Molecular Orbital Theory

Introduction :
Molecular orbital theory is a polycentric region in space, defined by its size and shape, associated with two or more atoms in a molecule and each has a capacity of two electrons with opposite spins. Thus, in a molecular orbital, electrons are revolving in the field of more than one nucleus. The molecular orbital to explain formation of chemical bond, relative bond strengths, paramagnetic or diamagnetic nature.

Feature of Molecular Orbital Theory:

• The main features of the Molecular Orbital Theory are:
• The atomic orbital of the combine atoms partly cover to form new orbital, called molecular orbital.
• As a result of this, the atomic orbitals lose their being identity.
• Thus in a Molecular Orbital Theory, electrons revolves in the field of more than one nucleus.
• The number of Molecular Orbital is produced is equal to the number of overlap atomic orbitals.
• Maximum capacity of a Molecular Orbital is two electrons with opposite spins.
• Only those atomic orbitals can come together to form Molecular Orbital Theory which has analogous energies as well as proper orientations.
• Molecular orbital theory obtained addition of wave functions of atoms involved,`Psi`(MO)=`Psi`_A + `Psi` _B   is called bonding molecular orbital.
• Molecular orbital theory obtained by subtraction of wave functions of atoms involved  `Psi`  ^*(MO)=`Psi`_A - `Psi`_B is called antibonding molecular orbital.
• Probability of bonding molecular orbital formation greater than that of antibonding molecular orbital formation.
• Molecular theory gives the electron probability distribution around a group of nuclei just gives the electron probability distribution around nucleus.
• The shape of the molecular orbital theory produced depends on the type of the combining atomic orbitals.
• Inner molecular orbital theories which do not take part in bond formation are called non-bonding molecular orbital theory.

 Conditions for the formation of molecular orbitals:

• Any two atomic on combination do not form molecular orbitals.

• In fact, there are certain limitations to the combination of atomic orbitals.

• The energies of combining atomic orbitals should of similar magnitude.

• Thus, a homonuclear diatomic molecule will not be formed. if 1s orbital of one atom overlaps with 2s-orbital of another atom.

• Combination of atomic orbitals takes place only, if overlapping takes place to a considerable extent, since greater the overlapping of atomic orbitals, the greater is the build-up of the charge between the nuclei.

• The combining atomic orbitals should have power over the same symmetry about the molecular axis.

Chemical equilibrium animations

Introduction :

The experimental observations of chemical equilibrium tell us that most of the chemical reactions when carried out in closed vessels do not go to completion. Under these a conditions, a reaction starts by itself or by initiation, continues for some time at diminishing rates and ultimately appears to stop. The reactants may still be present but they do not appear to change into products any more. What happens in such case is that the products of the reaction start reacting at the same rate as the reactants. In other words, the rate of the back reaction becomes equal to the rate of the forward reaction.

Characteristic features of chemical equilibrium

Thus, in a given time as much of the products are formed as react back to give the reactants. The composition of the reaction mixture at a given temperature is the same irrespective of the initial state of the system, i.e., irrespective of the fact whether we start with the reactants or the products. The reaction in such conditions is said to be in a state of equilibrium.

The attainment of equilibrium can be recognized by noting constancy of observable properties such as pressure, concentration, density or color whichever may be suitable in a given case.

The relationship between the quantities of the reacting substances and the products formed can be worked out readily with the help of the law of mass action.

The Laws of Mass Action of Chemical equilibrium

The laws of mass action states that the driving force of a chemical reaction is proportional to the active masses of the reacting substances. Assuming that the driving force determines the reaction rate, the law may be stated as follows: The rate at which a substance reacts is proportional to its active mass and the rate of the chemical reaction is directly proportional to the product of the active masses of the reacting substance.

Consider a general reversible chemical reaction

aA + bB ↔ mM + nN

According to the law of mass action, assuming that active masses are equivalent to molar concentrations,

The rate of the forward reaction, r_f α [A]^a [B]^b = K_f[A]^a [B]^b

The rate of the reverse reaction, r_r α [M]^m[N]ⁿ = K_r[M]^m [N]ⁿ

Where Kf and Kr are proportionally constants and square brackets represent the molar concentrations of the entities enclosed. At equilibrium, the rate of the frontward reaction is equal to the rate of the reverse reaction, that is, Kf[A]a [B]b = Kr[M]m [N]n

K_f /K_r = K_eq = [M]^m [N]ⁿ / [A]^a [B]^b

Historical development of the periodic table

We now know more than 100 elements, the elements were classified as metals, metalloids and non metals. Metals are good conductors of heat and electricity, they are shining and they are malleable and ductile. It would be difficult to study individually the chemistry of all the elements and their numerous compounds. The periodic table provides a systematic and extremely useful framework for organizing a lot of information available on the chemical behavior of the elements into a few simple and logical patterns. This gave rise to the necessity of classifying the elements into various groups or families having similar properties.

Introduction to the historical development of the periodic table 

There were many chemists who has contributed their theories for the historical development of periodic table.  Some of them are:
Dobereiner’s Triads
Lother-Meyer’s Arrangement
Newlands Law of Octaves

Dobereiner’s Triads contribution for the historical development of periodic table

In 1829, John Dobereiner (German Chemist) classified elements having similar properties into groups of three. These groups were called triads. According to this law when elements are arranged in the order of increasing atomic mass in a triad, the atomic mass of the middle element was found to be approximately equal to the arithmetic mean of the other two elements. For example lithium, sodium and potassium constituted one triad. However, only a limited number of elements could be grouped into traids.

Newlands Law of Octaves contribution for the historical development of periodic table
In 1865, John Newlands (English Chemist) observed that if the elements were arranged in order of their increasing atomic weights, the eighth element starting from a given one, possessed properties similar to the first, like the eighth note in an octave of music. He called it the law of octaves. It worked well for the lighter elements but failed when applied to heavier elements.

Lother-Meyer’s Arrangement contribution for the historical development of periodic table

In 1869, J. Lother-Meyer in Germany gave a more detailed and accurate relationship among the elements. Lother-Meyer plotted atomic volumes versus atomic weights of elements and obtained a curve. He pointed out that elements occupying similar positions in the curve possessed similar properties.

Modern periodic law

Introduction:
Of the 109 elements known today, 92 are natural and the remaining are man made. As it was very difficult to study the chemistry of each and every element and its related compounds, in the 19th century  Chemists like Dobereiner, Newlands, Dinitri Mendeleef and Moseley thought of a proper classification of elements and did monumental work in analysing properties of these elements and classifying them .

Modern Periodic Law
" The physical and chemical properties of elements are periodic functions of their atomic numbers " .
It is a fact that atomic number is more related to the nucleus and it gives the number  of protons in the nucleus whereas  a few physical and many chemical properties of elements are related to their electronic configuration but not to the number  of electrons merely. Hence, periodic law states as

" The physical and chemical properties of elements are periodic functions of their electronic configurations "
If elements are arranged in the increasing order of their atomic numbers, the physical and chemical properties are repeated according to their electronic configurations at regular intervals.
For example: hydrogen (H0, lithium (Li), sodium (Na), potassium (K), rubidium  (Rb) are their electronic configurations as shown in table below. The atomic numbers (Z) of these elements are  1,3,11,19,37 respectively.

Alkali Metals and their electronic configurations

H ( Z = 1 )           1s1 Li ( Z = 3 )           1s2 , 2s1 Na ( Z = 11 )        1s2 , 2s2 , 2p6 , 3s1 K ( Z = 19 )          1s2 , 2s2 , 2p6 , 3s2 , 3p6 , 4s1 Rb ( Z = 37 )         1s2 , 2s2 , 2p6 , 3s2 , 3p6 , 3d10 , 4s2 , 4p6 , 5s1

Since these elements have similar electronic configurations in their  outer  shells, ns¹ ( 'n'   is the principle number ) , they show similar physical  and chemical properties. They lose electron to get stability  and show a common  oxidation state of +1.  They are all monovalent. Their oxides, hydroxides, halides, etc.., show similar chemical properties. Thus, the properties of elements are  periodic  functions of their electronic configurations.

Present form of peridic table

Present form of periodic table is also known as Long form of periodic table.
Neils Bohr constructed the long form of the periodic table based on the electronic configurations of the elements. In the table, the vertical columns are  termed as "groups" and the horizontal rows as "periods". There are 18 groups and 7 periods in the periodic table.  All the elements are arranged in the increasing order of their atomic numbers and the atomic number increases by one unit from one element to the immediate next element as we move, from left to right in the periodic table .

Differentiating electron :
The electron by which the electron configuration of the given element differs from that of its preceding element is called differentiating electron is the last entering electron of its atom .
Periods in the long form of the periodic table : In each period, the differentiating electron enters the s-orbital in the element p-orbital in the last element . When s and p orbitals are completely filled with electrons as ns²np⁶  , the element is the noble gas with stable configuration of octet .

Periods and electronic configurations

Period	Energy Levels	Number of elements in the period
1st period 2nd period 3rd period 4th period 5th period 6th period 7th period	1s 2s                                   2p 3s                                   3p 4s                         3d      4p 5s                         4d      5p 6s            4f          5d      6p 4s            5f          6d       -	2 8 8 18 18 32 -

                        Table : Periods and energy levels in periodic table

Period	First element	Electronic configuration	Last element	Electronic configuration
1 2 3 4 5 6 7	H Li Na K Rb Cs Fr	1s1 [He] 2s1 [Ne] 3s1 [Ar] 4s1 [Kr] 5s1 [Xe] 6s1 [Rn] 7s1	He Ne Ar Kr Xe Rn -	1s [He] 2s 2p [Ne] 3s 3p [Ar] 3d 4s 4p [Kr] 4d 5s2 5 [Xe] 4f 5d 6s 6p -

Each electron in the atom is distinguished by four quantum numbers . Among the four quantum numbers, the principle quantum number ( n 0 defines the main energy levels of the shell. In the periodic table, as the shells are filled with electrons in the order n=1, n=2 , ...... , the periods are formed serially .
In the 1st period as the 1st energy level is filled with two  electrons, there are only two elements. They are hydrogen and helium. In the second period, the differentiating electron enters the 2s orbital in lithium and the second energy level is completely filled 2s²2p⁶ with electrons in neon. Thus the second energy level is now completely filled with eight electrons  and hence the second period has eight elements . In the third period , the differentiating electron enters 3s orbital in sodium. After 3s, then 3p gets filled with differentiating electron upto argon. Then the differentiating electrons does not enter 3d orbitals but enters 4s. Hence the 3rd period also has only eight elements .
In the 4th period , the energy level 4s is 1st filled i.e. from potassium. After 4s is filled the differentiating electron enters 3d orbitals from scandium to zinc. and these ten elements are called transition elements. then the differentiating electron enters into the 4p orbitals upto krypton. Krypton attains stability due to completely filled orbitals. Thus, the 4th period has 18 elements .
In the fifth period, the energy  levels are 5s, 4d, 5p are filed in a similar order with differentiating electrons as in the 4th period. The period starts with rubidium and ends wiyth xenon. The fifth period has 18 elements which include second transition series.
In the sixth period, the energy levels 6s, 4f, 5d, 6p get filled with differentiating electrons in the same order. After 6s is filled, the differentiating  electrons enter the 4f orbitals to form the 1s inner transition series with an exception of La that gets the differentiating e^-1 into 5d. 14 elements from cerium to lutetium get their differentiating electrons into 4f orbitals. These elements are therefore called 'f' block elements. Then 5d get filled, to give the third transition series and next 6p orbitals get filled upto radon. The 6th period is the longest period with a total of 32 elements. The 7th period is incomplete and has about 20 elements. The period includes the second inner transition series from thorium  to Lawrencium.

Periodic table cesium

Introduction:

• Lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs) and francium (Fr) constitutes Group 1 of the periodic table.
• Robert Wilhelm Bunsen and Gustav Robert Kirchhoff found the metal cesium in the year 1860.
• Cesium has chemical symbol ‘Cs’.
• Periodic table cesium has atomic number 55 and mass number 132.9054
• Periodic table cesium belongs to Group 1 and Period 6
• Group 1 elements are called alkali metals because their oxides and hydroxides dissolve in water to produce strong alkali’s.
• Group1 elements are highly reactive and highly electropositive elements.
• Francium is a radioactive element.

• Electron configuration cesium:

     1S², 2S², 2P⁶, 3S², 3P⁶, 3d¹⁰, 4S², 4P⁶, 4d¹⁰, 5S²,5P⁶, 6S¹

• Electrons per energy level: 2, 8, 18, 18, 8, 1
• Shell model:

Properties of periodic table cesium:

The properties of alkali metals are similar because they belong to the same group in the periodic table and possess similar electronic configuration.  A few of these properties are discussed below.
1)      Size: Atomic radius increases as we move down the alkali metal group because an extra shell of electrons is added down the group.  Hence, lithium is the smallest atom and francium is the largest atom among alkali metals.  Francium is an unstable element.

Element	Li	Na	K	Rb	Cs
Atomic radius (pm)	134	154	196	211	235

2)      Electronic configuration: All alkali metals have a similar electronic configuration with only one electron in the outermost s-orbital.  The electronic configuration of alkali metals are given by:

• Li:  [He] 2s¹

• Na: [Ne] 3s¹

• K:  [Ar] 4s¹

• Rb: [Kr] 5s¹

• Cs: [Xe] 6s¹

• Fr: [Rn] 7s¹

General electronic configuration group 1 elements can be written as [Rare gas] ns¹.
3)      Density: Alkali metals are the light metals.  Their density is low because of larger atomic volumes.  However, the density goes on increasing down the group because an increase in mass predominates over increase in volume down the group.  Li, Na, K are lighter than water.  Density of sodium and potassium are 0.972 g/cm³ and 0.867 g/cm³ respectively.  The density of potassium is less than that of sodium because of  unusual increase in atomic size of potassium.  The density of cesium is 1.67 g/cm³.
 4)      Ionization energy: Alkali metals have low ionization energies because the last electron is present in the outermost s-orbital and the removal of electron is easy.  As we move down the group, there is decrease in the ionization energy.

Elements	Li	Na	K	Rb	Cs
Atomic radius (pm)	520	495	418	403	376

5)      Electropositive character: Due to low ionization energy, alkali metals are highly electropositive.  They have a tendency to lose electrons readily and change to M⁺ ion.
M → M⁺ + e^-
As ionization energy decreases down the group, electropositive character increases from lithium to cesium.  Metals like Cs and Rb lose electrons even they expose to light.  This property is known as photoelectric effect.
6)      Oxidation states: All alkali metals exhibit an oxidation state of +1 because they have only one electron in the outermost shell which is lost during the reactions.  +2 state is not observed because the second ionization of alkali metals is very high than the first ionization energy.
7)      Metallic properties: The metallic character of alkali metals increases from Li to Cs due to low ionization energy.  They show strong metallic character.  Hence , They show strong metallic character.  Hence they are highly electropositive and less electronegative.  As they have only one unpaired electron, metallic bond is weak.  Hence they are soft metals and can be easily deformed.
8)      Flame test: When cesium metal is heated strongly in a non-luminous flame, the salts are ionized.  Cesium ions are later excited and the electrons jumps to high energy levels.  When these electrons return back, they emit radiations which fall on the visible region.  Periodic test cesium emits pale violet color to the flame.
9)      Reducing property: Alkali metals are powerful reducing agents because they have very low reduction potentials.  This indicates that electrons can be released from them very easily.

Elements	Li	Na	K	Rb	Cs
R.P. (volts)	-3.05	-2.71	-2.93	-2.99	-2.99

Where R.P.  = Reducing potential.
Lower the R.P.  Greater the reducing potential.  Hence alkali metals react readily with water to liberate hydrogen.
2Cs + 2H₂O → 2CsOH + H₂↑
10)  Reaction of periodic table cesium with air: When alkali metals are exposed to air, they tarnish rapidly due to formation of oxides on the surface.  Hence they are kept under kerosene to protect from the action of air.
When Cesium metal are heated in air they burn vigorously to form cesium superoxide.
Cs + O₂  →  CsO₂
11)  Diagonal relationship between periodic table Cesium and radium: The diagonal element relationship is the similarity between the first elements of a group with the second element in the next higher group.

Uses of periodic table Cesium:

• Cs is used as a catalyst in the hydrogenation of few organic compounds.
• Cs metal can be used in ion propulsion systems.  Although not usable in the earth’s atmosphere.
• Periodic table cesium is used in atomic clocks.
• Cs has high electron affinity.  Therefore it is used in electron tubes.
•  Cs is used in photoelectric cells and vaccum tubes.
• Periodic table cesium is used in Infra red lamps. 

W on the periodic table

Introduction :
Let us discuss about the symbol ‘W’ on periodic table. Though Peter Woulfe examined the mineral wolframite and concluded the presence of a new substance, it was Juan Jose and Fausto d'Elhuyar from Spain who purified tungsten in 1783. In Swedish tungsten refers to “heavy stone”. Let us explore more on ‘W’ on periodic table.

Fig:- tungsten

Some Properties of 'W' on periodic table:

Tungsten, which is also called Wolfram and denoted by W on periodic table, has an atomic weight of 183.85 with an atomic number of 74 making it a transition metal on the periodic table. This gives it an electronic configuration of [Xe] 6s² 4f¹⁴ 5d⁴ .
Cutting of a pure tungsten can be done with a saw, spun, drawn, forged, and extruded though impure tungsten is very brittle. Tungsten is a lustrous metal grayish-white in color. Tungsten is known to have the highest melting point compared to all other metals and the lowest vapor pressure of the metals. Because of this property, traditional processes such as smelting cannot refine tungsten. It has very high tensile strength at temperatures exceeding 1650°C. Oxidation of tungsten takes place at increased temperatures. It has very low effect on itself when reacted with acids, as it is highly corrosion- resistant. Very few metallic acids have the strength to attack tungsten.
Physical properties

• Density(g/cc) – 19.3
• Melting Point (K): 3680
• Boiling Point (K): 5930
• Appearance: tough gray to white metal
• Atomic Radius (pm): 141
• Atomic Volume (cc/mol): 9.53
• Tensile strength 50000 – 75000 @1000 degree Celsius, psi
• Reflectivity is 62%

Uses of Tungsten:

Filaments of electrical lamps and picture tubes of television are made from tungsten. It is used in multiple high temperature applications like metal evaporation materials, target for X-rays etc. Some compounds of tungsten are also used in fluorescent lighting such as magnesium tungstenates. Some of the tungsten compounds are also used in mixture of paints. Some lubricants used at high temperatures are also made of tungsten compounds.

Conclusion for tungsten that is 'W' on periodic table:

Therefore, from the above discussion, we can conclude that tungsten is one of strategic and indispensible metals and it is represented by the symbol ‘W’ on periodic table.

Breaking atomic bonds

Solids are characterized by incompressibility, rigidity and mechanical strength. This represent the molecules, atoms or ions that make up a solids which are closely packed. They are join together by strong cohesive forces and cannot move at random. Thus, in solids we have well ordered molecular atomic or ionic arrangements. Thus, it is extremely hard to break atomic bonds between these molecules.

Some solids like sodium chloride NaCl₂, sulphur S, and sugar (carbohydrates),  besides being incompressible and rigid, have also characteristic geometrical forms. Such substances are known be a crystalline solids. The X-ray crystallography studies reveal that their ultimate particles such as molecules, atoms or ions are arranged in unusual pattern throughout the entire three-dimensional (3D) network of crystal. This definite and ordered arrangement of molecules, atoms or ions lengthens over a large distance making it extra difficult in breaking atomic bonds.

The natural history of the Inter-atomic Force resulting in the breaking atomic bonds

Basically, an atom consists of a tiny positively charged body, located at its center called as nucleus. The nucleus, though small have all the protons and neutrons. Since the mass of an atom entirely owing to the presence of protons and neutrons, it is evident that almost the entire mass of an atom resides in the nucleus.

Between the atoms or ions or molecules the inter-atomic bonds is present. This type of breaking atomic bonds is set up by equilibrium between attractive and repulsive forces with the remaining force being zero (0). When the breaking atomic bonds is at stabile. It is evident that the atoms are far apart from the attractive forces between these molecules so it will govern and when they are very close packed together the repulsive force will becomes higher; both these help in ruining away as the separation increases. This report proves that the breaking atomic bonds result from inter-atomic force, as a function of atom separation. Fig 1: Representation of bonds between two molecules

Breaking atomic bonds is also characterized by bond energies

Enthalpy formation of the bond.

Bond energy for any particular type of bond in a compound may be defined as the average amount of energy required to dissociate (to break) one mole, viz., Avogadro’s number of bonds of that type present in the compound. Bond energy is also called the enthalpy of formation of the bond.