Fundamental Chemistry-I CHE(N)-101 PDF

CHE(N)-101 B.Sc. I Semester FUNDAMENTAL CHEMISTRY-I DEPARTMENT OF CHEMISTRY SCHOOL OF SCIENCES UTTARAKHAND OPEN UNIVERSITY HALDWANI (NAINITAL), UTTARAKHAND-263139  CHE(N)-101 FUNDAMENTAL CHEMISTRY-I...

CHE(N)-101 B.Sc. I Semester FUNDAMENTAL CHEMISTRY-I DEPARTMENT OF CHEMISTRY SCHOOL OF SCIENCES UTTARAKHAND OPEN UNIVERSITY HALDWANI (NAINITAL), UTTARAKHAND-263139  CHE(N)-101 FUNDAMENTAL CHEMISTRY-I SCHOOL OF SCIENCES DEPARTMENT OF CHEMISTRY UTTARAKHAND OPEN UNIVERSITY HALDWANI (NAINITAL) Phone No. 05946-261122, 261123 Toll free No. 18001804025 Fax No. 05946-264232, E. mail [email protected] htpp://uou.ac.in  Board of Studies Prof. P.D. Pant Prof. G.C. Shah Director, School of Sciences Professor Chemistry Uttarakhand Open University Department of Chemistry Haldwani, Nainital Kumaun University, S.S.J. Campus, Almora Prof. P.P. Badoni Prof. N.G. Sahoo Professor Chemistry Professor Chemistry Department of Chemistry Department of Chemistry H.N.B. Garhwal University Kumaun University, D.S.B. Campus, Pauri Campus, Pauri Nainital Dr. Shalini Singh Dr. Vinod Kumar Assistant Professor Assistant Professor Department of Chemistry Department of Chemistry School of Sciences, School of Sciences, Uttarakhand Open University, Uttarakhand Open University, Haldwani (Nainital) Haldwani (Nainital) Dr. Deep Prakash Dr. Charu C. Pant Assistant Professor Assistant Professor (AC) Department of Chemistry Department of Chemistry School of Sciences, School of Sciences, Uttarakhand Open University, Uttarakhand Open University, Haldwani (Nainital) Haldwani (Nainital) Dr. Ruchi Pandey Assistant Professor (AC) Department of Chemistry School of Sciences, Uttarakhand Open University, Haldwani (Nainital) Programme Coordinator Dr. Shalini Singh Department of Chemistry School of Sciences, Uttarakhand Open University, Haldwani, Nainital  Unit Written By Unit No. 1. Dr. K. S. Dhami (Retd. Professor.) 01, 02, 03, 04 Department of Chemistry D.S.B. Campus, Kumaun University Nainital 2. Dr. K. B. Melkani (Retd. Professor) 11, 12 Department of Chemistry DSB Campus Kumaun University, Nainital 3. Dr. Vinod Kumar 13, 15, 16 Assistant Professor Department of Chemistry, School of Sciences Uttarakhand Open University, Haldwani 4. Dr. Deep Prakash 14 Assistant Professor Department of Chemistry, School of Sciences Uttarakhand Open University, Haldwani 5. Dr. Charu Chandra Pant 09,10 Assistant Professor Department of Chemistry, School of Sciences Uttarakhand Open University, Haldwani 6. Dr. Kamal K. Bisht 04,05 Assistant Professor Department of Chemistry R.C.U. Govt. P.G. College, Uttarkashi 7. Dr. Girdhar Joshi 06, 07 Assistant Professor Department of Chemistry Govt. P.G. College, Gopeshwar 8. Dr. Vipin Chandra Joshi 08 Assistant Professor Department of Chemistry L.S.M. Govt. P.G. College, Pithoragarh  Course Editor 1. Dr. Vinod Kumar Assistant Professor Department of Chemistry School of Sciences, Uttarakhand Open University, Haldwani, Nainital 2. Dr. Deep Prakash Assistant Professor Department of Chemistry School of Sciences, Uttarakhand Open University, Haldwani, Nainital Title : : Fundamental Chemistry-I ISBN No.: : Copyright : Uttarakhand Open University Edition : 2023 Published by : Uttarakhand Open University, Haldwani, Nainital- 263139  CONTENTS BLOCK-1: ATOMIC STRUCTURE AND CHEMICAL BONDING Unit 1 : Atomic structure 1-31 Unit 2 : Periodic Properties 32-48 Unit 3 : Chemical bonding –I 49-79 Unit 4 : Chemical bonding –II 80-131 BLOCK-2: ORGANIC REACTION AND STEREOCHEMISTRY Unit 5 : Mechanism of organic reactions 132-160 Unit 6 : Stereochemistry- I 161-191 Unit 7 : Stereochemistry- II 192-218 BLOCK-3: ALIPHATIC HYDROCARBON Unit 8 : Alkane 219-242 Unit 9 : Alkene 243-268 Unit 10 : Alkyne 269-278 BLOCK-4: STATE OF MATTER Unit 11 : State of matter –I 279-324 Unit 12 : State of matter –II 325-347 BLOCK-5: LAB WORK Unit 13 : Laboratory hazards and safety precautions 348-356 Unit 14 : Inorganic exercise: Salt mixture analysis (I & II group) 357-399 Unit 15 : Organic exercise: Sterochemistry and functional group analysis of 400-414 organic molecules Unit 16 : Physical exercise: Determination of relative surface tension 415-421 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 UNIT 1 : ATOMIC STRUCTURE CONTENTS: 1.1 Introduction 1.2 Objective 1.3 Idea of de Broglie matter wave 1.4 Heisenberg’s Uncertainty Principle 1.5 Schrodinger wave equation (No derivation) 1.5.1 Significance of ψ and ψ2 1.5.2. Radial and angular wave functions 1.5.3. Probability distribution curve 1.6. Shape of different orbitals 1.7. Quantum Numbers 1.8. Pauli’s Exclusion Principles 1.9. Hund’s rule of maximum multiplicity 1.10. Aufbau principle 1.11. Electronic configuration of the elements 1.12. Effective nuclear charge. 1.13. Summary 1.14. Terminal Questions 1.15 References UTTARAKHAND OPEN UNIVERSITY Page 1 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 1.1 INTRODUCTION In the beginning of nineteenth century, John Dalton (1766-1844) put forward his atomic theory, he regarded atom as hard and smallest indivisible particle of matter that takes part in chemical reactions; the atoms of one particular element are all identical in mass and atoms of different elements differ in mass and other properties. Later on, various investigators around the end of nineteenth century and beginning of twentieth century did several experiments and revealed the presence of much smaller negatively charged particles, named electrons by J.J. Thomson (1897) and positively charged particles, named protons by Rutherford (1911) within an atom. These tiny particles were called subatomic particles. It was also established by Rutherford that the whole positive charge and most of the mass of an atom lies at nucleus. The positive charge on the nucleus was attributed to the presence of protons called the atomic number by Moseley (1912). The electrons were said to be arranged around the nucleus in the extra nuclear region in certain well defined orbits called energy shells and were said to be in constant motion (N. Bohr, 1913). Chadwick’s experiments (1932) also revealed the existence of yet another subatomic particle in the nucleus which did not have any charge and named as neutrons. Further investigations established that there were also present some other subatomic particles in the nucleus in addition to electrons, protons and neutrons. These particles are positrons, neutrinos, antineutrinos, pions (π-mesons) etc. The pions (Yukawa, 1935) are said to be continuously consumed and released by proton-neutron exchange processes. Thus, it is concluded that the atom no longer is an ultimate and indivisible particle of matter and the outer or valence shell electrons are responsible for chemical activity of the elements. 1.2 OBJECTIVE In the present chapter you will be able to the :  The preparation of the text of this unit is to acquaint the readers with the fascinating and exciting realm of the atoms. Accordingly, an attempt has been made to through light on the arrangement of the internal constituents of the atoms (the subatomic particles), their peculiarities and characteristics along with their behaviour towards their neighbour.  The arrangement of protons and neutrons in the nucleus and the rules governing the arrangement of electrons in the extra nuclear region of an atom and filling of orbitals UTTARAKHAND OPEN UNIVERSITY Page 2 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 belonging to higher energy shells prior to the entry of electrons in the orbitals of lower energy shells.  At the same time, the problem “what makes the electron cloud to acquire different shapes in three dimensional space around the nucleus?” has been entertained and various other interesting problems have also been taken into account.  In this unit you will be know about the quantum number and their type, De-broglie;s hypothesis and Heisenberg uncertainty principle.  Under this unit you able to different type rule of the electronic configuration and arrangement of electron in the their particular orbital 1.3. DE-BROGLIE’S MATTER WAVES: DUAL NATURE OF MATTER This is based on wave mechanical concept of an electron in an atom. Albert Einstein proposed dual character of electromagnetic radiation in 1905, viz. wave character based on Maxwell’s concept evidenced by diffraction, interference, polarisation kinds of phenomena and particle character based on Planck’s quantum theory witnessed by quantization of energy and hence photoelectric effect, i.e. the ejection of photo electrons from metal surface on striking electromagnetic radiation. On the basis of above analogy, French Physicist Louis de Broglie (1924) postulated that not only light but all material objects (both micro and macroscopic) in motion such as electrons, protons, atoms, molecules etc. possess both, wave and the particle properties and thus have dual character, i.e. the wave character and particle (corpuscular) character. He called the waves associated with material particles as matter waves which are now named de Broglie’s wave. These waves differ from electromagnetic or light waves in a sense that these are unable to travel through empty space and their speed is different form light waves. de Broglie’s relation de Broglie deduced a fundamental relation between the wave length of moving particle and its momentum by making use of Einstein’s mass energy relationship and Planck’s quantum theory. The material particle as a wave satisfies the Planck’s relation for a photon, i.e. UTTARAKHAND OPEN UNIVERSITY Page 3 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 E = hv ……….. (1.1) where h is Planck’s constant and v is the frequency of the wave. The frequency for light wave, v= and for particle wave, v = (c = speed of light wave and = speed of particle wave). At the same time, Einstein’s mass energy relationship is applicable to it, i.e. E = mc2 (for a photon) ……….. (1.2) or E = mv2 (for a particle where v ≠ c) ………... (1.3) where m is the mass and v the speed/velocity of the particle. From the equations 1.1 and 1.3, we have hv = m 2 ……… (1.4) ℎv or =m 2 or = mv = p (momentum) or = or ( ) …… (1.5) (momentum p = mv, mass x velocity) Here, corresponds to the wave character of matter and p its particle character. This is Known as de Broglie’s relation. From this relationship, it is concluded that “the momentum of a moving particle is inversely proportional to the wavelength of the wave associated with it”. It is important to note here from above discussion that de Broglie’s relation is applicable to material particles of all sizes and dimensions but the wave character is significant only for micro objects like electrons and is negligible for macro objects hence cannot be measured properly. This infers that de Broglies’s relation is more useful for smaller particles. de Broglie’s relation has been applied to a moving electron around a nucleus in a circular path in an atom to justify Bohr’s postulate which states that elections can move only in those orbits for which the angular momentum is equal to an integral multiple of , i.e. m r=n ……….(1.6) UTTARAKHAND OPEN UNIVERSITY Page 4 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 This moving electron is considered as a standing wave extended around the nucleus in circular path and not as a mass particle. If the circumference of the orbit is an integral multiple of the wave length, , i.e. 2 r=n ………(1.7) where r is the radius of the orbit and n is the whole number, the wave remains continually in phase, i.e. is a merging wave (Fig. 1.1 a) From equation 1.5, we have = = Putting the value of in equation 1.7, we get 2 r = n Fig 1.1 (a) merging waves, (b) Crossing waves or m r = n (on rearranging) ………(1.8) which is the same as equation 1.6, i.e. Bohr’s postulate mentioned above. If the circumference of the orbit is bigger or smaller than the value given above, the wave is out of phase, i.e. a crossing wave (Fig. 1.1 b) Fig. 1.1 a: in phase Fig. 1.1 b: out of phase de Broglie’s concept has been experimentally verified by Davisson and Germer, G.P. Thomson and later by Stern independently. 1.4. HEISENBERG’S UNCERTAINTY PRINCIPLE According to classical mechanics, a moving electron behaves as a particle whose position and momentum could be determined with accuracy. But according to de Broglie, a moving electron has wave as well as particle character whose precise position cannot be UTTARAKHAND OPEN UNIVERSITY Page 5 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 located because a wave is not located at a particular point rather, it extends in space. To describe the character of a subatomic particle that behaves like a wave, Werner Heisenberg in 1927 formulated a principle known as Heisenberg’s Uncertainty Principle. According to the principle “it is impossible to determine simultaneously both the position as well as the momentum (or velocity) of a moving particle at the same time with certainty (or accurately)” He also proposed a mathematical relationship for the uncertainty principle by relating the uncertainty in position with the uncertainty in momentum which is given below:...............(1.9) or x m ( ) (since p = m v and = mx ) ……….(1.10) where is the uncertainty or error in the position of the particle, and are the uncertainties in it’s momentum and velocity and h is Planck’s constant. This equation states that the product of and can either be greater than or equal to ( ) but never smaller than , a constant. If is measured more precisely (i.e. is small) then there is large uncertainty or error in the measurement of momentum ( is large) and vice versa. 1.5. CONCEPT OF PROBABILITY AND SCHRODINGER’S WAVE EQUATION From the uncertainty principle, it has been concluded that the exact position and exact momentum or velocity (related to kinetic energy) of a micro particle can be replaced by the concept of probability. For an electron in an atom we can say that there is probability of finding it in a particular region of space and in a particular direction (except for s-electron). To describe the wave motion of electron in hydrogen atom, Schrodinger in 1927 combined the de Broglie’s relation for the wavelength of a particle wave with the well known differential equation for standing waves and proposed a mathematical form called Schrodinger’s wave equation. This equation is now widely used to explain the behaviour of UTTARAKHAND OPEN UNIVERSITY Page 6 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 atomic and molecular systems. The equation for a single particle in three dimensional space, i.e. along x, y and z directions is given as follows: δ2ψ + δ2ψ + δ2ψ + 4π2 ψ = o ……….(1.11) δx2 δy2 δz2 λ2 In place of three partial differentials, symbol ‘∇’ (del) can be used, hence the above equation becomes ∇2ψ + 4π2 ψ = 0 ……….(1.12) λ2 where ∇2 (del square) is equal to δ2 + δ2 + δ2 and is known as laplacian operator. δx2 δy2 δz2 Putting the value of λ from de Broglie’s relation (i.e. λ = ), the above equation becomes ∇2 ψ + = 0 ……….(1.13) Extracting the value of v from kinetic energy, potential energy and total energy terms i.e. E = K.E+V where K.E. = and putting in the above equation, we get the final form of the equation as: ∇2 ψ + (E -V) ψ = 0 ……….(1.14) This equation is known as Schrodinger’s wave equation. 1.5.1. Significance of ψ and ψ 2 An electron, from the probability concept, is considered as a three dimensional wave system extended around the nucleus and is represented by the symbol ψ which denotes the wave function of the electron; ψ itself has no physical significance and simply represents the amplitude of electron wave. Schrodinger’s equation has several solutions for ψ, both real and imaginary. Some of the real values of ψ are appreciable while others are too small and hence neglected. If the value of ψ obtained as above is continuous, finite, single valued and electron probability in space related to ψ is equal to 1, then ψ is known as eigen function (meaning characteristic), ψ2 gives the probability of finding an electron of a given energy, E from place to place in a given region around the nucleus. Since, ψ often contains the imaginary quantity, UTTARAKHAND OPEN UNIVERSITY Page 7 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 but the probability of an electron in a given volume must be a real quantity, therefore the product ψ ψ* (ψ star) is used rather than ψ2 where ψ* is complex conjugate of ψ. This product will always be real whereas ψ2 may be real or imaginary. If ψ is real quantity, then ψ and ψ* both are same and hence ψ2 is also a real quantity and corresponds to probability density per unit volume. 1.5.2. Radial and angular wave functions: The radial wave function, R (r) The value of ψ appearing in Schrodinger’s wave equation in polar coordinates, (r,θ,∅), can be determined only when ψ is written in the following form (mention of equation is not required) : Ψ (r,θ, ɸ) = R (r) Θ(θ) Ф(ɸ) …………..(1.15) Where ψ (r,θ, ɸ), is known as total wave function, R (r) is the radial wave function and other two are angular wave functions. The radial wave function, R (r) is dependent on r only where r is the distance of electron from the nucleus and is independent of θ and ɸ. Therefore, R (r) deals with the distribution of the electron charge density as a function of distance (r) from the nucleus. R (r) depends on two quantum numbers n and l and can be denoted as Rn,l (r) or simply Rn,l. Both Rn,l and R2n,l are significant only for drawing the probability curves for various orbitals. The radial wave functions for all s-orbitals are spherically symmetrical. The angular wave function, ψ (θ, ɸ). The angular wave functions depend on the angles θ and ɸ and are independent of the distance (r). As given above in equation 1.15, these are represented as Θ (θ) and (ɸ). Their values depend on the quantum numbers l and m and can be written as Θ l,m and m, respectively. Therefore, the equation 1.15 can also be written as Ψn,l,m = Rn,l Θ l,mФ m ………….(1.16) This equation shows that the total wave function besides depending on r, θ, ɸ, also depends on the quantum numbers viz., n, l and m. Each permitted combination of n, l and m gives a distinct wave function and hence a distinct orbital. The angular wave functions together are used to predict the shapes of the orbitals. 1.5.3. Probability distribution curves: UTTARAKHAND OPEN UNIVERSITY Page 8 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Before discussing the distribution curves, let us know about the electron probability function. The probability or the chance of finding an electron in three dimensional space round the nucleus is known as electron probability function, D. For an extremely small spherical shell of radius r and thickness dr round the nucleus, the value of D can be given by D = ψ2 x volume of shell = ψ2 x 4πr2 dr ………… (1.17) and the electron probability between r = o and r = r would be equal to ψ2. 4πr2 dr. (ψ2 = R2 (r) or R2n,l) Radial probability distribution curves The square of the radial wave function multiplied by a volume element, dv, i.e. R2(r) x dv measures the probability of locating an electron at a distance from the nucleus and within a small radial space. This is same as electron probability function given above in which ψ2 can be replaced by R2n,l, meaning radial distribution. When R2 (r). dv or R2n,l. 4πr2 dr where dv= 4πr2 dr, is plotted against r, the distance from nucleus, we get radial probability distribution curves. The peak of the curve gives the distance from the nucleus where the probability is maximum and at distances smaller or greater than this, value of probability is less but not zero. Thus, it is observed that electron charge density decreases but volume of shell increases with r. Various such curves are shown below: UTTARAKHAND OPEN UNIVERSITY Page 9 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Fig. 1.2 Radial Probability distribution curves for 1s,2s,2p,3s,3p and 3d-orbitals. Simple sketches have been given in which the values of n and l have been shown and dr has been omitted. The important features of these curves are; (i). Curves start from the origin and the areas covered by the envelopes of a particular curve for a subshell (orbital) go on increasing from left to right so that the area of the last envelope is maximum. (ii). The number of minima where density of electronic charge is zero, appearing in a particular curve gives the number of radial nodes or nodal points for the orbital (subshell). The number of nodal points is equal to n-l-1. Thus for the electrons of 1s,2s,2p,3s,3p and 3d orbitals, the number of nodal points is 0,1,0,2,1 and 0, respectively. This is also evident from the curves of these orbitals. Evidently, 3s orbital (nodal points = 2) is bigger in size and more diffused than 1s (nodal point = 0) and 2s orbitals (nodal point = 1) both due to greater number of nodal points in it (see figure 1.2) 1.6. SHAPES OF ATOMIC ORBITALS AND ANGULAR PROBABILITY DISTRIBUTION CURVES The shapes of atomic orbitals depend θ and ɸ i.e. the product [Θ (θ) x Ф (ɸ)] or l,m x Фm is related with the shapes of the orbitals. The values of l,m x Ф m for s-orbital (l=0,m=0), p- orbital (l = 1, m = 0, ±1), and d-orbitals (l = 2, m = 0, ±1, ±2) can be obtained and correlated with the shapes of orbitals. For s-orbitals (l = 0, m = 0), the angular wave function o,o x Фo is independent of the angles and ɸ, i.e. there is no angular wave function and hence orbitals have only one orientation and are spherically symmetrical over all the directions, hence have spherical shape as well as are non-directional. Thus, s-orbitals are usually represented by circles. Greater the value of n and higher the number of nodal points for s-orbital, larger is the size of orbital. The electron density in s-orbitals could be shown by concentric shades as follows: UTTARAKHAND OPEN UNIVERSITY Page 10 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 1s-orbital 2s-orbital 3s-orbital (no nodal point) (1 nodal point) (2 nodal points) Fig. 1.3 Electron charge density pictures for 1s, 2s and 3s-orbitals. Nucleus has been shown by thick dot. For p orbitals (l = 1, m = 0, ±1), there are three values of m and therefore, there are three orientations of lobes of orbitals along cartesian coordinates viz. px, py and pz. The subscripts x, y and z indicate the axes along which orbitals are oriented. The three p-orbitals are similar in size, shape and energy but differ in orientation only. The angular wave function for these orientations is the product ,m x Фm. For l=1, m =0 orientation, the angular wave function 1,0 Ф0 is a real quantity and corresponds to pz orbital which is dumb-bell shaped curve along z- axis in three dimensional space (Fig. 1.4 c). For l = 1,m = +1 and l =1, m= -1 orientations, angular wave functions are 1,+1 x Ф+1 and 1,-1 x Ф-1 which have imaginary quantities and are avoided. The real values are obtained by the normalized linear combinations (addition and subtraction) of angular angular wave functions. Thus, addition process, i.e. 1,+1 x Ф+1 + 1,-1 x Ф-1 gives normalised wave function corresponding to px orbital. In three dimensional space, this gives dumb-bell shaped curve along x- axis (Fig.1.4a) The subtraction process, i.e. 1,+1 x Ф+1 - 1,-1 x Ф-1 gives normalised wave function corresponding to py orbital which is again dumb-bell shaped curve in three – dimensional space along y-axis (Fig. 1.4b). UTTARAKHAND OPEN UNIVERSITY Page 11 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Px orbital Py orbital pz orbital (a) (b) (c) Fig.1.4 The orientation of p- orbitals along x, y and z- axis. The (+) and (–) signs are algebraic signs of angular wave function and not the charge. The angular part of the wave function ψ ( , Ф) has (+)sign on one lobe and (–)sign on the opposite lobe although ψ2 ( , Ф) will be positive on both the lobes. Thus, for p-orbitals, the important points to be noted are: (i) Since x, y and z axes are perpendicular to each other, the three p-orbitals are also perpendicular to each other. (ii) Each of the three p-orbitals has two lobes on each side of the nucleus which is at the origin of the axes, hence the probability of finding the electron (s) in both lobes is equal. These lobes are separated by nodal planes passing through the nucleus. The electron density on the nodal plane is zero. (iii) Greater the value of n (principal quantum number or the shell number), larger is the size of p orbital i.e. 3p orbital is larger in size than 2p orbital though the shapes of both the orbitals are the same. (iv) The energy of the three p-orbitals with the same value of n is same i.e. all the three p- orbitals are degenerate. For d-orbitals (l = 2, m = 0, ±1, ±2), five orientations (or orbitals) are there corresponding to five values of m for l = 2. Depending on the permitted combinations of l and m, values for five d-orbitals, angular wave functions corresponding to different d-orbitals are as follows: For l = 2 and m=0, the angular wave function 2,0 x Ф0 has a real value and corresponds to dz2-orbital. For l =2 and m = ±1, we have two angular wave functions, 2,+1 x Ф+1 and 2,-1 x Ф-1. The values of these angular wave functions contain imaginary quantity and hence, these UTTARAKHAND OPEN UNIVERSITY Page 12 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 values are not accepted. The real and acceptable values are obtained from these by normalized linear combinations (addition and subtraction) of above functions. The addition process of above angular wave functions, i.e. 2,+1 x Ф+1 + 2,-1 x Ф-1 gives the wave function for dzx (or dxz) orbital and subtraction process, i.e. 2,+1 x Ф+1 - 2,-1 x Ф-1, gives the wave function for dyz, orbital, for l = 2 and m = ±2, we have two wave functions viz. 2,+2 x Ф +2 and 2,-2 x Ф-2. Again the values of these wave functions contain imaginary quantity and hence are not accepted. Real and acceptable values are obtained by the normalized linear comlimation of the two angular wave functions. The addition process of above angular wave functions, i.e., 2,+2 x Ф+2 + 2,-2 x Ф-2, gives the wave function for dx2-y2 orbital and subtraction process i.e., Θ2,+2 x Ф +2 - Θ2,-2 x Ф-2, gives the wave subtraction for dxy orbital. When these five angular wave functions for different orbitals obtained above are plotted in three dimensional space, we get the solid curves which give the orientations along the axes or in between the axes as shown below: dxy orbital dyz (or dxz) orbital dzxorbital dx2-y2 orbital dz2 orbital Fig. 1.5 Angular dependence and shapes of d-orbitals. The probability density is the square of the wave function and is positive everywhere. The lobes on the positive or negative side of both the axes are assigned (+) sign and those on UTTARAKHAND OPEN UNIVERSITY Page 13 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 positives side of one axis and negative side of the other or vice versa are assigned (–)sign. The characteristics of the d-orbitals may be summarized as follows: (i) dxy, dyz and dzx (or dxz) as well as dx2-y2 orbitals are double dumb-bell shaped and contain four lobes. The lobes of the first three orbitals are concentrated between xy, yz and zx planes, respectively and lie between their coordinate axes. The lobes of dx2-y2 orbital are concentrated along x and y axes. dz2 orbital has a dumb-bell shape with two lobes along z- axis with (+) sign and a concentric collar or ring around the nucleus in xy plane with (–)sign. (ii) The d-orbitals belonging to same energy shell are degenerate, i.e. have the same energy in a free atom. (iii) The d-orbitals belonging to all main energy shells have similar shape but their size goes on increasing as the value of n and number of nodal points increase. For example, the size of 5d-orbital (number of nodal points = 5 – 2–1=2) is larger than that of 4d-orbital (number of nodal points = 4 – 2 – 1=1). N.B. The shapes of f, g etc. orbitals are beyond the scope of the text. 1.7. QUANTUM NUMBERS These are the integral numbers and most of them (i.e. first three) have been derived from the mathematical solution of Schrodinger’s wave equation for ψ. These numbers serve as the address of the electrons in an atom and hence are also known as identification numbers. These describe the energy of an electron in a shell, radius of that shell (i.e. distance of electron from the nucleus), shape and orientation of the electron cloud (or orbital) and the direction of the spinning of the electron on its own axis. There are four quantum numbers viz. principal quantum number (n), azimuthal or subsidiary quantum number (l), magnetic quantum number (m) and spin quantum number (s). (i) Principal or Radial quantum number This quantum number represents the number of shell or main energy level to which the electron belongs round the nucleus. It is denoted by the letter n. It arises from the solution of radial part of ψ. This quantum number can have integral values 1,2, 3, 4………..etc. which are designated by the letters K,L,M,N……..etc. as follows (proposed by Bohr): Value of n Designation 1 K UTTARAKHAND OPEN UNIVERSITY Page 14 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 2 L 3 M 4 N It can be concluded that the principal quantum number (n) gives an idea of: (a) The shell or main energy level which the electron belongs to. (b) The distance (r) of the electron from the nucleus, i.e. the radius of the shell. (c) The energy associated with the electron. (d) The maximum number of electrons that may be accommodated in a given shell. According to Bohr-Berry scheme, the maximum number of electrons in nth shell = 2n2. Thus the first shell (n = 1) can accommodate (2 x 12 = 2) two elections, second, third and fourth shells with n = 2, 3 and 4 can accommodate eight (2x22 =8), eighteen (2x32 = 18) and thirty- two (2x42 = 32) electrons, respectively. (ii) Azimuthal or Subsidiary quantum number (l) This quantum number is also known as orbital angular momentum quantum number. It is denoted by the letter l and refers to the subshell which the electron belongs to. This quantum number describes the motion of the electron and tells us about the shape of the orbitals of a subshell. The values of l depend on the value of n (the principal quantum number) and may have all possible values from 0 to (n-1), i.e. l = 0,1,2,3……….(n-1). Thus, for a given value of n, total number of l values is equal to n, e.g. when n = 4, l = 0,1,2,3 (total 4 values of l). For each value of l, separate notation is used which represents a particular subshell as shown below; Azimuthal quantum number (l) 0 1 2 3 4 …… Notation for the sub-shell s p d f g …… These notations of subshells have been taken from the characteristics of the spectral lines in atomic spectra. Thus, s stands for sharp, p for principal, d for diffuse and f for fundamental. The subshells belonging to various shells are given below: N L Notation for the subshell 1 0 1s 2 0 2s UTTARAKHAND OPEN UNIVERSITY Page 15 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 1 2p 3 0 3s 1 3p 2 3d 4 0 4s 1 4p 2 4d 3 4f The main points to be noted for azimuthal quantum number are; (a) This gives an idea of the subshell which the electron belongs to. (b) Total number of subshells in a given shell is equal to the numerical value of n (main shell). (c) This quantum number corresponds to the orbital angular momentum of the electron. (d) This gives an idea of the shape of the orbitals of the subshell. (e) The maximum number of electrons that can be accommodated in a given subshell is equal to 2(2l+1). Thus s, p, d and f- subshells with l = 0, 1, 2 and 3 can have a maximum of 2, 6, 10 and 14 electrons, respectively, i.e. s2,p6, d10 and f14 (iii) Magnetic quantum number (m) This quantum number determines the direction of angular momentum of the electrons thereby describing the orientation of orbitals of a subshell in space. The value of m depends on the value of l thus showing that each subshell consists of one or more regions in space with maximum probability of finding the electron (i.e. orbitals). The number of such orbitals (or regions) is equal to the number of ways the electrons can orient themselves in space. This number is equal to (2l + 1) and values of m are represented as (+) l to (–) l through 0. Thus, each value of m represents a particular orbital within a subshell and total number of m values gives total number of orbitals in that subshell. For example, for s-subshell, m =0 corresponding to l=0, i.e. m has only one value indicating that s-subshell has only one orbital or one possible orientation of electrons which is spherically symmetrical around the nucleus. When l=1, (i.e. p-subshell), m has three values viz. +1, 0,-1 implying that p-subshell has three UTTARAKHAND OPEN UNIVERSITY Page 16 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 orbitals or orientations which are perpendicular to each other and point towards x, y, and z- axes. These are designated as px, py, and pz. For l = 2 i.e. d-subshell, m=+2,+1,0,-1,-2,i.e. five values meaning thereby that this subshell has five orbitals or orientations viz., dxy, dyz, dzx, dx2- y2 and dz2. On the same grounds it can be shown for f-subshell (l=3) that it has seven orbitals or orientations corresponding to seven values of m viz., +3,+2, +1,0,-1, -2 and -3. For p, d, and f subshells (l=1, 2 and 3) various m values may be summarized as follows: Subshell Value of l Values of m Total m values p - subshell 1 +1, 0, -1 3 d – subshell 2 +2,+1,0,-1,-2. 5 f – subshell 3 +3,+2,+1,0,-1, -2, -3 7 The main point to be noted for magnetic quantum number is that it determines the total number of orbitals present in any subshell belonging to preferred orientations of electrons in space. (iv) Spin quantum number (s) This quantum number arises from the direction of spinning of electron about its own axis. It is denoted by the letter s which can have only two values shown as (+) and (-) representing clockwise spin(α-spin) or anticlockwise spin (β-spin). These values i.e. (+) and (-) are also represented as ↑ (upward arrow) and ↓ (downward arrow). Being a charged particle, a spinning electron generates a so called spin magnetic moment which can be oriented either up or downward. The value of s for an electron in an orbital does not affect the energy, shape, size or orientation of an orbital but shows only how the electrons are arranged in that orbital. 1.8. PAULI’S EXCLUSION PRINCIPLE This principle was proposed by Pauli in 1924 and as an important rule, governs the quantum numbers allowed for an electron in an atom and determines the electronic UTTARAKHAND OPEN UNIVERSITY Page 17 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 configuration of poly electron atoms. In a general form, this principal states that “In an atom, any two electrons cannot have the same values of four quantum numbers”. Alternatively, this can be put in the form “any two electrons in an atom cannot exist in the same quantum state”. Consequently, it can be said that any two electrons in an atom can have same values of any three quantum numbers but the fourth (may be n or l or m or s) will definitely have different values for them. This can be shown as follows; Value of the all quantum number for any two electron in an atom n l m s Same Same Same Different Same Same Different Same Same Different Same Same Different Same Same Same Thus the values of all the four quantum numbers for any two electrons residing in the same orbital like s, px, py, pz, dxy etc. cannot be the same. For example, in case of 2 electrons in 1s- orbital (i.e. 1s2), the values of n, l and m are same for both the electrons but s has different values as shown below: n l m s 1st electron 1 0 0 + For 1s2 electrons 2nd electron 1 0 0 - The values of s may also be written in the reverse order but by convention the given order is preferred. The important conclusion drawn from this discussion is that “an orbital can accommodate only two electrons with opposite spins”  Application of Pauli’s Exclusion Principle This principle has been used to calculate the maximum number of electrons that can be accommodated in an orbital, a subshell and in a main shell. For example, for K-shell, n=1, UTTARAKHAND OPEN UNIVERSITY Page 18 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 l=0 and m=0 and s can have a value equal to either (+) or (-). These values of n, l, m and s give two sets of values of four quantum numbers as gives above. It is concluded that in K- shell,there shall be only one subshellwith one orbital i.e. the s-orbital is present which can contain only two electrons with s = (+) and (-). For L-shell, n=2, l=0 and 1. The corresponding values of m are 0 (for l=0) and +1, 0, -1 (for l=1). For each value of m, s will have two values, (+) and (-). This leads to eight sets of quantum numbers belonging to eight different electrons. These are shown below: n = 2, l = 0, m = 0, s = + These values correspond to two n = 2, l = 0, m = 0, s = - elections in 2s – orbital. n = 2, l = 1, m = +1, s = + These values correspond to two n = 2, l = 1, m = +1, s = - elections in 2px – orbital. n = 2, l = 1, m = 0, s = + These values correspond to two n = 2, l = 1, m = 0, s = - elections in 2py – orbital. n = 2, l = 1, m = -1, s = + These values correspond to two n = 2, l = 1, m = -1, s = - elections in 2pz – orbital. By convention, the first p-orbital is denoted as px, second as py and third as pz-orbital as given above.Therefore, we can say that an orbital can accommodate maximum two electrons. Further, since same values of 1 for a particular value of n corresponds to a particular subshell, total number of electrons in a subshell can be calculated, e.g., s-subshell contains two and p- subshell (l=1) will accommodate six electrons, respectively. Thus total number of electrons in L-shell will be eight (2 in s and 6 in p-subshell). Likewise, one can calculate total number of electrons in M-shell (18) and N- shell (32) etc. as well as d (10) and f (14) subshells. UTTARAKHAND OPEN UNIVERSITY Page 19 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 1.9. HUND’S RULE OF MAXIMUM MULTIPLICITY This rule states that “electron pairing in the orbitals of a subshell will not take place until each orbital is filled with single electron” (due to same energy of orbitals of a subshell). This is because it is easier for an electron to enter an empty orbital than an orbital which already possesses an electron. If an atom has three electrons in p-subshell, these can be arranged in three p-orbitals as follows: ↓↑ ↑ ↑ ↓ ↑ ↑ ↑ ↑ (a) (b) (c) Among these arrangements, the option(c) is the correct arrangement because this rule can be stated alternatively as “the most stable arrangement of electrons in the orbitals of a subshell is that with greatest number of parallel spins”. It implies that before pairing starts, all the electrons of the subshell have the same spins (parallel). This rule serves as a guideline for filling of multi orbital p, d and f subshells, e.g., the electron pairing in p, d and f-subshells will not start until each orbital of the given subshell contains one electron. Thus pairing starts in the three orbitals of p-subshell at fourth electron, in five orbitals of d-subshell at sixth electron and in seven orbitals of f-subshell at eighth electron, respectively. The electronic arrangements (or configurations) for p4, d6 and f8 systems have been illustrated here along with p3, d5 and f7: P3 : ↑ ↑ ↑ d5 : ↑ ↑ ↑ ↑ ↑ f7 : ↑ ↑ ↑ ↑ ↑ ↑ ↑ P4 : ↑↓ ↑ ↑ d6 : ↑↓ ↑ ↑ ↑ ↑ f8 : ↑↓ ↑ ↑ ↑ ↑ ↑ ↑ Here p3, d5 and f7 provide the examples of maximum multiplicity in the respective subshells and p4, d6 and f8 provide the examples where pairing of electrons in these subshells starts. 1.10. THE AUFBAU PRINCIPLE UTTARAKHAND OPEN UNIVERSITY Page 20 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Aufbau is a German word which means building up or construction. The building up of orbitals implies the filling of orbitals with electrons. This principle gives us the sequence in which various orbitals are filled with electrons. The principle can be stated as “in the ground state of poly electronic atoms, the electrons are filled in various subshells in the increasing order of their energy”. This means the electrons are filled in the subshell of the lowest energy first followed by the higher energy subshells. There are certain rules which constitute the Aufbau principle: (i) In general, the subshells with lower n values are filled first followed by those with higher n-values (called lower n rule). (ii) For any given principal quantum number n, the order of filling up of subshells is s, p, d and f. (iii) (n +l) Rule; sometime lower (n + l) rule is violated. In such cases (n+l) rule is applicable according to which the subshells are filled in order of increasing (n+l) values, e.g., 4s- subshell [(n+l) = 4+0 equal to 4] is filled before 3d subshell [(n+l) =3+ 2 equal to 5) due to lower (n+l) values. Keeping in mind the above discussion, various subshells can be arranged in the order of increasing energy as follows: Energy sequence of subshells for electron filling UTTARAKHAND OPEN UNIVERSITY Page 21 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 This relative order of energy of various subshells of an atom may also be given as follows: 1s energy released during the addition of electron. The net energy change is the energy absorbed (supplied) by the electron, hence the addition of second or third etc. electron to the anion is an endothermic process: A- (g) + e → A2 - (g) + (EA)2 (energy supplied) A2- (g) + e → A3 - (g) + (EA)3 (energy supplied) The electron affinity values for the elements of second period are given below: Element Li Be B C N O F (EA)1 in kJ/mole 60 ≤0 27 122 ≤0 141 328 The electron affinity values of Be and N are shown zero because it is very difficult to add an extra electron to the outer shells of these elements due to extra stability of the electronic configuration. UTTARAKHAND OPEN UNIVERSITY Page 67 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 The electron affinity values of halogens are very high because of the ns2 np5 outer shell electronic configuration and very strong tendency to accept the incoming electron thereby getting converted into the negative ions with noble gas configuration, i.e. ns2 np6. Though the first element of halogen group, is expected to have the highest value of EA,but its EA value is less than that of Cl. This is due to the smaller size and greater electron-electron repulsion in F-atom which opposes the entry of the incoming electron. The EA values of the noble gases are almost zero due to no tendency of accepting the additional electron because of stable ns2 np6 configuration. EA values of halogens and noble gas elements are given below (in k J/mole): Element F Cl Br I At He Ne Ar Kr Xe Rn (EA)1 value 328 349 325 295 280 ≤0 ≤0 ≤0 ≤0 ≤0 ≤0 Factors affecting the electron affinity All the factors which affect the ionization energy also affect the electron affinity. The main factors among them are discussed here: (i) Atomic size Smaller the atomic size, stronger is the attraction of nucleus for the incoming electron and hence greater is its electron affinity and vice versa, i. e. EA∝ (as is seen along a period) (ii) Effective nuclear charge (Zeff) Greater is the effective nuclear change of the elements, stronger is the attraction between it and the electron to be added to the atom. Thus with the increase in Zeff, other factors remaining the same, electron affinity of the elements also increases, i.e. EA∝ Zeff (as is seen along a period). (iii) Stable electronic configuration The atoms of the elements with stable electronic configuration do not show any tendency to accommodate the incoming electron (s). Hence the EA values for such elements is almost zero. For example, the elements of 2nd group with ns2 outer electronic configuration have zero UTTARAKHAND OPEN UNIVERSITY Page 68 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 EA values. The elements of 15th group with ns2np3 outer electronic configuration have zero or very low EA values. The noble gases with ns2np6 stable configuration in the outer shell also have zero EA values i.e. do not have any affinity for the electron (s) to be added to them. The electron affinity of an element can be determined by using the Born-Haber cycle. Periodic trends of electron affinity (i) Variation along the periods In general, with few exceptions, the electron affinity values of the elements go on increasing on moving from left to right in a period, i.e. from alkali metals to halogens. This is because atomic size decreases and the effective nuclear charge increases along a period. Both these factors increase the force of attraction between the nucleus and the incoming electron which is added easily to the outer shell of the host atom. Exceptions are the elements of 2nd, 15th and 18th groups. (ii) Variation in the groups The electron affinity values go on decreasing when we move from top to bottom down in a group. On descending a group, the atomic size and the nuclear charge both increase regularly. The increasing atomic size tends to decrease the EA values while increasing nuclear charge causes an increase in these values. The net result is that the effect produced by the progressive increase in size more than compensates the effect produced by progressive increase in nuclear charge and hence EA values decrease regularly down the group. 3.3.4 Electronegativity ( , chi) In a homoatomic molecule, the bonding pair of electrons lies at the middle of internuclear space. But this is not true for a hetroatomic molecule. As a result polarity is developed on the hetero atoms of the molecule due to the shifting of the bonding pair of electrons towards one particular atom. For example, in H2 or Cl2 molecules, the bonded pair of electrons lies at the middle of two nuclei, i.e. is equally attracted by both the atoms. But in HF or like molecules, the bonded pair of electrons is attracted with stronger force by F atom (in HF) and thus, is shifted towards it from its expected middle position. This causes the development of slight negative change on F and equal positive change on H atom, therefore HF is a polar molecule. UTTARAKHAND OPEN UNIVERSITY Page 69 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 This means an atom in a heteroatomic molecule with stronger affinity for bonding electrons is able to pull them towards itself and takes them away from the atom with weaker affinity for them. In the above example (viz. HF) F is said to have stronger affinity for bonded electrons as compared to that of hydrogen atom.To explain this tendency in heteroatomic molecules, Linus Pauling, in 1932, introduced the concept of electronegativity. According to him “electronegativity is the relative tendency or power of an atom of an element in the heteroatomic molecules to attract the shared pair of electrons towards itself”. Methods of evaluating electronegativity Various chemists have defined and proposed the methods for evaluating electronegativity. These are known as electronegativity scales. (i) Pauling’s Scale Pauling’s definition of electronegativity has been given in the beginning. He used thermodynamic data to calculate the electronegativity of different elements. He considered the formation of AB molecule by the combination of A2 and B2 molecules. A2 + B2 = 2 AB Or A2 + B2 = AB ……… (3.8) This reaction may also be written as (A-A) + (B –B) = A - B because A2, B2 and AB are covalent molecules. This is an exothermic reaction, means the formation of A-B molecules is accompanied by the release of energy, i.e. the bond dissociation energy of A-B covalent bond (EA-B) is always higher than the mean of the bond dissociation energy of A-A (EA-A) and B-B (EB-B) covalent bonds and EA-B> (EA-A+ EB-B) Pauling proposed that the difference in the EA-B and mean of EA-A and EB-B is related to the difference in electro negativities of A (χA) and B (χB) ∴ ∆ = E A-B- (EA-A+ EB-B) = 23 (χB - χA)2 (where χB> χA, ) …….(3.9) Thus, ∆ = 23 (χB - χA)2 Or χB -χA = 0.208 √∆ ……………(3.10) UTTARAKHAND OPEN UNIVERSITY Page 70 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 In place of arithmetic mean, he later used the geometric mean of EA-A and EB-B and expressed the equation as: ∆’ = EA – B- (EA-A x EB-B)1/2 = 30(χB - χA)2 ………(3.11) ∴ ∆’ = 30 (χB - χA) 2 ∴ χB - χA = 0.182 √∆’ ………….(3.12) Here χA and χB are the electronegativities of the atoms A and B. The factors 0.208 and 0.182 arise from the conversion of ∆ measured in kCal/ mole into electron volts. s-block p-block elements 1 2 13 14 15 16 17 18 H He 2.1 0 Li Be B C N O F Ne 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 Na Mg Al Si P S Cl Ar 0.9 1.2 1.5 1.8 2.1 2.5 3.0 0 K Ca Ga Ge As Se Br Kr 0.8 1.2 1.6 1.8 2.0 2.4 2.8 0 Rb Sr In Sn Sb Te I Xe 0.8 1.0 1.7 1.8 1.9 2.1 2.5 0 Cs Ba Tl Pb Bi Po At Rn 0.7 1.9 1.8 1.8 1.9 2.0 2.2 0 UTTARAKHAND OPEN UNIVERSITY Page 71 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Fr Ra 0.7 1.9 Table 3.5: Electronegativity values of s and p-block elements as determined by Pauling (on F = 4.0 scale) From this table it can be noted that the variation in the values of electronegativity is more pronounced among the non-metals. (ii) Allred and Rochow’s Scale Allred and Rochow proposed that the electronegativity of an element (say A) can be calculated by using the following equation: (χA)AR = + 0.744 …………(3.13) where ( A)AR = electronegativity of the element A on Allred and Rochow’s scale, Zeff = effective nuclear charge (Z – σ) at the periphery of the element A, r is radius of the atom of element A in Å. Putting the value of Zeff, the equation can be rewritten as (χA)AR = + 0.744 …………(3.14) The electronegativity values obtained by this method agree closely to those obtained by Pauling’s approach. These values for the elements of first three periods are given below: Table 3.6: Electrongativity values of s and p-block elements belonging to first three periods on Allred and Rochow’s scale Group 1 2 13 14 15 16 17 18 H He 2.20 3.2 Li Be B C N O F NA UTTARAKHAND OPEN UNIVERSITY Page 72 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 0.97 1.47 2.01 2.50 3.07 3.50 4.10 5.1 Na Mg Al Si P S Cl Ar 1.01 1.23 1.47 1.74 2.06 2.44 2.83 3.3 K Ca Ca Ge As Se Br Kr 0.91 1.04 1.82 2.02 2.20 2.48 2.74 3.1 Rb Sr In Sn Sb Te D Xe 0.89 0.99 1.78 1.72 1.82 2.01 2.21 2.4 Cs Ba Tl Pb Bi Po At Rn 0.86 0.97 1.44 1.55 1.67 1.76 1.90 - According to this scale, the inert elements also possess electronegativity. As per the definition given by Pauling, this scale seems to be arbitrary but it has its own importance. (iii) Mulliken’s scale It is based on the ionization energy and electron affinity of an atom of an element. According to Mulliken “the average of ionization energy (IE) and electron affinity (EA) of the atom of an element is a measure of its electronegaivity”. Thus, the electronegativity = …………(3.15) He proposed two relations for obtaining the electronegativity: (a) When the energies are measured in electron volts (eV), then χA = 0.374 + 0.17 = 0.187 + 0.17 ………(3.16) (b) When the energies are expressed in kJ/mole, then χA = ………..(3.17) All these terms χA, IEand EA are for the atom A. UTTARAKHAND OPEN UNIVERSITY Page 73 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Factors affecting the magnitude of electronegativity Various factors which affect the magnitude of the electronegativity of an element qualitatively are as follows: (i) Atomic size It has been observed that the smaller atom has greater tendency to attract the shared pair of electrons towards itself and hence has greater electronegativity. Thus electronegativity α (ii) Charge on the atom (or oxidation state of the element) Higher the amount of positive charge on the atom of an element means higher positive oxidation state, smaller is the size and more is the electronegativity, i.e. electronegativity α positive oxidation state (or charge). (iii) Effective nuclear charge (Zeff) With the increase in the magnitude of Zeff of an element, the electronegativity of that element also increases. This factor may effectively be used to explain the variation of electronegativity in a group or along a period. Thus, electronegativity α Zeff. (iv) Ionization energy and electron affinity According to Mulliken’s scale, electronegativity of an element depends on its ionizations energy and electron affinity, Thus, the atoms of the elements which have higher values of ionization energy and electron affinity also have higher values of electronegativity, i.e. electronegativity α IEand EA. (v) Type of hybridization of the central atom in a molecule It has been observed that electronegativity of an atom having hybrid orbital with greater s- character is high because the electronic charge in hybrid orbitals of an atom in a molecule which has greater s-character remains closer to the nucleus of that atom. For example, the s- character in sp3, sp2, and sp hybrid orbitals of CH4, C2H4 andC2H2 is 25%, 33% and 50%, respectively. Accordingly, the s-character of hybrid orbitals gives more electronegativity to C atom. Hence the electronegativity of carbon atom in these molecules is in the following increasing order: CH4< C2 H4 < C2 H2 Periodic trends of electronegativity (i) Variation in the groups of main group elements UTTARAKHAND OPEN UNIVERSITY Page 74 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 On going down a group of main group elements, the electronegativity values go on decreasing due to increasing atomic size and decreasing Zeff of the elements. At the same time, the electropositive character of the elements also increases causing a reduction in electronegativity values of the elements as well as their ionization energies and electron affinities. (ii) Variation along a period On moving from left to right across a period of main group elements i.e. from alkali metals to halogens, electronegativity values increase with increasing atomic number. This happens secause Zeff increases, electropositive character decreases, atomic size of the elements also decreases thereby increasing electronegativity. Ionization energy and electron affinity, in general, also increase along a period. Applications of Electronegativity On the basis of electronegativity, certain facts in chemistry can be explained which are given below: (i) To predict the nature of bonds With the help of the electronegativity difference χB – χA (where χBχA )….(3.19) (ii) To calculate the bond length In a heterodiatomic molecule of AB type, the bond length dA-B can be calculated provided the molecule has ionic character and the values of atomic radii rA and rB as well as the electronegatitvities χA and χB are known. This can be done by using the Schoemaker and Stevenson equation, viz. dA- B = rA + rB – 9 (χB – χA ) (χB>χA ) …………..(3.20) (iii) To predict the trends in acid-base character (a) The acidic character of the oxides has been bound to increase from left to right along a period because of decreasing χ0 – χB values (χ0 and χB are electro- negativities of oxygen and other atom), e.g. Oxide Na2O MgO Al2O3 SiO2 P4O10 SO2 Cl2O7 χB 0.9 1.2 1.5 1.8 2.1 2.5 3 χ0 – χB 2.6 2.3 2.0 1.7 1.4 1.0 0.5 Nature strongly basic ampoteric weakly acidic strongly strongly basic acidic acidic acidic (b) The acidic character of hydrides of the elements of the same period goes on increasing from left to right across a period. For example, the acidic nature of CH4, NH3, H2O and HF molecules, the hydrides of the elements of second period, increases in the order: CH4, < NH3, < H2O < HF because of the increasing electronegativity of the central atom and increasing elelctronegativity difference between the central atom and hydreogen atom i.e. χcentral atom – χH (c) The acidic character of oxyacids of the elements of the same group and in the same oxidation state, e.g. HClO4, HBrO4 and HIO4 decreases as the electronegativity of central halogen atom decreases as we move down the group form Cl to I (χCl = 3.0) and χI = 2.5 on Pauling’s scale). (iv) To explain the diagonal relationship UTTARAKHAND OPEN UNIVERSITY Page 76 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 It has been found that the elements of second period of the periodic table show similarities in properties with the elements lying diagonally opposite on right hand side in the third period This property is called diagonal relationship. These elements are shown below: Elements of 2nd periodLi Be B C N O F Elements of 3rd period Na Mg Al Si P S Cl This similarity in properties can be explained by various facts and one of them is the concept of electronegativity. The electronegativites of the diagonally opposite elements are almost the same and hence show similar properties. 3.4 TRENDS IN PERIODIC TABLE All the periodic properties, i.e. atomic and ionic radii, ionization energy, electron affinity and electronegativity show variation along the period and down a group. The trends for various properties have been discussed in the respective sections. 3.5 SUMMARY the summary of this unit is :  This unit contains a concise and comprehensive discussion of various periodic properties such as atomic and ionic radii, ionization energy, electron affinity and electronegativity, factors affecting these properties, periodic trends (or variation) of the properties, the methods of their determinations and their applications wherever necessary and available.  The periodic properties are the basis of the physical and chemical properties of the elements which can be predicted keeping in view the above property. TERMINAL QUESTIONS i) Arrange the following ions in the increasing of their size a. Na+, Mg2+, Al3+, F-, O2-, N3- b. C4-, N3- ,O2-, F- ii) Which atom or ion in the following pairs has smaller size and why ? a. Na, Na + b. Be, Mg UTTARAKHAND OPEN UNIVERSITY Page 77 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 c. Fe2,Fe3 iii) Explain giving appropriate reasons: a. The Cl— ion is larger in size than Cl atom. b. The atomic radius decreases with the increasing atomic numbers in a period. iv) Arrange the following in the decreasing order of their ionization energy: Be, B, N, O and F. v) Arrange the Be, B, N, O and F in the increasing order of their electron affinities. vi) EA values of the halogens are the highest in each period. Explain. vii) The noble gases have very high values of ionization energy but their electron affinity values are almost zero. Why? viii) Which of the following elements has the highest values of electronaffinity and why? a. Na, Cl, Si, Ar b. (i)1s2, 2s2, 2p1 (ii) 1s2, 2s2, 2p6, 3s1 (iii) 1s2, 2s2, 2p5 (iv) 1s2, 2s2, 2p3 ix) Distinguish between electron affinity and electronegativity. x) Which element among the following has the highest value of electro negativity and the highest value of electron affinity? F, Cl, O, Br, and I. xi) Which one of the following oxides is basic, amphoteric, and acidic in nature? a. MgO b. Al2O3 c. P4O10 xii) How does electron affinity depend on effective nuclear charge? 3.5 REFERENCES 1. Principles of Inorganic Chemistry: B. R. Puri, L.R. Sharma & K. C. Kalia, Milestone Publishers and Distributers, Daryaganj, Delhi (2013). 2. Selected topics in Inorganic Chemistry: W.U. Malik, G.D. Tuli & R.D. Madan, S. Chand & Co. Ltd., New Delhi (1993). 3. Comprehensive Inorganic chemistry: Sulekh Chandra, New Age International (Pvt.) Ltd., New Delhi (2004). 4. The Nature of the Chemical Bond: Linus Pauling, 3rd Edn., Cornell University Press, New York (1960). 5. A Simple Guide to Modern Valency Theory: G.I. Brown, Revised Edn., Longmans Green, UTTARAKHAND OPEN UNIVERSITY Page 78 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 London (1967). 6. Advanced Inorganic Chemistry: Satya Prakash, G.D. Tuli, S.K. Basu and R.d. Madan, Vol. I, 7th Edn., S. Chand & Co. Ltd, New Delhi (1998). 7. Shriver and Atkins’ Inorganic Chemistry: Peter Atkins et. al., 5th Edn., Oxford University Press, New York (2010). UTTARAKHAND OPEN UNIVERSITY Page 79 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 UNIT 4: CHEMICAL BONDING CONTENTS: 4.1 Objectives 4.2 Introduction 4.3 Covalent bond 4.3.1 Valence bond theory and its limitation 4.3.2 Directional characteristics of covalent bond 4.3.3 Sigma and pi covalent bond 4.4 Hybridization of atomic orbitals 4.4.1 Types of hybridization 4.4.2 Shape of simple inorganic molecules and ions 4.5 Valence shell electron pair repulsion theory (VSEPR) theory 4.6 Molecular Orbital theory 4.6.1 Homonuclear diatomic molecules 4.6.2 Heteronuclear (CO and MO) diatomic molecules 4.7 Multicenter bonding in electron deficient molecules 4.8 Bond strength 4.8.1 Bond energy 4.8.2 Measurement of bond energy 4.9. Percent ionic character 4.10 Summary 4.11Terminal Question 4.12 Answers 4.13 References UTTARAKHAND OPEN UNIVERSITY Page 80 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 4.1 INTRODUCTION The atoms are said to combine together because of the following two main reasons: (i) Concept of lowering of energy It has been observed that the aggregate (or the molecules) are lower in energy than the individual atoms from which they have been formed. This means when the individual atoms combine to form molecules through a bond, the potential energy of the combining atoms decreases and the resulting molecules are more stable than the free atoms. This energy difference between the free atoms and bonded atoms (or molecules) is generally 40kJ mol-1 or more. It follows from this that the process of bond formation between the atoms decreases the energy of the molecule formed from these atoms and forms a system of lower energy and greater stability. (ii) Electronic theory of valence (the octet rule) The atoms of the noble gases-helium to radon- do not, except a few cases, react with any other atoms to form the compounds and also they do not react with themselves. Hence they stay in atomic form. These atoms are said to have low energy and cannot be further lowered by forming compounds. This low energy of noble gas atoms is associated with their outer shell electronic configuration, i.e. the stable arrangement of eight electrons (called octet). It has also been established that the two electrons in case of helium atom (called doublet) is as stable as an octet present in other noble gas atoms. The chemical stability of the octet of noble gases led chemists to assume that when atoms of other elements combine to form a molecule, the electrons in their outer shells are arranged between themselves in such a way that they achieve a stable octet of electrons (noble gas configuration) and thus a chemical bond is established between the atoms. This tendency of the atoms to attain the noble gas configuration of eight electrons in their outer shell is known as octet rule or rule of eight and when the atoms attain the helium configuration, it is called doublet rule or rule of two. This octet rule was later called “Electronic Theory of Valence”. It may be noted here that in the formation of a chemical bond, atoms interact with each other by losing, gaining or sharing of electrons so as to acquire a stable outer shell configuration of eight electrons. This means, an atom with less than eight electrons in the UTTARAKHAND OPEN UNIVERSITY Page 81 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 outer shell is chemically active and has a tendency to combine with other atoms. Accordingly, three different types of bonds may exist in the molecules/aggregates. 4.2 OBJECTIVES The objective of writing the text of this unit is :  Under this unit you will be understand various facts regarding the driving force that makes the isolated atoms to combine to form the polyatomic molecules or ions as well as to find the answers of certain interesting questions.  In this unit you will be gaining about the valence bond theory and its limitation, directional characteristics of covalent bond and known about the Sigma and pi covalent bond.  Under this unit you enhance the knowledge in the concepts of the different type hybridization of atomic orbitals and shape of simple inorganic molecules and ions.  In this unit you will be able to about the valence shell electron pair repulsion theory (VSEPR) theory and the molecular orbital theory for the homonuclear diatomic molecules and heteronuclear (CO and MO) diatomic molecules.  And end of the this unit you able to known multi-center bonding in electron deficient molecules, Bond strength, Bond energy, Measurement of bond energy and Percent ionic character. 4.3 COVALENT BOND A covalent bond is formed between the two combining atoms, generally of the electronegative non-metallic elements by the mutual sharing of one or more electron pairs (from their valence shell). Each of the two combining atoms attains stable noble gas electronic configuration, thereby enhancing the stability of the molecule. If one electron pair is shared between the two atoms, each atom contributes one electron towards the electron pair forming the bond. This electron pair is responsible for the stability of both the atoms. A covalent bond is denoted by the solid line (-) between the atoms. Depending on the number of shared electron pairs i.e. one, two, three etc. electron pairs between the combining atoms, the bond is known as a single, double, triple etc. covalent bond. For example, UTTARAKHAND OPEN UNIVERSITY Page 82 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 H:H H-H Cl:Cl Cl-Cl single bond H:Cl H-Cl O::O O=O double bond N:::N N≡N triple bond multiple bond In the molecules, the bond strength and bond length has been found in the following order: Bond strength: triple bond > double bond > single bond Bond length: triple bond < double bond < single bond It may be noted that the covalent bond formation between multielectron atoms involves only the valence shell electrons that too, the unpaired electrons. Thus O-atom has two unpaired electrons in its valence shell and N-atom has three unpaired electrons thereby forming two and three bonds with themselves or other atoms. Polar and non-polar covalent bond In the examples given above, most of the bonds viz. single, double and triple covalent bonds, have been shown to be formed between the like atoms such as H-H, Cl-Cl, O=O and N≡N in H2, Cl2, O2 and N2, respectively. The bonded atoms in these molecules attract the bonding or shared pair of electrons by equal forces towards themselves due to equal electronegativity of the atoms. Hence the bonding pair of electron lies at the mid point of the internuclear distance ( or bond distance). This type of bond is known as the non-polar covalent bond. But if the covalent bond is formed between two unlike atoms of different elements, e.g. HCl, H2O, NH3 etc., the shared pair of electrons will not be equally attracted by the bonded atoms due to electronegativity difference. It shifts towards more electronegative atom and hence moves away from less electronegative atom. This develops small negative charge on more electronegative atom and equal positive charge on less electronegative atom. Such a molecule is called a polar molecule (this is different from ionic bond) and the bond present in such molecules is known as polar covalent bond. For example, UTTARAKHAND OPEN UNIVERSITY Page 83 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 4.3.1. Valence Bond Theory (VBT) and its limitations: This theory was put forward by Heitler and London in 1927 to explain the nature of covalent bond. They gave a theoretical treatment of the formation of the bond in H2 molecule and the energy changes taking place therein. Later, it was extended by Pauling and Slater in 1931 to account for the directional characteristics of the covalent bond. The main points called the postulates of this theory are given below: (i) The atoms involved in the bond formation maintain their individuality(identity) even after the bond is formed i.e. in the molecule. (ii) The bond is formed due to the overlapping of half filled atomic orbitals (or the interaction of electron waves) belonging to the valence shell of the combining atoms as these approach each other. Thus the spins of the two electrons get mutually neutralized. The electrons in the orbitals of inner shells remain undisturbed. (iii) The filled orbitals (i.e. containing two electrons) of the valence shell do not take part in the bond formation. However, if the paired electrons can be unpaired without using much energy, they are first unpaired by promoting to the orbitals of slightly higher energy and then can take part in bonding. For example, N can form NCl3 only retaining a lone pair while P can form both PCl3 and PCl5. (iv) The electrons forming the bond undergo exchange between the atoms and thus stabilize the bond. (v) The strength of the covalent bond depends on the extent to which the two atomic orbital overlap in space. This theory is based on two main theorems which are: (a) If ΨA(1) and ΨB(2) are the wave functions of the orbitals containing electrons in two isolated independent atoms A and B with energies EA and EB, respectively then the total wave function Ψ of the system can be given as a product of wave functions of two atoms, i.e. Ψ= ΨA(1). ΨB(2) ……(4.1) and the energy of the system by E=EA+EB …….(4.2) Where (1) and (2) indicate two electrons belonging to atoms A and B. (b) If a system can be represented by a number of wave functions such as Ψ1, Ψ2, Ψ3 ……, then the true wave function Ψ can be obtained by the process of linear combination of all these wave functions as: UTTARAKHAND OPEN UNIVERSITY Page 84 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Ψ= N(C1Ψ1+C2Ψ2+C3Ψ3+……) …..(4.3) Where N is normalization constant and C1, C2, C3…are the coefficients indicating the weight of each of Ψs. They are so adjusted as to give a state of lowest energy. The squares of the coefficients may be taken as the measure of the weight of each wave function to total wave function. The valance bond theory was first applied to the formation of H2 molecule. If the two H- atoms, viz. HA and HB are infinitely apart from each other, there is no interaction at all but if these are brought close together, HA- HB covalent bond is formed and the energy of the system is decreased. Now if the orbitals of the two H-atoms are represented in terms of wave functions ΨA and ΨB, then the wave function for the system HA.HB can be written as Ψ=ΨA(1). ΨB(2) ……(4.1 as given above) Where electrons belonging to HA and HB are 1 and 2. But once the bond is formed, the electrons 1 and 2 have equal freedom to get associated with either of the H-atoms. Thus due to the exchange of electrons between H-atoms, two possible covalent structures of H2 molecule may shown as HA(1).HB(2) and HA(2).HB(1). The wave functions of these structures are ΨA(1). ΨB(2) and ΨA(2). ΨB(1) respectively. Now the true wave function for H2 molecules can be obtained by linear combination of the wave functions for the two covalent structures. This can be done in two ways: (i) When the combination of these wave functions takes place in a symmetric way, i.e. by addition process, symmetric wave function Ψs is obtained: Ψs= ΨA(1). ΨB(2) + ΨA(2). ΨB(1) ……..(4.4) This is also known as covalent wave function, Ψ cov. (ii) When the combination of the above wave functions takes place in a asymmetric way i.e. by subtraction process, asymmetric wave function, Ψa, is obtained: Ψa= ΨA(1). ΨB(2) - ΨA(2). ΨB(1) …….(4.5) The value of Ψs does not change by exchange of electrons 1 and 2 but that of Ψa changes in this process. The two situations are presented graphically as follows: (Fig 4.1) The curve s is for addition process and curve a is for subtraction process of the wave functions. The calculated value of ro for the minimum energy state i.e. the bonding state is 87 pm against the experimental value of 74 pm. UTTARAKHAND OPEN UNIVERSITY Page 85 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Fig 4.1 Pauling has suggested that the bond between two H-atoms in H2 molecule is not absolutely covalent, it rather has partial ionic character. He proposed two ionic structures for H2 molecule in which both the electrons 1and 2 are either attached to HA or HB as given below, HA(1,2). H+B H+A.HB(1,2) If the above wave functions for these structures are Ψ(1) and Ψ(2), then Ψ(1)= ΨA(1). ΨA(2) …..(4.6) And Ψ(2)= ΨB(1). ΨB(2) ……(4.7) The consideration of ionic structures as given above of H2 molecule converts the equation 4.4 to Ψs=[ΨA(1). ΨB(2) + ΨA(2). ΨB(1)] +λ [Ψ(1)+Ψ(2)] or Ψs=[ΨA(1). ΨB(2)+ ΨA(2). ΨA(1)] + λ[ΨA(1). ΨA(2)+ ΨB(1). ΨB(2)]..(4.8) or Ψs =Ψcov. + Ψionic …..(4.9) the coefficient λis used in equation 4.8 is a measure of the degree to which the ionic forms contribute to the bonding. Thus three important contributions to covalent bonding may be summarized as follows: (i) Delocalization of electrons over two or more nuclei (ii) Mutual screening (iii) Partial ionic character. Limitations of Valence Bond theory: UTTARAKHAND OPEN UNIVERSITY Page 86 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 (i) The formation of coordinate covalent bond (also known as dative bond) cannot be explained on the basis of this theory because according to this theory a covalent bond is formed as a result of overlapping of half filled orbitals of the combining atoms and the paired orbitals of the atoms do not take part in normal covalent bond formation. ii) The odd electron bond formation between the atoms cannot be explained by this theory because a covalent bond is an electron pair bond means two electrons are required for a bond. iii) This theory is unable to explain the paramagnetic behaviour of oxygen molecule because paramagnetism is a property caused by the presence of unpaired electrons and in an oxygen molecule, according to VBT, two electron pair bonds are present between the oxygen atoms and hence it should be diamagnetic. iv) In some molecules, the properties like bond length and bond angles could not be explained by assuming simple overlapping of atomic orbitals of the atoms. 4.3.2 Directional characteristics of covalent bond: The covalent bonds are directed in space. This fact is evidenced by the stereoisomerism and a wide variety of geometrical shapes shown by the covalent compounds. It is also possible to measure the actual bond angles between covalent bonds in the molecules because of the directional nature of bonds. An important fact about the covalent bonds is that these are formed by the overlapping of pure as well as hybridised atomic orbitals. All these atomic orbitals except the pure s-orbitals, are oriented in the particular directions which determine the direction of covalent bonds i.e. the direction in which the overlapping orbitals have the greatest electron density. From this discussion we can conclude that it is the directional nature of p, d and f orbitals which accounts for the directional nature of the covalent bond. For example, the three p-orbitals are directed along the three axes x,y and z and the bonds formed by their overlapping are also directed towards the three axes. Though the s-orbitals are spherically symmetrical around the nucleus, their overlapping along the molecular axis gives a bond in that direction. Let us discuss the modes of overlapping of pure and some of the hybridised atomic orbitals: (i) s-s overlapping This type of overlapping occurs between the s-orbitals of the combining atoms thereby giving the s-s covalent bond. This type of overlapping always occurs in the direction of molecular or internuclear axis. UTTARAKHAND OPEN UNIVERSITY Page 87 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Fig 4.2 ovrelapping of two s-orbitals along molecular axis (ii) s-p overlapping The overlapping taking place between the s-orbital of one atom and p-orbital of another atom is called s-p overlapping. The resulting bond is the s-p covalent bond formed in the direction of the orientation of p-orbital taking part in overlapping (fig. 4.2). (iii) p-p overlapping When the p-orbital of one atom overlaps with the p-orbital of another atom, this process is called p-p overlapping and the bond so formed is known as p-p covalent bond. The necessary condition for this type of overlapping is that the p-orbitals must be of the same type, i.e. px and px, py and py and pz and pz. The px-py or px-pz type of overlapping does not occur (fig 4.3). If an atom possesses two or three half filled orbitals, they can simultaneously overlap with another similar atom (or other atoms as well) thereby forming multiple bonds (both σ and π), for example oxygen molecule. Similarly bonding in N2 can be explained. Fig 4.3 overlapping of orbitals forming σ and πbonds Overlapping of the hybrid orbitals with pure atomic orbitals UTTARAKHAND OPEN UNIVERSITY Page 88 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 The s and p-orbitals may overlap with hybrid orbitals to give the directional covalent bonds such as s-sp (BeH2), s-sp2 (BH3 ,C2H4), s-sp3 (CH4 and higher alkanes), p-sp (BeCl2), p-sp2 (BCl3), p-sp3 (CCl4), p-sp3d (PCl5), p-sp3d2 (SF6) p-sp3d3(IF7) etc. bonds in the directions of hybrid orbitals. d and f - orbitals in non-metallic elements (which mostly form covalent compounds) do not generally take part in overlapping as such to form covalent bonds but d- orbitals may participate in hybridisation, e.g. in PCl5, SF6, higher intehalogens etc. and form covalent bonds by the overlapping of hybrid orbitals with atomic orbitals in the directions of hybrid orbitals. (v) Overlapping of the hybrid orbitals among themselves. This type of overlapping mainly occurs among the organic compounds, e.g. sp-sp(C2H2), sp2-sp2(C2H4), sp3-sp3(C2H6) etc. Here only the overlapping of hybrid orbitals with themselves has been given. 4.3.3 Sigma (σ) and pi (π) covalent bonds: σ Covalent bonds The covalent bond formed between the two atoms by axial or head on overlapping of pure or hybrid atomic orbitals belonging to valence shells of the atoms is called a σ bond. Pure s-orbitals of the atoms on overlapping with s or p atomic orbitals or hybrid orbitals of other atoms always form σ bonds. Pure p-orbitals of the atom when overlap with s and p- orbitals (of the same symmetry) or hybrid orbitals of other atoms also form σ bonds. d and f- orbitals by themselves seldom take part in σ bond formation through the d-orbitals are sometimes involved in hybridisation and thus form a σ bonds, e.g. PCl5, SF6, IF7 etc. The overlapping of hybrid orbitals between two atoms always gives σ bond. (i) Pure atomic orbital overlapping Fig 4.4 formation of σ bond by atomic orbitals (ii) Hybrid atomic orbital – hybrid atomic orbital overlapping UTTARAKHAND OPEN UNIVERSITY Page 89 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Fig 4.5 formation of σ bond by hybrid orbitals In this case only partial overlapping has been shown though other hybrid orbitals will also form σ bonds, generally with atomic orbitals of other atoms. Similarly sp3-sp3σ bond formation may also be shown. π (pi) Covalent bond A covalent bond formed between two atoms by side to side or lateral (perpendicular to the molecular axis) overlapping of only p-atomic orbitals or sometimes p and d- orbitals belonging to the valence shell of the atoms is called a π bond. If in a molecule, a particular atom uses one of its p-orbitals for σ bond formation then rest of the two p-orbitals are used to form the π bonds by lateral overlapping. For example, if x axis is taken as the molecular axis, then π bond is formed by py - py or pz-pz overlapping as happens in the oxygen and nitrogen molecules. Fig 4.6 formation of π bond by lateral overlapping of atomic orbitals For σ and π bonds, the following points are important: (i) A σ bond is formed by axial overlapping of either pure or hybrid atomic orbitals of the two combining atoms while a π bond results from the lateral overlapping of the pure atomic orbitals. UTTARAKHAND OPEN UNIVERSITY Page 90 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 (ii) A σ bond is stronger than a π bond due to greater extent of overlapping of orbitals along the inter nuclear axis than in lateral overlapping. (iii) A σ bonds determine the direction of the covalent bond and bond length, π bonds have no effect on the direction of the bond. However, their presence shortens the bond length. (iv) There is free rotation of the atoms about a σ bond because the electron cloud overlaps symmetrically along the internuclear axis while this is not possible about a π bond because the electron clouds overlap above and below the plane of the atoms. (v) A σ bond has its free existence between any two atoms in a molecule while π bond is formed between the atoms only when σ bond already exists. The shapes of covalent molecules and ions can be explained by employing (a) the concept of hybridisation and (b) VSEPR Theory. 4.4 HYBRIDISATION OF ATOMIC ORBITALS It is the theoretical model used to explain the covalent bonding in the molecules and is applied to an atom in the molecule. To explain the anomaly of expected mode of bonding (according to VBT) shown by Be, B and C in their compounds where these elements should be zero-valent, mono-valent and bivalent due to the presence of 0,1 and 2 unpaired electrons in their valence shells and the observed bonding exhibited by them, i.e. these are bivalent, trivalent and tetra-valent due to the availability of 2,3 and 4 unpaired electrons in their valence shells in those compounds, a hypothetical concept of hybridisation was put forward. According to this concept, before the bonding occurs in the compounds of Be, B and C, one of the 2s electrons gets promoted to the vacant 2p orbital due to the energy available from the heat of reaction when covalent bonds are formed or perhaps due to the field created by the approaching atoms, thereby making 2,3 and 4 unpaired electrons available in the valence shell of the atoms of these elements. These orbitals having unpaired electrons then mix up together or redistribute their energy to give rise a new set of orbitals equivalent in energy, identical in shape and equal to the number of atomic orbitals mixed together. This process is known as hybridisation, the atomic orbitals are said to be hybridised and the new orbitals formed are called the hybrid orbitals. The hybrid orbitals so formed then overlap with the half filled orbitals of the approaching atoms and form covalent bonds. UTTARAKHAND OPEN UNIVERSITY Page 91 FUNDAMENTAL CHEMISTRY-I CHE(N)-101 Salient features (or the Rules) of hybridisation i) The atomic orbitals belonging to the valence shell of the central atom/ion of a molecule/ion with almost similar energies mix up together or hybridise to give the hybrid obitals. But the atomic orbitals of the central atom participating in the π bond formation are excluded from the hybridisation process. ii) The number of hybrid orbitals produced is equal to the number of atomic orbitals undergoing hybridisation. The hybrid orbitals like pure atomic orbitals can accommodate a m