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PAPER III - PHYSICAL CHEMISTRY - I

UNIT - I Symmetry elements and symmetry operations: definition of identical and equivalent elements - configurations-symmetry operations and symmetry elements - rotation-axis of symmetry- reflections-symmetry planes-inversion center-improper rotations-rotation-reflection axis-effect of performing successive operations (commutative and non - commutative) - inverse operations. Groups and their basic Properties: Definition of a group - basic properties of a groupdefinition of Abelian group-isomorphic group-similarity transformation and classesgroup multiplication tables - symmetry classification of molecules into point groups (Schoenflies symbol only) difference between point group and space group.

UNIT-II Definition of reducible and irreducible representations-irreducible representations as orthogonal vectors-direct product rule-the great orthogonality theorem and its consequences (statement only proof not needed)-determinations of the characters for irreducible representation of C2v and C3v point groups using the orthogonality theoremcalculation of binary co-ordinates in the character tables for C2v and C3v point groups— calculation of character values of reducible representations per unshifted atom for each type of symmetry operation-determination of total Cartesian representation— determination ot direct sum from total Cartesian representation. Group theory and vibrational spectroscopy-vibrational modes as basis for goup representation- symmetry selection rules for IR and Raman spectra (mutual exclusion principle)-classification of vibrational modes. Anx.23 D - M Sc Chemistry (SDE) 2007-08 Page 7 of 16

UNIT I
II

1. The time-dependent and time-independent schrodinger equations — Born’s interpretation of the wave function. Requirements of the acceptable wave function. 2. Algebra of operators. Sums and products of operators. Commutator. Linear operators. Eigen functions and eigen values. Correspondence between physical quantities in classical mechanics and operators in quantum mechanics. Hamiltonian operator. Angular momentum operator. Quantization of angular momentum and its spatial orientation. Average (expecation) values. Postulates of quantum mechanics.

UNIT-IV 1. Particle in a one—dimensional box. Quantization of energy. Normalization of wave function. Orthogonality of the particle in a one—dimensional box wave functions. Illustration of the uncertainty principle and correspondence principle with reference to the particle in a one dimensional box. Particle in a three-dimensional box. Separation of variables. 2. Solving of Schrodinger equation for the one—dimensional harmonic oscillator. Harmonic oscillator model of a diatomic molecule. Illustration of the uncertainty principle and correspondence principle with reference to harmonic oscillator. 3. Solving of Schrodinger equation for a rigid rotor. Rigid rotor model of a diatomic molecule.

UNIT-V 1. Schrodinger equation for the H-atom (or H-like species) separation of variables (solving of radial equation is not needed but nature of solution is given), energy levels. Radial factors of the H-atom wave functions. Orbitals and orbital shapes. Probability density and radial distribution functions. The most probable distance of the H-atom (or H-like species) 1S electron. 2. Need for approximation methods. The perturbation theory (first order only). Application of the perturbation method to He-atom. 3. The variation method. Application of variation method to He-atom.

UNIT-VI Themodynamics and Non-ideal systems: Chemical potential and the definition of fugacity. Determination of fugacity of gases by graphical method and from equations of state. Variation of fugacity with temperature. Fugacity and the standard state for non - ideal gases. Definition of activity. Activity coefficient. Temperature coefficient of activity. Standard states. Applications or activity concept to solutions. The rational and practical approaches. Measurement of activity of solvent from colligative properties. Determination of activity of solute. Anx.23 D - M Sc Chemistry (SDE) 2007-08 Page 8 of 16 Third Law of Thermodynamics: Probability and third law. Need for third law. Nernst heat theorem and other forms stating third law. Thermodynamic quantities at absolute zero. Statistical meaning of third law and apparent exception.

UNIT-VII Quantum statistics: Maxwell - Boltzmann statistics. Thermodynamic probability. Thermodynamic probabilities of systems in equilibrium. Boltzrnann expression for entropy. Stirling’s approximation. States of maximum thermodynamic probability. Legrangian multipliers, thermodynamic probabilities of systems involving energy levels. Maxwell - Boltzmann distribution law. Evaluation of alpha and beta in M.B. distribution law. Partition function: Partition function - definition, justification of nomenclature, microcanonical and canonical ensembles. Molecular partition function and canonical function. The relation between the total partition function of a molecule and the separate partition functions.

UNIT-VIII ‘Translational partition function, rotational partition function. Effect of molecular symmetry on rotational partition function. Ortho and para hydrogen. Vibrational partition function. Electronic partition function. Heat capacities of solids: Einstein’s and Debye’s theories of heat capacities of solids. Bose-Einstein and Fermi-Dirac Statistics: Bose-Einstein distribution law. Entropy of Bose- Einstein gas. Plank distribution law for black-body radiation. Fermi - Dirac distribution law. Entropy of a Fermi-Dirac gas. PAPER VI - PHYSICAL CHEMISTRY-II

UNIT-I Theories of reaction rates: Arrhenius theory. Hard - sphere collision theory of gas - phase reactions. Activated complex theory or absolute reaction rate theory(ARRT) for ideal gas reactions (in terms of partition functions). Relation between activated - complex theory and hard - sphere collision theory. Thermodynamic formulations of activated complex theory & kinetic isotopic effect.

UNIT-II 1. Reactions in solution: Comparison between gas-phase and solution reactions. The influence of the solvent on the reactions between ions. Influence of ionic strength on rates of reactions in solution - Primary salt effect. Influence of pressure on rates of reactions in solution Significance of volume and entropy of activations. Anx.23 D - M Sc Chemistry (SDE) 2007-08 Page 13 of 16 2. Study of Fast reactions: Flow methods, pulse methods, relaxation methods, Shock-tube method & nuclear magnetic resonance method.

UNIT-III 1. Homogeneous catalysis: Specific and general acid - base catalysis. Bronsted catalysis law. Hammett acidity function. Enzyme catalysis (single substrate reaction only). Michaelis-Menton law. Influence of pH and temperature on enzyme catalysis. 2. Surface phenomenon and heterogeneous catalysis: Adsorption and free energy relation at interfaces. Gibb’s adsorption isotherm. Physisorption and chemisorption. Adsorption isotherms (Freundlich & Langmuir). Kinetics of heterogeneous catalysis. Langmuir - Hinshelwood and Langmuir - Rideal - Eley mechanisms.

UNIT -IV 1. Interionic attraction theory: Debye — Huckel — Onsager equation. Falkenhagen effect. Wien effect. Activity and activity coefficient. Ionic strength. Debye — Huckel limiting law and its applications. 2. Theories of double layer. Helmholtz — Perrin - Gouy chapmann — Stern theories.

UNIT-V 1. Polarography: Current — voltage relationships. The dropping mercury electrode. Diffusion current. Half— wave potentials. Applications of polarography. Amperometric titrations. 2. Fundamental principles of coulometric methods. Constant current and controlled potential methods. Simple applications.

UNIT-VI Circular dichroism and optical rotatory dispersion-basic principles-basic principles of O.R,D. and C.D.-Cotton effects-Octant rule-axial halo ketone rule-application of O.R,D. and C.D. Turbidimetry and Nephelometry-applications. Thermal analysis: Differential thermal analysis (DTA) and differential scanning calorimetry (DSC)basic principles-thermo gravimetric analysis.

UNIT-VII Electron spectroscopy: ESCA (XPS): principle, chemical shifts-description of SCA spectrometer, X-ray sources, sample analysis, detectors and recording devices-applications. Auger electron spectroscopy (AES) and ultra-violet photo electron spectroscopy (UPS/PES)-principles and applications. Chromatography: Theory, instrumentation and applications in the chemical analysis of the following: GLC and HPLC

UNIT-VIII Chemical crystallography: Anx.23 D - M Sc Chemistry (SDE) 2007-08 Page 14 of 16 Neutron diffraction and Electron diffraction. X-ray diffraction-an elementary discussion of structural factors-Fourier synthesis and analysis. Structure of rutile, fluorite and antifluorite, zinc blend, wurtzite, diamond and graphite.

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