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INORGANIC CHEMISTRYFor

B.Sc. 1st Year

(For M.D.U. Rohtak C.D.L.U. Sirsa and Kurukshetra Universities)

B. K. VERMANIDepartment of Chemistry

D.A.V. College Chandigarh

ByS. KIRAN VERMANIDepartment of Chemistry

Govt. College Chandigarh

VTVEK PATHANIADepartment o f Chemistry

Panjab University Chandigarh

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STH-8202-140-INORGANIC CHEMISTRY I

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P r e f a c e

The Comprehensive Inorganic Chemistry (B.Sc. Part I) has been written strictly in accordance with the new syllabus suggested by the UGC. It also contains other chapters to meet the requirements of the syllabi approved by the M.D.U. Rotak, Kurukshetra, C.D.L.U., Sirsa and the neighbouring universities in North India. Overall, it should serve the needs of the B.Sc. (1st year, Inogranic Chemistry) students of all the Indian Universities.

We.have benefitted greatly from the standard books on the subject written by Western and Indian authors. We make no claim for originality. Our humble contribution lies perhaps in compiling the facts and interpretations available in standard texts.

The in-chapter exercises, some basic questions with answers and multiple choice questions have been incorporated in each chapter. Multiple Choice Questions have become the standard item in almost all the examinations and the entrance tests for admission to higher studies.

We have benefitted a great deal from discussions with several teachers and we take this opportunity to thank them here. Our thanks are to Dr. D.S. Gill and Dr. R.P. Sharma, Professors, Department of Chemistry, Panjab University, Chandigarh, who contributed a great deal to this text.

The presenting of this book is a concrete form of ideas that have been lingering in mind for a long time. The driving force behind this work is the inspiration, motivation of that Supreme Guiding Light, for whom our words fail to express gratitude.

We wish to thank our inspiring publisher Sh. R.K. Gupta and his efficient staff for the unstinted assistance provided at all stages for publishing this book. We owe a considerable debt to their patience, wisdom and understanding.

We shall appreciate bearing from the student and the teacher community. Their feedback will go a long way in further improvement of the subsequent editions of this book.

—AUTHORS

S y l l a b u s

B.Sc. I YEAR

Paper I (Theory) Inorganic Chemistry Max. Marks : 37Time : 3 Hrs.

Note : Ten questions will be set, two questions from each section. The candidate will be required to attempt five questions in all, selecting one question from each section. As far as possible questions will be short answer type and not essay type.

Section I

Atomic Structure 6 Hrs.Idea of de Broglie matter waves, Heisenberg uncertainty principle, atomic orbitals,

Schrodinger wave equation, significance of v|/ and v|i2, quantum numbers, radial and angular wave functions and probability distribution curves, shapes ofs,p , d orbitals. Aufbau and Pauli exclusion principles, Hand’s multiplicity rule. Electronic configurations of the elements, effective nuclear charge.

Periodic Properties 5 Hrs.Atomic and ionic radii, ionization energy, electron affinity and electronegativity—defini

tion, methods of determination or evaluation, trends in periodic table and applications in predicting and explaining the chemical behaviour.

Section n

Covaleut Bond 10 Hrs.Valence bond theory and its limitations, directional characteristics of covalent bond,

various types of hybridization and shapes of simple inorganic molecules and ions. Valence shell electron pair repulsion (VSEPR) theory to NH3, H30 +, SF4, C1F3, IC12~ and H20. MO theory, homonuclear, heteronuclear (CO and NO) diatomic molecules, multicenter bonding in electron deficient molecules,bond strength and bond energy, percentage ionic character from dipole moment and electronegativity difference.

Weak Interactions—Hydrogen bonding, van der Waals forces. 2 Hrs.Section III

Ionic Solids 8 Hrs.Ionic structures, radius ratio effect and coordination number, limitation of radius ratio

rule, lattice defects, semiconductors, lattice energy and Born-Haber cycle, solvation energy and solubility of ionic solids, polarizing power and polarisability of ions, Fajan’s rule. Metallic bond- free electron, valence bond and band theories.

s-Block Elements 6 Hrs.Comparative study, diagonal relationships, salient features of hydrides, solvation and

complexation tendencies including their function in biosystems, an introduction to alkyls and aryls.

Section IV

p-Block Elements-I 12 Hrs.Comparative study (including diagonal relationship) of groups 13-17 elements, com

pounds like hydrides, oxides, oxyacids and halides of groups 13-16, hydrides of boron-diborane and higher boranes, borazine, borohydrides.

Section V

p-Block Elements-n 8 Hrs.Chemistry of fullerenes, carbides, fluorocarbons, silicates (structural principle),

tetrasulphur tetranitride, basic properties of halogens, interhalogens and polyhalides.

Chemistry of Noble Gases 3 Hrs.Chemical properties of the noble gases, chemistry of xenon, structure and bonding in

xenon compounds.

C o n t e n t s

Chapters Pages

Syllabus (vi)1. Atomic Structure ... 12. Periodic Properties ... 673. Chemical Bonding ... 110

(A) Covalent Bond ... 110(B) Ionic Solids ... 201(C) Weak Interactions ... 252

4. s-Block Elements : Alkali and Alkaline Earth Metals ... 2705. Chemistry ofp-Block Elements ... 3026. Chemistry of Noble Gases ... 386

Appendix University Question Papers ... 413

r 1 B Atomic StructureA

L V

1. Wave nature of the electron : The de-Broglie relation

2. Heisenberg uncertainty principle3. The Schrodinger wave equation4. Significance of \|/ and \\i25. Quantum numbers6. Pauli’s exclusion principle7. Radial and angular wave func

tions and probability distribution curves

8 . Shapes of s, p, d orbitals9. The Aufbau principle

10. Hund’s multiplicity rule11. The electronic configurations of

the elements12. Effective nuclear charge

Basic Questions with Answers Multiple Choice Questions Exercises

J o h n Dalton, the father of atomic theory, is reputed to have said, “Thou canst not split an atom". He was proven wrong by the combined efforts of J.J. Thomson, Ernest Rutherford and James Chadwick, who discovered, respectively, the electron, the proton and the neutron. The first ideas of the modern atom are due to Lord Rutherford. Niels Bohr proposed that electrons move around the nucleus in orbits. Each orbit is associated with specific energy. If an electron jumps from one orbit to another, there will be change in energy. For example, if an electron goes from orbit 1 (energy Ej) to orbit 2 (energy E2), the change in energy is given by E2 - Er This energy change is accom panied by absorption of radiation. The energy of the radiation is given by the equation

E2 - Ej = hv where v is the frequency of radiation and h is the planck constant. The frequency of radiation is related to wavelength (X) by the relation

Cv = y where C is the velocity of light.

Bohr’s theory for the structure of Hydrogen atom was highly successful, however, the extensions of Bohr’s ideas to atoms with more than two electrons did not agree with the experimental evidences. It appeared that in no way the theory could be modified to work for Helium and other atoms. It soon became apparent that there was a fundamental problem with Bohr Model. The idea of an electron moving about the nucleus in a well-defined orbit at a fixed distance from the nucleus with a definite energy had to be abandoned.

1. WAVE NATURE OF THE ELECTRON : THE de BROGLIE RELATION

Prior to 1900, the dual nature of light had been postulated. Then, in 1924, Louis de Broglie suggested that if light can have a particle nature, then matter might have wave properties. He looked a mathematical relationship which could bridge the properties of wave and matter. The most important property of matter is mass and the most important property of waves is wavelength.

He showed that the wavelength X, associated with a particle of mass m, moving with speed v would be

mvwhere h is Planck’s constant. De Broglie’s idea got experimental evidence from Davisson and Germer’s diffraction experiment which showed that a beam of electron indeed have wave properties. Moreover the observed wavelength of the electron was exactly that predicted by de- Broglie.

Using the de Broglie equation, it is possible to show that the Bohr quantum number n arises in a natural way. To do this, consider Fig. 1. Imagine the electron of the hydrogen atom in the form of a wave moving in a circular path about the nucleus. If the wave is to be stable, it must trace the same path in successive orbits. This is the case for n = 3 wave, where three wavelengths bring the electron exactly back to its starting point.

Fig. 1

The condition also applies to the n = 4 wave; four wavelength correspond exactly to a trip

around the circle. The n = 3 — wave is unstable ; the electron does not trace the same path insuccessive orbits (the second orbit is shown by dotted path). The general condition for stability is 2nr = nX where 2nr is the circumference of the orbit, X is the wavelength of the electron and n is an integer.

hSubstituting X = — in the above equationmv

h nhZnr = n — or mvr = —— mv 2nThis is the condition that Bohr imposed arbitrarily on the momentum of the electron in

the hydrogen atom. Using the de-Broglie relation, this condition becomes physically reasonable.

2. HEISENBERG’S UNCERTAINTY PRINCIPLE

Werner Heisenberg (1901) pointed out that if an electron is exhibiting dual nature (wave and particle), it is not possible to know the exact location of the electron on the wave as the wave is extending throughout a region of space. Heisenberg’s Uncertainty Principle is defined as “It is impossible to determine simultaneously the position and momentum o f the electron with great accuracy or certainty”.

hMathematically, this principle can be stated as Ap x Ax > —

where Ax is the uncertainty in the determination of position, Ap is the uncertainty in the determination of the momentum and h is the Planck’s constant. In other words, the product of uncertainty in the simultaneous determination of the position and momentum of a particle is equal or greater than the Planck’s canstant.

Since the, minimum product of Ax and Ap is constant = 1-06 x 10-34 kg m2 s_1, it

means that1

Ax°c .ApTherefore, it is concluded that if uncertainty in position is more, then uncertainty in

momentum would be less and vice versa. In order to understand the physical concept of the uncertainty principle, let us try to measure both the position and the momentum of an object by impact of light radiations (photons). If the object is of reasonable size, its position or velocity will not be changed by the impact of light photons. Hence it will be possible to know both the position and velocity of the object to a reasonable degree of precision. But if the object is extremely small like electron, then it will suffer a change in its velocity and path due to the impact of even a single photon of light used to observe it.

In the light of uncertainty principle, Bohr concept of the atom, which regards the electron as rotating in definite orbits around the nucleus with definite velocities becomes unacceptable. It is not possible to know exactly the position of an electron rather it is possible to predict the probability of finding an electron moving with a particular velocity in a given region of space around the nucleus at a given time.

According to Bohr Model, an electron in the n = 1 orbit of the hydrogen atom follows a circular path having a radius of 53 pm, with a momentum of 1.99 x 10-24 kg m s_1. If we assume that the'uncertainty of the momentum is 1% of its value, or 1.99 x 10-26 kg m s-1, then the uncertainty in its position is

106 x 10“34 Ax = x 10“26 = 5-3 x 10 9 m = 5300 pm

The uncertainty in the position of the electron is a hundred times the radius of the Bohr orbit. The Bohr model thus calculates the position and the momentum of the electron more accurately than is possible within the limitations of the Heisenberg uncertainty principle.

Shortly after de Broglie proposed idea of duality of matter, Erwin Schrodinger (1926) applied this idea to describe the behaviour of the electron in the hydrogen atom. In Schrodinger wave model of an atom, the discrete energy levels or orbits proposed by Bohr are replaced by mathematical functions Psi (\|/) which are related with the probability of finding electrons at various places around the nucleus. The Schrodinger wave equation (S.W.E.) for an electron wave propagating in three dimensions in space is written as

02\|/ 32\j/ 02\|/---~r + ---- + ---TT + 8n2m (E - V)¥ = 0dx* dyz dzzwhere V|/ = amplitude of the wave function associated with the electron

x, y ,z = Cartesian coordinates (three dimensional space coordinates) in = mass of the electron h = Planck’s constant E = total energy of the systemV = potential energy of the system.

The above equation can also be written as

...(1 )

V2\|/ +8n2m

(E - V)y = 0 ...(2)

d \\l d \J/ 82\j/where V2\|/ (del Squared x Psi) = -^2 + ^ 2 + ^ 2

V2 is known as Laplacian mathematical operator. It means that mathematical operator V2 operates upon the mathematical function \|/ (V2\|/ does not mean that V2 is multiplied by y).

The wave mechanical model of the atom began in 1927 when Schrodinger developed a mathematical wave equation to describe the wave motion of the electron in a hydrogen atom. He considered that the nucleus is surrounded by a vibrating electron wave which may be mathematically compared with stationary or standing wave formed by a vibrating string fixed between two points as shown in Fig. 2.We must realise that the electron in a hydrogen atom is under constraint imposed by the attraction of the nucleus. Therefore, Fig. 2. A standing wave,there is nothing unusual in describing an electron motion by an equation analogous to that used to describe a “standing or stationary” wave system whose solution in one dimension is given by the sine wave equation (3).

Since wave equation can be expressed as2m

\|/ = A sin —r— ...(3)A,where \\i is the amplitude of the wave for any value ofx (distance from the origin along the space coordinate in one direction), A is a constant and X is the wavelength.

On double differentiation* w.r.t. x, we getd\\i 271 271Xdx = A . T cos ~k~

d2\\i = A. 2n 2ti ( sin 27ix- 47I2 a ■ 2tixA cin ___

dx2 X '' A. A X J = A.2 X*. oill ASubstituting the value of A sin from eq. (3), we get

d2y -47i2 d2\y 4n2 A, 2 _ i 2 ^ 0r . 2 + ,2 V - 0 dx1 K dx K

...(4)

hFrom de-Broglie’s equation A = —mvSubstituting in equation (4), we get

d2\\i 4tr2m V dx2 ' h2

...(5)

This is the equation for wave motion of electron in one dimension i.e. , x axis. The sameequation in three dimensions (x ,y and z axis) may be written as

d2\|/ 02\y 02\)/ 47t2m2i’2— T + ^ - + ^ - + ------5---- V =0dx2 dy2 dz h ...(6)

or„ 471 m v

V2V + 2 V _ 0 h...(7)

Considering the electron as a particle, the total energy (E) of an electron = K.E. + P.E.The K.E. of the electron is given as

K.E = ~ mv2 and P.E. = V

E = 7T mu2 + V or E - V = - mu2 z z

or„ 2(E - V)

2(E - V) = mv2 or v2 = -----------mSubstituting the value of v2 in eq. (7)

V2V + - 7 7 —. (E - V)\j/ = 0 h

...(8)

ord2\\i d2\\i d2\\i 8n2ma*’ V + a*2 + a ’

- r2m

a2 a2 a2 a* 2 + ay 2 + dz2

+ v v|/ = Ev|/

— v 2 + v2m

where /? = •— and above equation is obtained by rearranging eq. (9).271

The equation (10) car. also be written as

V = E v

where V2 is the Laplacian operator,

or Hv|/ = E\|/

- f t 2 2where H is Hamiltonian operator equals to h -------- v + V.2mThe Schrodinger equation, being a second order differential equation, has large number

of solutions, many of them having no significance at all.Several wave functions called \|/p vj/2, i|/3 ..... will satisfy conditions 1, 2, 3 and 4 to the

wave equation (8 ). Each of these wave functions has a corresponding energy Ep E2, E3 ........Such wave function which gives certain definite and acceptable value of the total energy E is called eigen function. The acceptable value of total energy E obtained by such a solution is called Eigen value.

4. SIGNIFICANCE OF vj/ AND y2

A well known form of Schrodinger equation is

V2v[/ +8n2m 1 ?

(E - V)\|/ = 0 ...(8)

This is also called Time Independent Schrodinger wave equation.As already pointed out, V2 stands for the Laplacian operator, m is the mass of material particle whose total energy is E and potential energy is V. \|/ is called the wave-function which has no physical meaning except that it represents the amplitude o f the electron wave in three dimensions and is a function o f the space coordinates. Its significance may be explained by analogy with electromagnetic waves.

An electron is described by a wave function, \j/, which is a mathematical function of coordinates x, y and 2 . Selection of acceptable values of \|/ is made according to the following conditions :

1 . \|/ must be continuous.2. \j/ must be finite.3. must be single valued.4. The probability of finding the electron over all the space from plus infinity to minus

infinity must be equal to one.

Comprehensive Inorganic Chemistry

Publisher : Laxmi Publications ISBN : 9788170086871Author : B K Vermani, SKiran Vermani & VivekPathania

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Comprehensive Inorganic Chemistry