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## Inorganic Chemistry

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**Inorganic Chemistry**Bonding and Coordination Chemistry Books to follow Inorganic Chemistry by Shriver & Atkins Physical Chemistry: Atkins C. R. Raj C-110, Department of Chemistry**Bonding in s,p,d systems: Molecular orbitals of diatomics,**d-orbital splitting in crystal field (Oh, Td). Oxidation reduction: Metal Oxidation states, redox potential, diagrammatic presentation of potential data. Chemistry of Metals: Coordination compounds (Ligands & Chelate effect), Metal carbonyls – preparation stability and application. Wilkinson’s catalyst – alkene hydrogenation Hemoglobin, myoglobin & oxygen transport**H2 // Na+Cl- // C60**CHEMICAL BONDING:A QUANTUM LOOK**“ A moving ball**I know it all ” Failure of Classical Mechanics • Total energy, E = ½ mv2 + V(x) • p = mv ( p = momentum ) • E = p2/2m + V(x) ……… . . Eq.1**Newton’s second law is a relation between the acceleration**d2x/dt2 of a particle and the force F(x) it experiences. • Therefore, v = p/m • Or, p• = F(x) “ Hit the ball hard, it will move fast Hit it soft, it will move slow” • Continuous variation of energy is possible. Macroscopic World: “Classical Mechanics - the God”**Certain experiments done in late 19th century and early 20th**century gave results, totally at variance with the predictions of classical physics. All however, could be explained on the basis that, classical physics is wrong in allowing systems to possess arbitrary amounts of energy. • For example, photoelectric effect.**Max Planck E = h**A young Max Planck was to give a lecture on radiant heat. When he arrived he inquired as to the room number for the Planck lecture. He was told, "You are much too young to be attending the lecture of the esteemed professor Planck." 1900 German physicist “Each electromagnetic oscillator is limited to discrete values and cannot be varied arbitrarily”**Plank had applied energy quantization to the oscillators in**the blackbody but had considered the electromagnetic radiation to be wave.**Classical expectations**As intensity of light increases, force increases, so KE of ejected electrons should increase. Maximum KE of ejected electrons is independent of intensity, but dependent on ν Electrons should be emitted whatever the frequency ν of the light. Actual results: For ν<ν0 (i.e. for frequencies below a cut-off frequency) no electrons are emitted J.J. Thomson Hertz PHOTOELECTRIC EFFECT When UV light is shone on a metal plate in a vacuum, it emits charged particles (Hertz 1887), which were later shown to be electrons by J.J. Thomson (1899). Light, frequency ν Vacuum chamber Collecting plate Metal plate I Ammeter Potentiostat**No electrons are ejected, regardless of the intensity of the**radiation, unless its frequency exceeds a threshold value characteristic of the metal. • The kinetic energy of the electron increases linearly with the frequency of the incident radiation but is independent of the intensity of the radiation. • Even at low intensities, electrons are ejected immediately if the frequency is above the threshold.**Major objections to the Rutherford-Bohr model**• We are able to define theposition and velocity of each electron precisely. • In principle we can follow the motion of each individual electron precisely like planet. • Neither is valid.**Werner HeisenbergHeisenberg's name will always be associated**with his theory of quantum mechanics, published in 1925, when he was only 23 years. • It is impossible to specify the exact position and momentum of a particle simultaneously. • Uncertainty Principle. • x p h/4 where h isPlank’s Constant,a fundamental constant with the value 6.62610-34 J s.**1879 – 1955**Nobel prize 1921**July 1, 1946**Einstein was the father of the bomb in two important ways: 1) it was his initiative which started U.S. bomb research; 2) it was his equation (E = mc2) which made the atomic bomb theoretically possible.**Einstein could never accept some of the revolutionary ideas**of quantum mechanics. When reminded in 1927 that he revolutionized science 20 years earlier, Einstein replied, "A good joke should not be repeated too often."**Einstein**h = ½ mv2 + • KE1/2mv2 = h- • is the work function • h is the energy of the incident light. • Light can be thought of as a bunch of particles which have energy E = h. The light particles are called photons.**If light can behave as particles,why not particles behave as**wave? Louis de Broglie The Nobel Prize in Physics 1929 French physicist (1892-1987)**Louis de Broglie**• Particles can behave as wave. • Relation between wavelength and the mass and velocity of the particles. • E = h and also E = mc2, • E is the energy • m is the mass of the particle • c is the velocity.**Wave Particle Duality**• E = mc2 = h • mc2 = h • p = h /{ since = c/} • = h/p = h/mv • This is known aswave particle duality**Flaws of classical mechanics**Photoelectric effect Heisenberg uncertainty principle limits simultaneous knowledge of conjugate variables Light and matter exhibit wave-particle duality Relation between wave and particle properties given by the de Broglie relations The state of a system in classical mechanics is defined by specifying all the forces acting and all the position and velocity of the particles.**Wave equation?Schrödinger Equation.**• Energy Levels • Most significant feature of the Quantum Mechanics: Limits the energies to discrete values. • Quantization. 1887-1961**The wave function**For every dynamical system, there exists a wave function Ψ that is a continuous, square-integrable, single-valued function of the coordinates of all the particles and of time, and from which all possible predictions about the physical properties of the system can be obtained. Square-integrable means that the normalization integral is finite If we know the wavefunction we know everything it is possible to know.**Derivation of wave equation**Time period = T, Velocity = v, v = l/T, Frequency, n = 1/T, v = n l****An Electron Wave is similar to waves of light, sound & string Wave motion of a String: Amplitude vs. Position**y**1 x π 3π/2 T/2 3π 5π π/2 2π 5π/2 7π/2 9π/2 T 2T 4π -1 Displacement y (m) A Time t (s) -A**Displacement y (m)**T/2 T 2T A Time t (s) -A • Maximum displacement A • Initial condition**y**x Displacement of a particle in SHM y(x) = A sin 2x/ A = maximum amplitude y = amplitude at point x at t = 0 At x = 0 , /2, , 3/2, 2, the amplitude is 0 At x = /4, 5/4, 9/4, the amplitude is maximum.**y**x A wave eqn. is born If the wave is moving to the right with velocity ‘v’ at time ‘t’ • y(x,t) = A sin 2/(x-vt) • = v/ • y = A sin 2n(x/v - t) • Differentiating y W.R.T x, keeping t constant • d2y/dx2 + (4p2/ l2) y = 0**In three dimension the wave equation becomes:**• d2y/dx2 + d2y/dy2 + d2y/dz2+(4p2/l2)y = 0 • It can be written as2y+(4p2/l2)y= 0 • We have l = h/mv • 2y + (4p2m2v2/h2) y = 0 • E = T + V or T = (E-V) (E = total energy) • V = Potential energy, T = Kinetic energy • T = 1/2 mv2 = m2v2/2m • m2v2 = 2m(E-V)**{(-h2/82m)(2/x2 + 2/y2 + 2/z2) + V} **= E 2y + (8p2m/ h2)(E - V) y = 0 • This can be rearranged as • {(- h2/8p2m) 2 + V}y = Ey • Hy = Ey • H = [(-h2/8p2m)2 + V)Hamiltonian operator d2y/dx2 + (4p2/ l2) y = 0**-e**r +Ze How to write Hamiltonian for different systems?{(-h2/82m)2 + V} = E • Hydrogen atom: • KE = ½ m (vx2 + vy2 + vz2) • PE = -e2/r, (r = distance between the electron and the nucleus.) • H = {(-h2/82m) 2 –e2/r} • 2 + (82 m/h2)(E+e2/r) = 0 • If the effective nuclear charge is Ze • H = {(-h2/82m )2 –Ze2/r}**H2+ Molecule**e (x,y,z) ra rb A RAB B the wave function depends on the coordinates of the two nuclei, represented by RA and RB, and of the single electron, represented by r1.**e (x,y,z)**ra rb A B Rab H2+ {(-h2/82m)2 + V} = E • PE = V = -e2/ra – e2/rb+ e2/Rab • H = (-h2/82m)2 + ( – e2/ra - e2/rb + e2/Rab) • The Wave equation is • 2 + (82 m/h2) (E+ e2/ra + e2/rb – e2/Rab) = 0 Born-Oppenheimer approximation**e1 (x1, y1, z1)**He Atom r12 r1 e2 (x2, y2, z2) r2 Nucleus (+2e) {(-h2/82m)2 + V} = E • V = -2e2/r1 – 2e2/r2 + e2/r12 • H = (-h2/82m) (12 + 22)+ V • The Wave equation is • (12 + 22 ) + (82 m/h2)(E-V) = 0**e1 (x1, y1, z1)**r12 e2 (x2, y2, z2) ra2 H2 ra1 rb2 rb1 A B Rab • PE = V = ? • H = (-h2/82m)(12 + 22)+ V • The Wave equation is • (12 + 22 ) + (82 m/h2)(E-V) = 0**V = -e2/40[1/ra1+1/rb1 + 1/ra2 +1/rb2-1/r12-1/Rab]**attractive potential energy Electron-electron repulsion Internuclear repulsion**a**V=0 x =0 x =a Particle in a box An electron moving along x-axis in a field V(x)**a**V=0 x =0 x =a d2 /dx2 + 82 m/h2 (E-V) = 0 Assume V=0 between x=0 & x=a Also = 0 at x = 0 & a d2/dx2 + [82mE/h2] = 0 d2/dx2 + k2 = 0 where k2 = 82mE/h2 Solution is: = C cos kx + D sin kx • Applying Boundary conditions: • = 0 at x = 0 C = 0 = D sin kx**a**V=0 x =0 x =a • = D sin kx • Applying Boundary Condition: • = 0 at x = a, D sin ka = 0 • sin ka = 0 or ka = n, • k = n/a • n = 0, 1, 2, 3, 4 . . . • n = D sin (n/a)x • k2 = 82m/h2[E] or E = k2h2/ 82m • E = n2 h2/ 8ma2k2= n2 2/a2 • n = 0 not acceptable: n = 0 at all x • Lowest kinetic Energy = E0 = h2/8ma2**a**V = V = x = 0 x = a Energy is quantized An Electron in One Dimensional Box • n = D sin (n/a)x • En = n2 h2/ 8ma2 • n = 1, 2, 3, . . . • E = h2/8ma2 , n=1 • E = 4h2/8ma2 , n=2 • E = 9h2/8ma2 , n=3**MAX BORN**Characteristics of Wave Function He has been described as a moody and impulsive person. He would tell his student, "You must not mind my being rude. I have a resistance against accepting something new. I get angry and swear but always accept after a time if it is right."**Characteristics of Wave Function: What Prof. Born Said**• Heisenberg’s Uncertainty principle: We can never know exactly where the particle is. • Our knowledge of the position of a particle can never be absolute. • In Classical mechanics, square of wave amplitude is a measure of radiation intensity • In a similar way, 2 or * may be related to density or appropriately the probability of finding the electron in the space.**The wave function is the probability amplitude**Probability density