation. In terms of kinetic molecular theory the intermolecular forces in such solids are less than ordinary solids, hence on heating high-energy molecules at solid surface overcome the attractive forces and directly convert into vapours. Example: Camphor, Naphthalene, Iodine, Solid CO2 etc CLASSIFICATION OF SOLIDS: Solids are classified as, (1) Crystalline solids

(2) amorphous solids

1) CRYSTALLINE SOLIDS: The solids in which particles (atoms, ions, molecules) are arranged in a regular pattern with definite geometrical shapes are called crystalline solids. Example: Diamond, NaCl, Metals etc. 2) AMORPHOUS SOLIDS: The solids in which particles (atoms, ions, molecules) are not arranged in a regular pattern and thus have no definite geometrical shapes are called amorphous solids. Example: Plastic, rubber, glass etc DIFFERENCE BETWEEN CRYSTALLINE SOLIDS AND AMORPHOUS SOLIDS: S. No

Properties

Crystalline solids

Amorphous solids

1

Geometry

These solids have These solids have no definite geometrical definite geometrical shapes. shapes.

2

Melting point

These solids have These solids have no sharp melting point. sharp melting point.

3

Cleavage plane

4

Anisotropy and isotropy

These solids have different physical properties in different directions and are called anisotropic.

5

Symmetry

These solids have They do not possess symmetry when they Symmetry. are rotated about an axis

and

cleavage These solids break They do not break down at fixed down at fixed cleavage planes. cleavage plane. These solids have same physical properties in all directions and are called isotopic.

TYPES OF CRYSTALS: There are four types of crystals. (1) Atomic crystal (2) Ionic crystal (3) Covalent crystal (4) Molecular crystal 1) ATOMIC CRYSTALS: They are also called as metallic crystals because they are found in metals. Their atoms are held together by metallic bonds Example: Ag, Au, Fe, etc. PROPERTIES: 1) They have lustrous surface (shining surface) 2) They have high melting point. 3) They conduct electricity and heat. 4) They are malleable (converted into sheets) 5) They are ductile (converted into wires). 2) IONIC CRYSTALS: In these crystals positively and negatively charged ions, held together by electrostatic forces of attraction. Example: NaCl, CaCl2 etc. PROPERTIES: 1) They have high melting point . 2) They conduct electricity in fused state and in solution from. 3) They are brittle (easily breakable) and hard.

3) COVALENT CRYSTALS: In these crystals atoms are held together by covalent bonds there fore they are called as covalent crystals. Example: Graphite, diamond etc. PROPERTIES: 1) They have high melting point. 2) They have high refractive index. 3) They have low density. 4) MOLECULAR CRYSTALS: They are composed of molecules. Their molecules are held together by: i) Hydrogen bounding (Attraction between ‘H’ of one molecule and an electronegative atom of other molecules.) ii) Weak Vander waals forces (Attraction between atomic nuclei of one molecule and electrons of other molecules) Example: I2, CO2, etc. PROPERTIES: 1) They have low melting point. 2) They do not conduct electricity and heat. 3) They are brittle. 4) They are composed of molecules. ISOMORPHISM: DEFINITION: When two substances that have the same crystalline structure but different properties are said to be isomorphous and this property is called isomorphism. Examples: Isomorphous Atomic Ratio Crystal structure 1) Nacl and MgO 2) Zn SO4 and N:SO4

1:1 1:1:4

Cubic Orthorhombic

POLYMORPHISM: When one substance that can occurs in more than one crystalline from with similar properties is called polymorphous and this property is called polymorphism. EXAMPLE: CaCO3 in nature occurs in two crystalline forms. (i) Calcite (Ca CO3) : It is Trigonal crystal or Rhombohedral. (ii) Aragonite (Ca CO3) : It is orthorhombic crystal. UNIT CELL: DEFINITION: The smallest unit of crystal showing all the properties of that crystal is called as unit cell. UNIT CELL DIMENSIONS:

The edges and angles of unit cell are collectively called as cell dimensions. EDGES: All edges of unit cell are represented by a, b, c, etc. ANGLES: All angles between different edges are represented by α,β,γ. etc.

CRYSTAL LATTICE OR SPACE LATTICE: When atoms, ions ,or molecules constituting a crystal are replaced by points , then this three dimensional array of points is called as crystal lattice or space lattice. CRYSTAL ARRANGEMENT OR CRYSTAL SYSTEM: The pattern of arrangement of crystals with respect to their edges , lengths and angles is called crystal system. There are seven crystal systems as: 1) Cubic: In this system all three axes are of equal length and all angles of 90, i.e. a =b = c ,  =  = γ = 90 Example: NaCl, diamond etc. 3) TETRAGONAL: In this system two axes are of same length but third is different and all angles are of 90.

a=bc,

 =  = γ = 90

Example: SnO2 , BaSO4 4) ORTHORHOMBIC: In this system all there axes are of different length but all angles are of 90 abc  =  = γ = 90 Example: Fe SO4, Zn SO4. 7H2O, KNO3

4) TRIGONAL OR RHOMBOHEDRAL: In this system all three axes are of equal length as well as angle are equal but greater than 90 and Less than 120O a = b= c  =  = γ  90o 120 Example: NaNO3, KNO3, Ice.

5) HEXAGONAL: In this system two axes are of equal length but third is different two angles are of 90 and third 120 a=bc  = =90, γ = 120 Example: Graphite, CdS (Cadmium Sulphide), ZnO

6) Monoclinic: In this system all three axes are of unequal length, one of the axe is at 90 to the other two. abc  = γ = 90O,  90O EXAMPLE: Ca SO4, Na2 CO3 .10H2O 7) TRICLINIC: In this system all three axes are of different length and angles are also different. a bc      90 Example: dichromate).

Cu SO4 .5H2O, K2 Cr2 O7 (Potassium

CHAPTER NO. 3 THE ATOMIC STRUCTURE The word atom comes from the Greek word meaning “not divisible.” Ancient Greek philosophers conceived of the idea of the atom, which they defined as the smallest possible piece of a substance. Greek philosophers developed a theory of matter that was not based on experimental evidence, but on their attempts to understand the universe in philosophical terms. According to this theory, all matter was composed of tiny, indivisible particles called atoms. If a sample of a pure element was divided into smaller and smaller parts, eventually a point would be reached at which no further cutting would be possible—this was the atom of that element. In 1808 an English scientist John Dalton put forward the atomic theory on scientific basis, “called Daltons Atomic Theory”. Today it is well known that atom is made up of many particles out of which, electrons, protons and neutrons are fundamental particles. Evidence for the presence of electrons, protons and neutrons in an atom is derived through many experiments. These are discussing one by one. FARADAY’S EXPERIMENT OR PASSAGE OF ELECTRICITY THROUGH SOLUTION OR CLUE ABOUT ELECTRONS Michael faraday in 1834 established the relationship between the quantity of electricity passed and the amount of substances deposited or liberated at the electrodes during electrolysis. Electrolysis is a process in which an electric current ionizes a solution into ions, cations the positively charged ions and anions the negatively charged ions. During electrolysis, these ions travel to the oppositely charged electrodes i.e., cation towards cathode and anions towards anode. These ions give up their charge and are liberated as neutral particles. There is some elementary unit of electric charge associated with these ions, which can be calculated. The basic unit of electric charge was later named by stony in 1891 as electron. OR OR OR.

DISCHARGE TUBE EXPERIMENT CROOKES’S TUBE EXPERIMENT PASSAGE OF ELECTRICITY THROUGH GASES AT REDUCED (LOW) PRESSURE DISCOVERY OF CATHODE RAYS OR ELECTRONS

INTRODUCTION A German instrument maker, Hein-rich Geissiler, initiated the experiment of passage of electricity through gases. He instrumented a simple apparatus known as discharge tube .In 1859 William Crookes, a British scientist, extended this work, so this discharge tube is now called Crookes’s tube and this experiment as Crookes’s tube experiment. CONSTRUCTION Two metal plates are sealed in a glass tube containing some gas. At the lower end the tube is attached with vacuum pump for pressure controlling. The plate connected to negative terminal is called cathode and the plate connected to positive terminal as anode.

EXPERIMENT Gases do not conduct current at ordinary temperature and pressure. When the pressure of the gas is reduced, it becomes good conductor of electricity. At a pressure of 1cm of Hg and a current of few thousand volts, the spark occurs. When the pressure is reduced to few mm of Hg the spark disappears and the two electrodes are seen to glow. When the pressure is reduced to 0.001 mm of Hg, the glow disappears and the wall of the glass tube begins to glow with a brilliant light. Since these rays are emitted from cathode so these are called cathode rays. CONCLUSION It is found that the properties of cathode rays always remain the same ir-respective of the nature of the cathode metal (electrode) or the gas enclosed in the tube. In 1891 G.J Stony name these cathode rays as electrons. It means that all matter emits the same kind of electrons. This indicates that all electrons possess the same properties no matter what gas is used in the tube or what material is used for the electrode. This is a strong indication that electron is a fundamental particle of an atom or electrons are constituents of all matter. PROPERTIES OF CATHODE RAYS i. These rays travel in straight line, as they produce shadow of object placed in their path. ii. These rays penetrate small thickness of matter. iii. These rays carry a negative charge. iv. These rays can be deflected by an electromagnetic field. v. The rays can exert mechanical pressure, showing they possess kinetic energy. vi. These rays neither depend upon the material of which the electrodes were made nor upon the gas which is field in the tube. vii. These rays now called electron carry a fixed unit of charge and a fixed mass. viii. They carry a negative charge of 1.602x 10-19 Coulomb = 4.803 x 10-10 e.s.u. ix. Their e/m ratio is 1.76 x 10-8 Coulomb /gram. x. Their mass is 9.115 x 10-31 Kg = 0.00055 a.m.u. POSITIVE RAYS OR CANAL RAYS (DISCOVERY OF PROTONS) In 1886, Eugene Gold Stein discovered that in the Crookes’s tube or discharge tube, if thin holes are made in the cathode (perforated cathode) then some radiations appear behind the cathode. These rays carry positive charge and are called positive rays or canal rays. J.J Thomson discovered that positive rays, unlike cathode rays, have value of e/m dependent on the gas present in Crookes’s tube. The lightest particle found was that from hydrogen. This particle, which has a mass 1836 times that of electron is called proton (Greek, Protos = first).

PROPERTIES OF POSITIVE RAYS

i- These rays carry positive charge, which is equal to 1.602 x 10-19 Coulombs or 4.803x10–10 esu. ii- They travel in straight line. iii- The value of e/m depends on the gas present in Crookes’s tube. iv- The mass of proton is 1.67 x10-27kg = 1.0073 a.m.u. v- They are composed of heavy particles as compared to electrons. CHADWICK EXPERIMENT (ARTIFICIAL RADIOACTIVITY) (DISCOVERY OF NEUTRON ) Rutherford’s model of atomic structure left one major problem unsolved. It was known that hydrogen atom contains only one proton and that the helium atom contains two protons. Therefore, the ratio of the mass of a helium atom to that of a hydrogen atom should be 2:1.However in reality the ratio is 4:1. Rutherford and others postulated that there must be another type of subatomic particle in the nucleus, the proof was provided by English physicist, James Chadwick in 1932. When a stable element is bombarded with alpha () particles or He++ ions, its nucleus becomes unstable. It stabilizes itself after disintegration and emits radioactive radiations. This is called Artificial Radioactivity. James Chadwick in 1932 when bombarded a thin sheet of beryllium “Be” with  – particles he found that very energetic radiations, similar to γ- rays are given out. Latter experiments showed that the rays actually consisted of electrically neutral particles carry no charge, but their mass was comparable with that of an atom of hydrogen. Chadwick named these particles ‘Neutrons’. The neutrons must have come out from atoms on disintegration of the bombarded element. The equation of Chadwick experiment is 9 + 2He4  6C12 + on1  neutron 4Be The mystery of the mass ratio could now be explained. In the helium nucleus there are two protons and two neutrons, but in the hydrogen nucleus there is only one proton and no neutrons; therefore, the ratio is 4:1. PROPERTIES OF NEUTRONS iThey carry no electrical charge. iiTheir mass is 1.0087 a.m.u. iiiThey are highly energetic particles. RADIOACTIVITY (CONFIRMATION OF ELECTRONS AND PROTONS) INTRODUCTION In 1895 a French scientist, professor Henry Becquerel found that a mineral named pitchblende (Uranium oxide ore) emit some invisible rays. These rays affect the photographic plate by causing the fog on these plates. One of Becquerel’s students, Marie Curie, suggested the name “RADIOACTIVITY” for this phenomenon. Later Pierre curie, Marie curie and Lord Rutherford also investigated these substances like Radium, Thorium e.t.c. These substances, which emit radiation, are called radioactive substances and this property is called radioactivity. DEFINITION The spontaneous emission of radiations by certain elements is called radioactivity and these elements are called radioactive elements. Most of the elements after lead (pb) in the periodic table are naturally radioactive.

An element after giving radiation’s break down to more stable element, this process is called “DECAY” and will continue until the formation of lead. TYPES OF RADIATIONS When the radiation’s emitted by radioactive substances are subjected to power full magnetic and electric field perpendicular to the direction of emission. Then the radiation’s spilt into three different streams of rays, which are labeled α, β & γ-rays.

PROPERTIES OF ALPHA (α) RAYS (i) NATURE They consist of α – particles. They have a mass of 4 a.m.u. and charge of +2. They are helium nuclei and may be represented as 2He4. (ii) VELOCITY α – rays are ejected from radioactive nuclei with very high velocity, about one-tenth that of light. (iii) PENETRATING POWER α – rays have very little power of penetration due to large size and heavy mass. They are penetrating in air in the range of 1 – 2 cm. (iv) IONOZATION They are very god ionizers of gases. α – rays break away electrons from gas molecules and convert them to positive ions. PROPERTIES OF BETA (β) RAYS (i) NATURE They are fast moving electrons. They are negatively charged with mass equal to that of electron. (ii) VELOCITY Their velocity is 10 times more than that of - rays. Their velocity is about equal to light. (iii) PENETRATING POWER These rays have greater penetrating power than  rays and range is 1-2 m in air at atmospheric pressure. (iv) IONOZATION Their ionizing power is less than - rays due to smaller mass. PROPERTIES OF GAMMA (γ) RAYS (i) NATURE They are a form of electromagnetic radiation. They have no mass and charge. (ii) VELOCITY Their velocity is equal to light.

(iii) PENETRATING POWER These rays are very penetrating as compared to  and -rays. They can pass through 15-20 cm of lead. (iv) IONOZATION These rays are poor ionizers of gases. CONCLUSION The evidence of radioactivity shows that the atom is not an indivisible particle. It can emit electrons and helium nuclei i.e. β rays and α rays. This is confirmation of electron and proton.

PLANK’S QUANTUM THEORY OF RADIATIONS INTRODUCTION The exchange of energy from matter to radiation and vice versa is thought to take place according to quantum theory of radiation. This theory was proposed by a German physicist, Max plank in 1900. POSTULATES OF PLANK’S QUANTUM THEORY There are three postulates of this theory. (i) Emission or absorption of energy in the form of radiation is not continues. (ii) Emission or absorption of energy takes place in packets. One packet is called quantum (or photon) i.e. the amount of energy emitted or absorbed is quantized and occurs in packets or multiple of those packets, h, 2h, 3h and so on. (iii) The energy of quantum of radiations (E) is directly proportional to frequency ().  = Number of waves per second. E  Or E = h Where E = energy  = Frequency h = Plank’s constant SPECTRA INTRODUCTION If a narrow beam of light is allowed to fall on a prism, then it is resolved into its constituent colour. This phenomenon is called dispersion and the bend is called spectrum. DEFINITION A band of rays with different wavelengths into which a radiation is decomposed is called spectrum. TYPES OF SPECTRUM There are two types of spectrum. (i) Continues spectrum or visible spectrum. (ii) Line spectrum or Atomic spectrum or discontinuous spectrum. (i) CONTINUOUS SPECTRUM When narrow beam of white light (sun light or incandescent lamp or arc light) is allowed to fall on a prism it is resolved into seven different colours. The band of colours is called continues spectrum. The seven colours are Violet, Indigo, Blue, Green, Yellow, Orange and Red (VIBGYOR). The colour of light depends on its wavelength. Violet colour has the shortest wavelength (about 4000 Ao) and Red colour has the longest wavelength (about 7000 Ao). The colours cannot be marked separately. There are no boundary lines between colours. There are no dark spaces. The entire colours are continuous therefore this spectrum is called continuous spectrum.

(ii) DISCONTINUOS OR LINE SPECTRUM If the light from the discharge tube or from a gas source passes through a prism, some discrete sharp lines on a completely dark background are obtained. Such spectrum is called line spectrum. The lines can be marked separately. There are dark spaces. Each line of the spectrum corresponds to a definite wavelength. This shows that electrons are arranged around the nucleus in definite energy levels. When an atom is excited then the electrons jump and the differences of energy appear as line. Each element produces characteristic set of lines. This helps in identification of elements so line spectrum comes to serve as ‘fingerprints’ for the identification of elements.

EXAMPLE Na produces yellow lines; K produces violet lines; Ba, Green line etc. X – RAYS In November 1895, Professor William Roentgen, a German scientist discovered that when cathode rays collide with anode a very penetrating radiation is produced. These are Electro magnetic radiations of very short wave length. Their frequency depends upon the material of anode. These rays were called Roentgen rays. These rays are now called XRays. Roentgen found that X- rays are not deflected by electric magnetic fields. These rays have the ability to penetrate paper, rubber glass metal and human flesh. X- rays had played a vital role in the determination of structure of atom at subatomic levels and give an idea about atomic number.

ATOMIC NUMBER ‘Z’ Henry Moseley in 1911 while working in Rutherford’s laboratory studied the different wavelengths of X- rays produced from anodes of different metals. He observed that the wavelengths of the X-rays emitted decreased regularly with the increasing atomic mass. He concluded that this was due to the number of positive charges in the nucleus. He called the number of positive charges as the ‘atomic number’. Thus atomic number of an element is the number of protons in its nucleus. RUTHERFORD’S MODEL OF AN ATOM (EVIDENCE OF NUCLEUS AND ARRANGEMENT OF PARTICLES) INTRODUCTION

After the discovery of electron and proton from an atom, question arose that how these particles are arranged in an atom. In order to find their position in an atom, Lord Rutherford in 1911 put forwarded his model of atom after performing experiment. EXPERIMENT He bombarded a very thin gold foil 0.00004cm thick with α – particles. α – particles were obtained from polonium. He observed the effect of bombardment on photographic plate.

OBSERVATION He observed that majority of  – particles passed through the foil without deflection, few α particles i.e. out of 20,000 α – particles only one was deflected with a wide range of an angle more than 90. On the basis of this observation he concluded the following assumptions. ASSUMPTIONS (i) The central portion of an atom is nucleus, where the mass of an atom is concentrated. (ii) The nucleus carries a positive charge “+ve” as some α-particles are deflected with angle greater than 90. (iii) The dimension of nucleus is negligible comparison with the radius of an atom. (iv) There must be negatively charged electrons out side the nucleus and at fairly large distance arranged in some manner. (v) The most of the volume of an atom consist of empty spaces as most of α-particles pass through atom and the electrons revolve and spin in these empty spaces (extra- nucleus region). (vi) All the fundamental particles except electrons lie in the nucleus and are called nucleons. CONCLUSION Lord Rutherford on the basis of α- particles scattering experiment, proposed a model of atom, similar to solar system in which the nucleus occupies the position of sun and series of electronic spinning in orbits around a center (nucleus) in very much the same way as the planets of the solar system. WEAKNESSES OR DEFECTS OR OBJECTIONS (i) According to the classical electromagnetic theory, the revolving electron will emit energy continuously due to being charged (–ve) body. The orbit of revolving electron will become smaller and smaller until it would fall in the nucleus. But in actual practice, the electron does not fall in the nucleus. (ii) If the revolving electron radiates energy continuously then it spectrum would be continuous but in actual practice we get line spectrum. OPINION OF SCIENTISTS According to classical principles of physics the Rutherford’s atomic model could not exist. SOLUTION Neils Bohr in 1913 solved this problem and removed defects in Rutherford’s model of atom.

BOHR’S THEORY INTRODUCTION This theory was put forwarded by Danish physicist Neils Bohr in 1913. He proposed a theory for the electronic structure of atom. BASIS OF THEORY (i) This theory is put forwarded to remove the defects in Rutherford’s atomic model. (ii) This theory depends upon plank’s quantum theory of radiations. (iii) This is the theory of only that atom or ion which contains only one electron. Therefore this is the theory of hydrogen atom. POSTULATES OF BOHR’S THEORY (i) The electron revolves around the nucleus in fixed, stationary circular orbits or shells. These orbits have different energies so they are called energy levels or energy states or stationary states. (ii) The electron in a particular orbit has a particular energy and as long as it keeps revolving in that orbit it does not radiate energy. (iii) If the electron absorbs energy equal to the energy difference between the two orbits, the electron is excited i.e. it jumps to higher energy state. If it falls back to lower level it must emit energy equal to the energy difference between to two orbits. If this energy is absorbed or emitted as light, a single photon (quantum) of absorbed or emitted light must account for the required energy difference. So that ΔE = h ΔE = E2 – E1 Where ΔE = Difference between the energies of final and initial orbits. h = Plank’s constant = 6.625 x 10-34 J.S  = Frequency. (iv) The electron of an atom has angular momentum (mvr). The angular momentum of an electron is integral multiple of

h 2

1h 2 nh For nth orbit it is equal to 2 For first orbit it is equal to

So according to Bohr’s theory mvr=

nh . 2

Here ‘mvr’ becomes the angular momentum of the electrons. 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 an integral multiple of h/2.These stationary states correspond to energy levels in the atom. BOHR’S THEORY AND HYDROGEN ATOM DERIVATION OF RADIUS OF ELECTRON IN HYDROGEN ATOM Consider hydrogen atom with single electron revolving around a single positively charged nucleus.

 Ze +

r

e– (m)

Let. m = mass of electron e = charge on the electron r = radius of electron v = velocity of electron Ze = Positive charge on the nucleus Two equal forces centrifugal force mv2/r and centripetal force, which is due to the attraction between the electron and nucleus Ze. e/r .

mv 2 Ze 2  2 r r

––––––––––––– (i)

From Bohr’s postulate, we know that

nh 2 nh V  2 mr mvr 

OR

––––––––––––– (ii) ––––––––––––– (iii)

Now substitute the value of ‘V’ in equation (i)

mv 2  Ze 2    2  r  r  2

m  nh  Ze 2    2 r  2 mr  r

m  n 2 h 2  Ze 2   r  4 2 m 2 r 2  r 2 n 2 h 2 m Ze 2  2 2 2 m 2 r r 2 2 n h Ze 2  2 4 2 mr 3 r 2 2 n h r3  4 2 mZe 2 r 2 n2h2 r 4 2 mZe 2

––––––––––––– (iv)

r = radius of electron. n = Number of shell. h = Plank’s constant (6.625 x 10-34 J.S.) π = 3.14 m = mass of electron = 9.11 x 10–31 Kg Z = Atomic Number. e = charge on electron which is 1.602 x 10–19 C For ‘H’ atom Z = 1, n = 1

for the first orbit we get r = 0.529 x 10-8 cm = 0.529 A We can also write the equation (ii) for the radius as.

  h2   n 2 aO r  n  2 2   4 mZe  2

DETERMINATION OF ENERGY The single electron of hydrogen atom has kinetic energy as well as potential energy their sum is total energy (E). i.e. E = K.E + P.E First of all calculate the K.E. We know that K.E = ½ mv2 From Bohr’s equation we get

mv 2 Ze 2  2 r r m v2 

OR

Ze 2 r Ze 2  r r2

Multiply both sides by ‘½’ we get 2 2 1 mv 2  1  Ze  Ze 2 2 r 2r 2 Ze But K.E = ½ mv2 = 2r

Now calculate P. E. P.E = Work done by an electron (It must has –ve sign). P.E = force x distance P.E =

 Ze 2  r   Ze 2     r2  r 

E = K.E + P.E

1 Ze 2  Ze 2      2 r  r  Ze 2  2Ze 2  Ze 2 E=  2r 2r E=

––––––––––––– (v)

n2h2 in equation (v)  2 mZ 2 Ze 2  n2h2 2 2 mZe 2

Now substitute the value of r 

Ze 2 Ze 2 E=   2(r )  n2h2 2 2 2  4 mZe E =  Ze 2 

  

n2h2 2 2 mZe2

2 2 mZe 2 n2h2

E=

 Ze 2 

E=

 2 2 mZ 2 e 4 n2h2

–––––––––––––––– (vi)

EXPRESSION FOR FREQUENCY () When an atom (or gas) is heated, its electrons jump to higher orbit ‘n 2’ (excited state) from lower orbit ‘n1’(ground state) ,atom is said to be excite.

The excited state is unstable. Electrons have to come to ground state by radiating energy. Then ΔE = E2 – E1 = h

E1 

E2 

 2 2 mZ 2 e 4 2

n1 h 2  2 2 mZ 2 e 4 2

n2 h 2

or h or ΔE = E2 – E1

h 

 2 2 mZ 2 e 4   2 2 mZ 2 e 4     n22h2 n 21 h 2  

h 

 2 2 mZ 2 e 4 2 2 mZ 2 e 4  n22h2 n 21 h 2

or

h 

 2 2 mZ 2 e 4 2 2 mZ 2 e 4  n 21 h 2 n22h2

or

2 2 mZ 2 e 4  1 1  h   2  2 2  h n 1 n 2 

or

2 2 mZ 2 e 4  1 1    2  ––––––––––––– (vii) 3 2  h n 1 n 2 

This is the expression for frequency of emitted wave or protons when an electron jumps from higher energy level (n2) to lower energy level (n1). CALCULATION OF WAVE NUMBER ( ) Wave number is defined as number of waves per unit distance (in cm) and frequency is defined as number of waves per second. Velocity of light is “c”, then =c

2 2 mZ 2 e 4 1 1  2 3 2 h n 1 n 2 2 2 4 2 mZ e 1 1 C   2 3 2 h n 1 n 2 2 2 4 2 mZ e 1 1    2 3 2 hC n 1 n 2

We know that   or or But

2 2 mZ 2 e 4 all are constants and are equal to RH h 3C

Where RH is called Rydberg constant Its value is 109678 per cm.

  RHZ 2

1 1  2 2 n1 n 2

––––––––––––– (viii)

Here  = wave number RH = Rydberg’s constant Z = Atomic Number n1 = Lower orbit n2 = Higher orbit Calculate the wave number  for the radiation when an electron jumps from fourth orbit to the second orbit.

Q: Ans:

Data:

 =? RH = 109678cm-1 Z = 1 n1 = 2 n2 = 4 Solution

 1

1  2 n2   n1 1   1   10967  (1) 2  2  2  4  2 1 1    10967  1    4 16   4 1 3    10967     16   16 3 109678 16

  RH Z 2 

2



 = 20567.625cm–1

––––––––– Ans

HYDROGEN ATOM SPECTRUM The simplest element is hydrogen. It contains only one electron and a singly charged positive nucleus. Its spectrum gives a large number of series. Balmer in 1885 studied the spectrum of hydrogen by taking it in a discharge tube under low pressure. The hydrogen atom spectrum consisted of a series of lines called Balmer series. The lines of the Balmer series are seen in the visible part of spectrum. Balmer determined the wave number of each one of the lines in the series and found that the series could be represented by.

 1 1   2 2 n1  Z

  RH 

Where n1 = 3, 4 ------------RH = Rydberg constant = 109677cm-1 Later Lyman identified another series in the hydrogen spectrum. These were in the ultra violet region of the spectrum. Wave number (v) of each of these lines of this series was also given by similar formula.

1 1   2  2 n1  1

  R H 

When n1 = 2, 3 ------------Paschen also discovered a series in the infrared region. The wave number of each of the lines of this series was given by

 1 1   2 2 n1  3

  RH 

Where n1 = 4, 5 ---------Brackett and Pfund also discovered two series in far infrared region. The wave number was also given by same equation. Here ∞ would mean that the electron is completely removed from atom

Energy level diagram for the line spectrum of hydrogen BOHR’S THEORY AND HYDROGEN SPECTRUM According to Bohr’s theory when hydrogen atom absorbs energy its electron jumps from ground state (n1= 1) to excited state (n2 = 2, 3, 4, 5, …). When an electron jumps from higher energy level to lower energy level, different series (Lyman, Balmer, Paschen, Brackett, and Pfund) are obtained with different frequencies of radiations. The wavelength of Lyman series is less than 4000AO. The wavelength of Balmer series is between 4000AO to 7000AO.

While the wavelength of Paschen, Brackett, and Pfund series is more than 7000AO.

HEISENBERG’S UNCERTAINTY PRINCIPLE According to Bohr’s theory an electron behaves as a particle and revolves around the nucleus. In 1924, de-Broglie put forward a wave equation. According to de-Broglie concept an electron behaves as a wave having wavelength and frequency. The electron of an atom has a dual nature. It has position as well as momentum (mxv). In 1925 a German physicist Werner Heisenberg pointed out the defect in Bohr’s atomic theory and put forward an uncertainty principle, known as Heisenberg’s uncertainty principle. It states that it is impossible to describe the position and the momentum of an electron in an atom simultaneously (at the same time). In other words, if the position is certain (known), then the momentum is uncertain (not known) and if momentum is known then the position is not known. MATHEMATICALLY ∆x . ∆Px ≈ h Where ∆ x is uncertainty in position ∆ Px is uncertainty in momentum h is plank’s constant If ∆x → 0 means position is known Then ∆ Px ≈ h/∆x = h/0 = ∞ not known From uncertainty principle we get the idea about the probability distribution of electron. Thus the Bohr’s idea of electrons in circular orbits was discarded by Heisenberg’s principle. QUANTUM NUMBERS INTRODUCTION To resolve the defects in Bohr’s atomic theory Schrödinger in 1926 put forward a wave equation, which solves the problem. He gave three possible solutions known as quantum numbers. There are four quantum numbers; three of them are obtained by solving Schrödinger wave equation, which are: (1) Principal quantum number(n) (2) Azimuthal quantum number (l) (3) Magnetic quantum number (m) The fourth quantum number was introduced by Dirac, which is (4) Spin quantum number (s) DEFINITION These are the numbers which are used to describe the behavior of an electron in atom. These are constant which describe the energy, size, shapes, orientation in space and direction of movement of an electron in an orbital.

(1)

PRINCIPAL QUANTUM NUMBER (n) It describes the size and the energy of the orbital; in other words it describes the shell. The values of principal quantum numbers (n) are, 1, 2, 3, 4, -----------. It is represented by ‘n’ The shells are called K, L, M, N, etc depending upon the values of ‘n’ If n = 1 1st orbit or K – shell If n = 2 2nd orbit or L – shell If n = 3 3rd orbit or M – shell If n = 4 4th orbit or N – shell Maximum electrons in any shell are filled according to formula (2n2). K – shell contains maximum 2x 12 = 2x1 = 2 electrons L – shell contains maximum 2x22 = 2 x 4 = 8 electrons M – shell contains maximum 2x32 = 2 x 9 = 18 electrons N – shell contains maximum 2x 42 = 2 x 16 = 32 electrons (2)

AZIMUTHAL QUANTUM NUMBER (l) It is also called secondary or subsidiary quantum number. It describes the size, energy and the shape of the orbital, in other words it describes sub-

shells. The value of Azimuthal quantum number (l) depends upon the value of principal quantum number (n). i.e. l = (n-1) , (n-2) , (n-3)----------or l = 0,1,2,3,----------The sub-shells are named as s,p,d,f,- depending upon the value of (l). S = Sharp. P = Principal d = Diffuse f = Fundamental If l = 0 the sub-shell is ‘s’ l = 1 the sub-shell is ‘p’ l = 2 the sub-shell is ‘d’ l = 3 the sub-shell is ‘f’ If n = 1, K-shell, then L = 0, so ‘s’ sub-shell is present it constrains ‘2’electrons. n=2, L –shell, then L= 0, 1, so s and p sub-shell are present it contains 2 and 6 electrons respectively. n = 3, M-shell, then L= 0, 1, 2, so s, p, and d sub-shells are present, it contains 2, 6 and 10 electrons respectively. n = 4 N-shell then L= 0, 1, 2, 3, so s, p, d, and f sub-shells are present, it contains 2, 6, 10 and 14 electrons respectively. Maximum number of electron in sub –shells are. S=2 P=6 d = 10 f = 14 (3) MAGNETIC QUANTUM NUMBER (m) It describes different orientations or axis of an orbital in space in applied magnetic field. In other words it describes orbital. It is represented by (m). The value of magnetic quantum number (m) depends up the values of Azimuthal quantum number (l). If l = 0, s-sub-shell, then m = 0

l = 1, p-sub-shell, then m = -1, 0, +1 l = 2, d-sub-shell, then m = -2, -1, 0, +1, +2, l = 3, f-sub-shell, then m = -3, -2, -1, 0, +1, +2, +3 In each magnetic quantum number (m) there are two electrons. So s-sub-shell (2e–) has only one orientation or axes. p-sub-shell (6e–) has three orientations or axes. d-sub-shell (10e–) has five orientations or axes. f-sub-shell (14e–) has seven orientations or axes. (4)

SPIN QUANTUM NUMBER (s) It was introduced by Dirac. This quantum number shows the spin of electrons. It is represented by (s). The values of spin quantum numbers are + ½ and – ½ . According to Dirac half of the electrons would have clockwise spins (↑) and the other half of the electrons would have anticlockwise spins (↓).

Clock Wise

Anticlock Wise

ENERGY LEVELS AND ENERGY SUB-LEVELS According to Bohr’s atomic theory the electron revolves around the nucleus in all possible planes in circular path or circular orbit. The circular orbits are around the nucleus at definite distances and have definite energies. These are called “Energy levels” or shells. They are represented by the principal quantum number (n). These orbits are designated as n=1,2,,3,4,-------and named as K,L,M,N,----------. Each shell contains a maximum number of 2n2 electrons where ‘n’ is number of shell. S. No. Designation Maximum number of electrons 1 K 2 x 12 = 2 x 1 = 2 2 L 2 x 22 = 2 x 4 = 8 3 M 2 x 32 = 2 x 9 = 18 4 N 2 x 42 = 2 x 16 = 32 The spectral study shows that some electrons in given energy levels have different energies. On the basis of study of spectral lines in the spectrum, the energy levels are divided into sub-energy levels or energy sub-levels. They are denoted by letters S,P,d, and f for the first four series based on the term sharp (s), Principal (p) diffuse (d) and fundamental (f) . The number of sub-energy levels in energy levels or shells is equal to its value of (n). K energy level (n – 1) contains only one sub-energy level i.e. S. L energy level (n = 2) contains 2 sub-energy levels i.e. S,P. M energy level (n = 3) contains 3 sub-energy levels i.e. S,P,d. N energy level (n = 4) contains 4 sub-energy levels i.e. S,P,d,f. S contains maximum number of 2 electrons. P contains maximum number of 6 electrons. d contains maximum number of 10 electrons. f contains maximum number of 14 electrons.

SHAPES OF ORBITAL These are certain regions in the space around the nucleus where there is a maximum probability of finding the electron. This region is called orbital. S, p, d, and f are orbitals. An orbital can accommodate a maximum pair of electrons provided their spin is opposite. SHAPES OF S – ORBITAL All ‘S’ orbitals are spherical in shape with the nucleus at the center. In ‘s’ orbital the probability of finding the electron uniformly distributed around the nucleus. It has only one possible orientation in space in the magnetic field. It has no nodal plane. y-axis z-axis

x-axis

SHAPES OF P – Orbital The p- orbitals are dumb-bell shaped. They are oriented in space along x-axis, y-axis, and z-axis and are called Px, Py and Pz orbitals. All the three p-orbitals are perpendicular to each other. These are degenerated orbitals, that are of equal energy. Each p-orbital has two lobes. Each lobe is like a pear. The point where the two lobes meet each other is refereed as the nodal plane along which the probability of finding the electron is zero.

SHAPES OF ‘d’ AND ‘ f ’ ORBITALS In d –sub shell there are five orbitals, their shapes are sausage- like. In f- sub-shell there are seven orbitals, their shapes are complicated. ELECTRONIC CONFIGURATION The distribution of electrons in the available orbital is governed by certain rules or principal such as: (i) Auf bau Principal (ii) (n + L) Rule (iii) Pauli’s Exclusion principal (iv) Hund’s Rule (i) AUF BAU PRINCIPAL Aufbau is a German word which means “building up”. This principal describes the distribution of electrons in available orbitals. This principal states that; “For any given atom the electrons are filled to the orbitals of lowest energy in sequence, two electrons to each orbital”. According to this principal the electrons are filled in order of increasing orbital energy starting with 1s orbital or the electrons are filled to the orbitals of lowest energy in sequence, two electrons to each orbital. The electrons are filled according to the atomic number. We can build up the electronic configurations of the atoms by placing the electrons in the lowest available orbitals until the total number of electrons added is equal to the atomic number ‘z’. (ii) (n + l) RULE This rule was given by wiswesser. Here “n” is the principal quantum number and shows the number of shells. ‘l’ is Azimuthal quantum number, it has following values: For ‘s’ the value of ‘l’ is 0 (zero) for ‘p’ the value ‘1’ is 1(one) for ‘d’ the value of ‘l’ is 2(two) and for ‘f’ the value of ‘l’ is 3(three). This rule states “Electrons tend to occupy the orbital of minimum energy.” The energy of an orbital can be determined from (n + l) value. In building up the electronic configuration of the element the orbital with the lowest value of (n + l) fills first, when two orbital have the same value of (n + l) the orbital with the lower value of ‘n’ fills first. (n + L) VALUES 1S 1+0 (1) 4d 4+2 (6) 6d 6+2 (8)

2S 2+0 (2) 4f 4+3 (7) 6f 6+3 (9)

2P 2+1 (3) 5S 5+0 (5) 7S 7+0 (7)

3S 3+0 (3) 5P 5+1 (6) 7P 7+1 (8)

3P 3+1 (4) 5d 5+2 (7) 7d 7+2 (9)

3d 3+2 (5) 5f 5+3 (8) 7f 7+3 (10)

4S 4+0 (4) 6S 6+0 (6)

THE ORDER OF FILLING IS 1S,2S, 2P, 3S, 3P, 4S, 3d, 4p, 5S, 4d, 5P, 6S, 4f, 5d, 6P, 7S, 5f, 6d, 7P,6f,7d, 7f,

4P 4+1 (5) 6P 6+1 (7)

PAULI’S EXCLUSION PRINCIPAL This principal was enunciated by Wolfgang Pauli in 1925. It states that “Two electrons in an atom can never have the value of four quantum numbers identical”. OR “In an atom no two electrons can have the same set of four quantum numbers”. According to this principal two electrons in the same orbital may have maximum three same quantum numbers but their spin must be opposite. Consider two electrons present in the first orbit of an atom. (iii)

For 1st electron n = 1, l = 0, m = 0, S = + 1/2 (↑) For 2nd electron n = 1, l = 0, m = 0, S = – 1/2 (↓) From Pauli’s exclusion principal we get the idea that an orbital always contains maximum two electrons with opposite spins. Two electrons with opposite spins would be called a pair of electrons (↑↓). EXAMPLE: H1 He2 Li3 Be4 B5

= = = = =

1s↑ 1s↑↓ 1s↑↓ 1s↑↓ 1s↑↓

2s↑ 2s↑↓ 2s↑↓

2px↑

2py

2pz.

SIGNIFICANCE (i) The maximum number of orbitals in a particular energy levels is equal to n2. For example K, L, M and, N contains 1, 4, 9 and 16 orbitals. (ii) An orbital cannot contain more than two electrons. HUND’S RULE This is the rule of maximum multiplicity. This rule implies on degenerated orbitals (orbitals having same energy). This rule stated that the electrons remains unpaired as for as possible. It states that if there are available orbitals of similar energies i.e. degenerated orbitals then electrons are normally filed in separate orbitals with similar spin rather then in the same orbital with opposite spins. Thus if two orbitals of equal energy are available for two electrons, the two electrons would not live in one orbital, but each orbital will contain one electron. This can be represented (iv)

as (↑) (↑) where the circles represented an orbital. Hence the Hund’s Rule indicates that the (↑) (↑) arrangement is more stable than the arrangement (↑↓). EXAMPLE 2p has three degenerated orbitals i.e, 2px, 2py and 2pz, these orbitals are filled according to Hund’s rule as follows. 2px↑, 2py↑, 2pz↑ The electronic configuration given below would be against Hund’s rule. 2px↑↓, 2py↑↓, 2pz↑↓ Electrons with similar spins are called unpaired electrons ↑ ↑. The number of unpaired electrons is the valency of the atom. ↑↓ 1S ↑↓ N7 = 1S ↑↓ O8 = 1S ↑↓ F9 = 1S ↑↓ Ne10 = 1S

EXAMPLE: C6 =

↑↓ 2S, ↑↓ 2S, ↑↓ 2S, ↑↓ 2S ↑↓ 2S

↑ 2Px ↑ 2Px, ↑↓ 2Px, ↑↓ 2Px ↑↓ 2Px

↑ 2Py, ↑ 2Py, ↑ 2Py, ↑↓ 2Py ↑↓ 2Py

2Pz ↑ 2Pz ↑ 2Pz ↑ 2Pz ↑↓ 2Pz

Valency 2 3 2 1 zero

ATOMIC RADIUS INTRODUCTION Atoms generally combine to form molecules. These molecules may be composed of same atoms (Homo-nuclear) or dissimilar atoms (Hetro – nuclear). The inter nuclear distance between two bonded atoms is called bond distance or bond length. Half of it is called atomic radius. DEFINITION The radius of an atom is taken as half of bond length between two bonded atoms (diatomic molecules). EXPLANATION According to wave mechanics, an electron cloud be any where around the nucleus, hence it would be improper to talk of a fixed radius of an atom. The presence of other atoms also affects the outer charge distribution. Still it is useful to talk about the radius of an atom. The radius of an atom is taken as half of the bond length between two homo nuclear diatomic molecules like, H – H, Cl – Cl, O = O, etc.

2 EXAMPLE r The bond length of C – C atoms in diamond is 1.54 AO giving the radius of carbon atom as

1.54 rA  rA = = 0.77AO. 2 2

In case of hetro – nuclear diatomic molecules A and B, the bond length is rA + rB and the atomic radius is

rA  rB . If any one of the radii is known, the other can be found. 2

USE OF ATOMIC RADIUS The knowledge of atomic radius is useful in predicting the chemical behavior e.g. ‘P’ combines with ‘Cl’ to from PCl5 but does not combine with ‘I’ to give PI5 because ‘I’ atom is much bigger than ‘Cl’ and 5 of the ‘I’ atoms cannot be accommodated around a single ‘P’ atom. IONIC RADIUS Ionic radius represents the size of ion. It is defined as, the distance of the outer most shell electrons from the nucleus of an ion. Ionic radii are known from X – rays analysis. Ions are formed either by the removed of electron or addition of electron to a neutral atom. When an electron is removed from a neutral atom, positive ion (cation) is formed. M → M++ e– When an electron is removed from a neutral atom, negative ion (anion) is formed. M + e – → M– Cations have smaller radii than neutral atoms. EXAMPLE Radius of Na atom = 1.57Ao

Radius of Na+ ion = 0.95Ao This is because after the removal of an electron the effective charges on the nucleus increases and pull the remaining electrons more firmly. Anions have larger radii than neutral atom. EXAMPLE Radius of Cl atom = 0.99AO Radius of Cl ion = 1.81AO This is because an excess of negative charge results in greater electron repulsion. In case of ion having same electronic configuration (Iso-electronic) the ionic radii decrees with increasing nuclear charge. Element Na Mg Al At: No: 11 12 13 Ion Na+ Mg++ Al+++ Ionic Radius 0.95Ao 0.65Ao 0.53Ao Ionic radius increases along the group i.e. from top to bottom Ionic radius decreases along the period i.e. from left to right. IONIZATION POTENTIAL (I.P) OR IONIZATION ENERGY INTRODUCTION When an atom loses electron, it becomes positively charged ion. Energy is required to ionize an atom. This amount of energy is called ionization potential or ionization energy. DEFINITION It is defined as the minimum amount of energy required to remove the most loosely bound electron from a neutral gases atom, ion or molecules to produce positively charged ion. UNIT I.P is expressed in kilo joules per mole (KJ/mol). EXAMPLE The amount of energy required for the removal of one electron from sodium atom is 495 KJ/mol. This is the first ionization potential of sodium. Na → Na++ e∆H = +495 KJ/mol. EXPLANATION The amount of energy required for the removal of first electron is called first ionization potential similarly the energy required to remove the second and third electron from an atom is called second and third ionization potential. Al → Al++ + 2e– 1st I.P + +++ – Al → Al + 2e 2nd I.P ++ +++ Al → Al + 3e– 3rd I.P The second I.P is always greater than the first I.P because after the removal of first electron the positive charge on the nucleus becomes unbalanced and binds the remaining electrons more firmly. So it is difficult to remove second electron. FACTORS I.P depends upon the following factors.

(1) ATOMIC SIZE Smaller the atomic size greater will be the I.P. (2) NUCLEAR CHARGE OR ATOMIC NUMBER The I.P. values of elements increases with the increasing charge on their nuclei or atomic numbers and vice versa. (3) SHIELDING EFFECT The I.P. values of elements increases with the decrease in shielding effect and vice versa. TREND IN PERIODIC TABLE The value of I.P decreases from top to bottom in the group. The value of I. P increases from left to right in the period. NATURE OF BONDING Electrons of groups IA and IIA of the periodic table have relativity low I.P, so they have tendency to remove electrons easily and form positive ions to produce ionic bonds. All the metal when combine non-metals form ionic bond. It is an example of endothermic reaction. ELECTRON AFFINITY INTRODUCTION Metals have property to lose electron and acquire positive charge to form positive ion. Nonmetals try to gain that electron to complete their valence shell acquire stable electronic configuration. For doing so they release energy, this energy is called electron affinity. DEFINITION The amount of energy released when an electron is added to a neutral gases atom to form a negative ion. UNIT The unit of electron affinity is kilo joules per mole (KJ/mol). EXAMPLE When an electron is added to Chlorine atom to produce Chloride ion (Cl–), 348KJ/mole energy is released. Cl(g) + e–  Cl– ∆H = – 348 KJ/mole EXPLANATION This is the property of certain elements to acquire one or more electrons in their outer most orbits to get the stable electronic configuration of nearest noble gas. FACTORS Electron affinity depends upon the following factors. (i)

ATOMIC SIZE Smallest the atomic size greater will be the electron affinity.

(ii) NUCLEAR CHARGE OR ATOMIC NUMBER The E.A. values of elements increases with the increasing charge on their nuclei or atomic numbers and vice versa.

(iii) SHIELDING EFFECT The E.A. values of elements increases with the decrease in shielding effect and vice versa. TREND IN PERIODIC TABLE Electron affinity decreases from top to bottom in a group. Electron affinity increases left to right in a period

NATURE OF BONDING E.A of elements of group V1A and VIIA of the periodic table is relatively high, so they have tendency to again electron, to produce negatively charged ion and produce ionic bond. The halogens have largest E.A due to small atomic radii and greater attraction for electrons. E.A is an example of exothermic reaction. ELECTRONEGATIVITY: It is the force with which an atom attracts shared pair of electrons towards itself in a covalent bond. It is represented by E.N. The E.N. values of elements depend upon the following factors. (i)

THE ATOMIC SIZE. The E.N. values of elements decrease with the increasing atomic size and vice versa.

(ii)

THE ATOMIC NUMBER OR THE CHARGE OF THE NUCLEUS: The E.N. values of elements will increase with the increasing atomic numbers OR the charge on their nuclei and vice versa.

(iii)

THE SHIELDING EFFECT: The E.N. values of elements increase with the decrease in the shielding effect and vice versa.

TREND IN THE PERIODIC TABLE The E.N. values of elements increase from left to right and decrease from top to bottom in the periodic table. It is therefore maximum for fluorine (4.0) at the top right corner and minimum for francium (0.7) at the bottom lower corner. ELECTRONEGATIVITIES AND THE NATURE OF CHEMICAL BONDS The nature of a chemical bond can be decided on the basis of E.N. difference between the two bonded atoms. When E.N. difference is zero, it will be a pure covalent bond. If it is less than 1.7, the bond will be an ionic covalent. In case the E.N. difference exceeds 1.7, then it would be an ionic bond. For example H – H and Cl – Cl is pure covalent or non – polar covalent bonds. The examples of polar covalent bonds are H – O – H, H – S – H etc. The chemical bonds formed between the elements of I, II groups and those of VII group of the periodic table are good examples of ionic bonds. e.g. Na+ Cl–, Br–Mg2+Br–, K+I– etc.