Law of Constant Proportion / Definite Proportion / Fixed Proportion

Louis Proust in 1799 after analysis of large number of compounds arrived at the generalized statement of the law of constant proportion. It states that, “A pure chemical compound, irrespective of its source of method of preparation, always contains the same elements combined together in same definite proportions by weight.”
Thus, if the element ‘A’ and ‘B’ combine chemically to form the compound AB, then in whatever manner AB is formed, it is always composed of same two elements ‘A’ and ‘B’ combined together in the same fixed ratio or proportion by weight.

For example: Sulphur dioxide can be obtained when
         (i).     Sulphur is burnt in air,    
                                    S   +    O₂------>SO₂

         (ii).    Copper is heated with conc. sulphuric acid

                                    Cu  +   2H₂SO₄ ------------>  CuSO₄   +   2H₂O   +   SO₂

         (iii).   Dilute hydrochloric acid is added to sodium bisulphate

                                    NaHSO₃   +   HCl  ---------->   NaCl   +   H₂O   +   SO₂

In each case, sulphur and oxygen in the sulphur dioxide obtained are found to be in the same ratio of 32 : 32 or 1 : 1 by weight.

Law of Conservation of Mass

Antoino Lavoisier (Known as Father of Chemistry) in 1774 established this law, which states, “Whenever a chemical change or physical change takes place the total mass of reacting species (reactants) is exactly equal to the total mass of the products of the reaction.”

 Thus, according to this law there is no increase or decrease in total mass of matter during a chemical or a physical change. In other words, “Matter can neither be created nor destroyed.” Hence this law is also known as “Law of Indestructibility of Matter”.

Experimental Verification              

Landolt Experiment

                  Landolt verified the law by various experiments conducted by him. In one of the experiment, Landolt took two solutions (i) sodium chloride, NaCl and (ii) Silver nitrate AgNO₃. Separately in the two limbs of H – shaped glass tube known as Landolt Tube. The two limbs were sealed and the tube was weighed. The tube was tilted to mix two solutions. Sodium chloride reacts with silver nitrate and precipitate of silver chloride was formed.

                        AgNO₃  +  NaCl    AgCl¯  +  NaNO₃

The tube was again weighed, Landolt observed that total mass remained practically constant after the reaction.

Limitations
                  In all the chemical reactions, energy is evolved or absorbed which would be at the expense of change in mass. In ordinary chemical reactions, this change in mass is so small that it can not be registered on the most sensitive balance. This suggests that some matter of the reaction mixture gets converted into energy such as light, heat etc. Thus mass and energy are interconvertible. The mass is converted to energy by Einstein’s relation E = mc².

Concept of ORBITALS

According to Heisenberg's Uncertainty Principle, it is not possible to determine precisely the position and momentum of an electron in the atom simultaneously. Therefore, Bohr's concept of well defined orbits is ruled out. According to quantum mechanics the probability of finding an electron does not become zero even at large distances from the nucleus. Therefore it is not possible to draw a boundary that will enclose the region of 100% probability. However, for the sake of simplicity arbitrary boundaries are drawn which encloses the region where probability of finding the electron is maximum, this region is known as an Orbital. Thus, An orbital may be defined as the region of space around the nucleus where the probability of finding an electron is maximum.

Stability of Half-Filled and Fully Filled Orbitals

The exactly half-filled and fully filled orbitals have greater stability than other configurations.

The reason for their stability are symmetry and exchange energy.

(a).    Symmetry

         The half-filled and fully-filled orbitals are more symmetrical than any other configuration and symmetry leads to greater stability.

(b).     Exchange Energy

The electrons present in the different orbitals of the same sub-shell can exchange their positions. Each such exchange leads to the decrease in energy known as Exchange Energy. Greater the number of exchanges, greater the exchange energy and hence greater the stability. As the number of exchanges that take place in the half-filled and fully-filled orbitals is maximum, thus exchange energy is maximum and hence maximum stability.

AUFBAU’s Principle

Aufbau is a German word meaning to build up. The principle states that, "the filling of electrons in various sub - shell takes place in the increasing order of their energies". Hence lower energy sub-shell are filled up first and successively higher energy sub-shell are filled. The energy of various sub-shell are determined by ( n + l ) rule, where 'n' is principle quantum number and 'l' is Azimuthal quantum number. Lower the value of (n + l ), lower the energy of the sub-shell. In case, the value of ( n + l ) is equal for two sub-shells, the one with lower value of 'n' has lower energy. Thus, the increasing order of energies of the various sub-shells is;

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p and so on.

This can be conveniently remembered by simple diagram as follows;

HUND’s Multiplicity Rule

This rule states, "that the pairing of electrons in degenerate orbitals of a particular sub-shell does not take place until all the orbitals of the sub-shell are singly occupied and the singly occupied orbitals must have the electrons with parallel spin".

    

PAUL’S Exclusion Principle

Wolfgaug Pauli put forward the principle which restricts certain values of quantum numbers for an electron in an atom and hence the name exclusion principle. The principle states, “No two electrons in an atom can have the same set of four quantum numbers ( n, l, m, s ). For example, In ‘1s’ orbital (n = 1), according to Pauli’s Exclusion Principle there are only two possible arrangements of quantum numbers possible, i.e.
n =1, l = 0, m = 0, s = +½ ( 1st electron )
n =1, l = 0, m = 0, s = -½ ( 2nd electron )
This follows that a maximum of only two electrons can be accommodated in an orbital and they must possess opposite spins.

Shapes of Orbitals

S – Orbitals

For s-orbitals, l= 0 and hence, m can have only one¬ value I.e., m = 0. This means that the probability of finding the electron in s-orbitals is same in all directions at a particular distance. In other words, s-orbitals are spherically symmetrical.

The s-orbital of higher energy levels are also spherically symmetrical, however, they are more diffused and possesses spherical regions within them where probability of finding the electron is zero. These are called nodes. In 2s orbital there is one node. Number of nodes in an orbital is equal to ( n - l -1).

P- orbitals

For p-orbitals l = 1 and hence, m can have three possible values + 1, 0, - 1. This means that there are three possible orientations of electron cloud in a ‘p’sub-shell. These three orientations or orbitals of a ‘p’ sub-shell are designated as Px, Py and Pz respectively. Px, Py and Pz orbitals are oriented along x-axis, y-axis and z-axis respectively. Each p-orbital has two lobes which are separated by a plane of zero probability called nodal plane. Each p-orbital is, thus, dumb¬bell shaped.

Difference Between Orbit and Orbital

ORBIT	ORBITAL
It is well-defined circular path followed by electron around nucleus.	It is a region of space around the nucleus where the probability of finding an electron is maximum.
It represents two dimensional motion of electron around nucleus.	It represents three dimensional motion of electron around nucleus.
The maximum no. of electrons in an orbit is 2n2.	The maximum no. of electrons in an orbital is 2.
Orbit is circular in shape.	Orbitals have different shapes.

Distribution of Electrons in Deferent Energy Levels

Quantum Numbers

The numbers used for completely specifying each electron of atom are known as Quantum Numbers. Four such quantum numbers are found to be necessary for describing completely an electron.

1. PRINCIPAL' QUANTUM NUMBER (n)

This number gives the average distance of the electron from the nucleus and hence gives the shell number (i.e. principal energy level) to which the electron belongs. Thus it gives an idea of the position, of the electron around the nucleus. The energy of the electron depends upon this number. Higher the principal quantum number, greater is its distance from the nucleus, greater is its size and also higher is its energy. It takes the value from 1 to infinity. But only values from 1 to 7 have so far been established for atoms of the known elements. These are designated either as 1, 2, 3, 4, 5, 6, and 7 or as K, L, M, N, 0, P and Q respectively. The maximum number of electrons in ‘n’ principal quantum number is given by 2n².

2. AZIMUTHAL QUANTUM NUMBER (l )

This number represents the sub-level to which the electron belongs and also determines the shape of the orbital. Azimuthal quantum number is also known as Subsidiary or Angular quantum number. It is represented by letter ‘l’.

The value of ‘l’ depends upon the value of principal quantum number ‘n’. For a particular value of ‘n’, the ‘l’ can take the values from 0 to n-1. Each value of ‘l’ represents one particular sub-shell. For example,

For n = 1, n –1 = 0; so, l = 0

For n = 2, n –1 = 1; so, l = 0,1

For n = 3, n –1 = 2; so, l = 0,1, 2

For n = 4, n –1 = 0; so, l = 0,1, 2, 3

The various sub-shells represented by Azimuthal quantum number ‘l’ are s, p, d and f i.e. l = 0, denotes ‘s’ sub-shell, l = 1, denotes ‘p’ sub-shell, l = 2, denotes ‘d’ sub-shell and l = 3, denotes ‘f’ sub-shell. Azimuthal quantum number also gives the angular moment of electron in a particular sub -shell. The angular moment of electron in a particular sub-shell is given by l( l+1) h/2π.

3. MAGNETIC QUANTUM NUMBER(m) 

This quantum number gives the number of orbitals present in a particular sub-shell and orientation of the orbital in the space. Like ‘l, the value of ‘m’ is dependent upon the value of ‘l’ and can take only integral value from to – l to + l through zero. In general, for each value of ‘l’ there will be 2l + 1 values of m.

(a). For l = 0 (s sub-shell); m = 0. Hence there is only one orbital in the ‘s’ sub-shell.

(b). For l = 1 (p sub-shell), m = – 1, 0 and +1. Hence there are three orbitals in the ‘p’ sub-shell. The three corresponding orbitals are written as px, py and pz.

(c). For l = 2 (d sub-shell), m = –2, –1, 0, +1 and +2. Hence d sub-shell have five orbitals represented by dxy, dyz, dzx, dx2-y2 and dz2.

(d). For l = 3 ( f sub-shell), m = –3, –2, –1, 0, +1, +2 and +3. Hence there are seven orbitals present in the ‘f’ sub-shell.

SPIN QUANTUM NUMBER (s)

This quantum number arises due to the spinning of the electron about its own axis. The spin can be clockwise represented by +½ S or anti-clockwise represented by –½ S. The +½ S value indicates clockwise spin (generally represented by an arrow pointing upwards, i.e.↑) and –½ S indicates anti-clockwise spin (generally represented by an arrow pointing downwards, i.e.↓).

Thus, the four quantum numbers gives the complete address of an electron in an atom. So, they are also known as Postal Index numbers of an electron.

Limitation's of BOHR'S Model

Bohr’s theory was unable to explain the following observations;

(i). Bohr’s Model could not explain the spectra of atoms containing more than one electron.

(ii). It could not explain the Zeeman effect. In presence of magnetic field, each spectral line gets split up into fine lines, the phenomenon, is known as Zeeman effect.

(iii). It could not explain the Stark effect. In presence of electric field, each spectral line gets split up into fine lines, the phenomenon, is known as Stark effect.

(iv). The main objection to Bohr’s model was raised by Heisenberg’s uncertainty principle. According to Heisenberg’s uncertainty principle, it is impossible to determine simultaneously the exact position and the momentum of a small moving particle like an electron. But, according to Bohr’s model electron moves in well-defined orbits around the nucleus, and hence its position as well as momentum can be determined simultaneously, which is against the uncertainty principle. So, electron moves in well-defined orbits around the nucleus is impossible.

Hydrogen Spectrum

Although hydrogen atom has only one electron, yet its spectrum consists of a large number of, lines. Bohr gave following explanation for this interesting problem.

In the ground state the single electron of a hydrogen atom keeps on rotating in the first energy level. But when energy is supplied to it (i.e. to gas), it is excited and its electron jumps to a higher energy level (2, 3, 4 or 5, etc.) by absorbing a photon of energy. Further since a given sample of hydrogen contains a very large number of atoms (almost infinite) and hence infinite electrons, different atoms absorb different amounts (quanta or photon) of energy. Hence the single electron in different atoms will jump to different energy levels depending upon the energy absorbed by the atom. For example, some of the hydrogen atoms may absorb energy to Jump directly from energy level 1 to 3, while still others may jump to higher energy levels 4, 5, 6 etc. by absorbing suitable energy.

The electrons then tend to fall back, almost immediately, to one or other of the lower energy levels in one or more jumps. For example, some electrons, say in energy level 4, may return directly to ground state (energy level l), others may first fall to energy level 3 and then to 1, while some others may first fall to energy level 2 and then to 1. This also happens to electrons excited to other energy levels, viz. 2, 3, 5, 6, 7 and 8. Thus, in general, different excited electrons adopt different routes to return to the ground state.

During each jump from a higher to a lower level, different amount of energy is released which appears in the form of a photon of light of specific frequency and thus gives a different line in the spectrum. Hence although hydrogen atom has only one electron, a number of lines (each corresponding to the energy of a photon released) appear in its atomic spectrum.

Spectral series

(i) Lines appearing in the atomic spectrum due to fall of electrons from higher energy levels (i.e. 2, 3, 4, 5, 6, etc.) to the lowest energy level, i.e. 1 were discovered by Lyman and hence named as Lyman series.

(ii) Lines appearing due to fall of electrons from energy levels 3, 4, 5, 6, 7, etc. to the energy level 2 were named as Balmer series.

(iii) Similarly, the Paschen, Brackett and Pfund series correspond to the fall of electrons from higher energy levels to energy levels 3, 4 and 5 respectively.

Calculation of Radius of Orbits

Consider an electron of charge ‘e’ revolving around a nucleus of charge ‘ze’, where ‘z’ is the atomic number and ‘e’ the charge on a proton. Let ‘m’ be the mass of the electron, ‘r’ be the radius of the orbit and ‘v’ the tangential velocity of the revolving electron. The electrostatic force of attraction between the nucleus and the electron (coulomb’s law) = ze × e / r² .

The centrifugal force acting on the electron = mv² / r

Bohr assumed that these two opposing forces must be balancing each other exactly to keep the electron in orbit. Thus,

Z²/ r² = mv²/r

For hydrogen z = 1, therefore,

e²/ r² = mv²/r -------(1)

Multiplying both sides by ‘r’

e²/r = mv² -------(2)

According to one of the postulates of the Bohr’s theory, angular momentum of the revolving electron is integral multiple of h/2π.

mvr = nh/2π

v = nh/2πmr

Substitute the value of ‘v’ in equation (2),

e²/r = m﴾ nh/2πmr)²

So, r = n²h²/4π²me² -------(3)

Energy of Electron in Each Orbit

For hydrogen atom, the energy of the revolving E, is the sum of its kinetic energy ( ½ mv²) and potential energy ( –e²/r).

E = ½ mv² – e²/r ----------- (4)

From equation (1)

mv² = e²/r

Substituting the value of mv² in (3)

E = ½ e²/r – e²/r

Or,

E = –e²/2r -------------(5)

Substituting the value of ‘r’ from equation (3) in (5),

E = – e²/2 × 4π2me²/n²h²

E = – 2 π²me⁴/n²h²

By using proper integer for ‘n’ (quantum number), we can get the energy for each orbit.

BOHR’S Model of Atom

In 1913, Neil Bohr proposed a new model of the atom which not only explained the drawbacks of Rutherford’s model but also the emission spectrum of hydrogen. Bohr’s theory was based on Plank’s quantum theory and was built on the following postulates;

1. Electrons revolve round the nucleus only in certain circular orbits. These orbits are associated with definite energies and are called Energy Shells or Energy Levels.

2. Only those orbits are permitted in which angular momentum (mvr) of electron is an integral multiple of h/2π i.e.

mvr = nh/2π

where, m = mass of electron, n = number of orbit in which electron is present, v = velocity of the electron, r = radius of the orbit, h = Planck’s constant.

3. As long as the electron remains in a particular orbit, it does not lose or gain energy. This means that energy of an electron in a particular orbit remains constant. That is why, these orbits are also called as Stationary States. This orbital rotation without emitting energy follows the Newtonian law; i.e. the force of attraction between the nucleus and electron is equal to the centrifugal force of moving electron.

4. When energy some external source is supplied to the electron, it may jump to some higher energy level by absorbing a definite amount of energy. When electron jumps back to the lower energy level it radiates same amount of energy in the form of light radiations.

Atomic Spectrum of HYDROGEN

When an electric discharge is passed through the hydrogen gas filled in the discharge tube at low pressure, light radiations are emitted by hydrogen. When these light radiations are passed through the prism, a spectrum consisting of bright lines known as Atomic Spectrum of Hydrogen is obtained.
In 1884, J. J Balmer observed that there were four prominent coloured lines in the visible region of hydrogen spectrum. This series of four lines in the visible region was named as the Balmer Series. Later on, by careful observation four other spectral series were discovered in the infra-red and ultra-violet regions of hydrogen spectrum. These series were named after their discoverers. Thus, atomic spectrum of hydrogen have five spectral series.

Name Region where located 1. Lyman Series 2. Balmer Series 3. Paschen Series 4. Brackett Series 5. Pfund Series Ultra-violet Visible Infra-red Infra-red Infra-red

Rydberg in 1890, gave a formula to calculate the wavelength of the various lines present in the particular series. The equation is as follows;
1/λ = R [ 1/n1² - 1/ n2² ]
Where, R is called Rydberg constant and its value is 109,677cm^-1, n1 and n2 are whole numbers and for particular series n1 has particular value and n2 varies. E.g.
For Lyman Series,   n1 = 1, & n2 = 2,3,4-----
For Balmer Series,   n1 = 2, & n2 = 3,4,5-----
For Paschen Series, n1 = 3, & n2 = 4,5,6-----
For Brackett Series, n1 = 4, & n2 = 5,6,7-----
For Brackett Series, n1 = 5, & n2 = 6,7,8-----

Spectrum

When a beam of polychromatic light is passed through a prism, it is broken up into its constituent colors. This array of colors is known as Spectrum.
There are two principle classes of spectrum;

(a). EMISSION SPECTRUM
When the radiations emitted from the source are passed directly through the prism, the spectrum so obtained is known as Emission Spectra. (The source can be made to emit the radiations by heating the source to high temperature or by passing electric discharge).
Emission Spectrum is further classified into Continuous Emission Spectrum and Line Emission Spectrum.
i) Continuous Emission Spectrum:-
When the different colors of the spectrum overlap each other, a band of colors is obtained. Such a band of colors is known as Continuous Spectrum. Thus, the continuous spectrum obtained during the study of emission spectrum is known as Continuous Emission Spectrum. This type of spectrum is obtained whenever matter in bulk is heated.
ii) Line Emission Spectrum:-
When the different colors of the spectrum are separated from each other by dark spaces, the spectrum so obtained is known as Line Spectrum. Thus, the Line Spectrum obtained during the study of emission spectrum is known as Line Emission Spectrum. This type of spectrum is obtained whenever matter in atomic state is heated. Each line in spectrum corresponds to a particular wavelength. It has been observed that each element gives its own characteristic spectrum. No two elements can have identical line spectrum, as no two human beings have identical Finger-prints. Hence, line spectrum is also known as Finger-Print of atoms.

(b). ABSORPTION SPECTRUM
When the light from a source emitting a continuous spectrum is first passed through the substance taken in liquid form or gaseous form, and then passed through the prism the spectrum so obtained is known as Absorption Spectrum. In Absorption Spectrum some of the colors are missing which leave dark lines or bands at their places.
The Absorption Spectrum is further classified into Continuous Absorption Spectrum and Line Absorption Spectrum.
i) Continuous Absorption Spectrum
This type of spectrum arises when the absorbing material absorbs a continuous range of wavelengths. In this type of spectrum the dark lines overlap each other to form a continuous band.
ii) Line Absorption Spectrum
In this spectrum, sharp dark lines are obtained. This type of spectrum is obtained when the absorbing substance is in vapor state.

Electromagnetic Spectrum

The different electromagnetic radiations have different wavelengths. The visible light have radiations of wave lengths between 3800Å - 7600 Å. Different colors in the visible light correspond to different wavelengths. In addition to the visible light there are many other electromagnetic radiations, such as X-rays, U.V. - rays, I. R. - rays, radio waves, microwaves etc.

The arrangement of all electromagnetic radiations in the increasing order of their wavelengths or decreasing order of their frequencies is called Electromagnetic Spectrum.

Characteristics of the Waves

The various characteristic properties of the wave are as follows;

1. Wave-Length
The distance between the two consecutive troughs or crests of a wave is known as Wave-length of the wave. It is denoted by λ (Lambda).
2. Frequency
The number of waves made per second is called Frequency. It is denoted by ν (nu) . Its unit is hertz (Hz).
3. Velocity
The distance travelled by a wave in one second is called Velocity of the wave .It is denoted by letter c. The frequency (ν) and wavelength (λ) are related to velocity (c) by the relation:
C = ν λ
4. Wave number
It may be defined as the number of wavelengths per centimeter. It is equal to the inverse of wavelength expressed in centimeters. It is denoted by ν.
ν = 1/λ
5. Amplitude
It is the height of the crest or depth of a trough of a wave. It is generally expressed by the letter ‘a’. The amplitude of a wave determines the intensity of the radiation.