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integrals

Post author By Miraj Ahmad Ansari
Post date December 2, 2020

IIT JAM CHEMISTRY / TIFR Basic Mathematical Concepts integrals

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← maxima and minima → ordinary differential equations

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December 2020

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Basic Mathematical Concepts

7 Topics

maxima and minima

ordinary differential equations

vectors and matrices

elementary statistics and probability theory

Atomic and Molecular Structure

9 Topics

Fundamental particles

Bohr’s theory of hydrogen-like atom

wave-particle duality

uncertainty principle

Schrödinger’s wave equation

quantum numbers

shapes of orbitals

Hund’s rule and Pauli’s exclusion principle

electronic configuration of simple homonuclear diatomic molecules

Theory of Gases

4 Topics

Equation of state for ideal and non-ideal (van der Waals) gases

Kinetic theory of gases

Maxwell-Boltzmann distribution law

equipartition of energy

10 Topics

Crystals and crystal systems

NaCl and KCl structures

atomic and ionic radii

radius ratio rules

Born-Haber cycle

heat capacity of solids

Chemical Thermodynamics

6 Topics

Reversible and irreversible processes

first law and its application to ideal and nonideal gases

thermochemistry

entropy and free energy

criteria for spontaneity

Chemical and Phase Equilibria

8 Topics

Law of mass action; Kp, Kc, Kx and Kn

effect of temperature on K

ionic equilibria in solutions

pH and buffer solutions

solubility product

phase equilibria–phase rule and its application to one-component and two-component systems

colligative properties

Electrochemistry

8 Topics

Conductance and its applications

transport number

EMF and free energy

concentration cells with and without transport

concentration cells with and without transport

Debey-Huckel-Onsagar theory of strong electrolytes

Chemical Kinetics

8 Topics

Reactions of various order

Arrhenius equation

collision theory

transition state theory

chain reactions – normal and branched

enzyme kinetics

photochemical processes

5 Topics

Gibbs adsorption equation

adsorption isotherm

types of adsorption

surface area of adsorbents

surface films on liquids

2 Topics

Beer-Lambert law

fundamental concepts of rotational, vibrational, electronic and magnetic resonance spectroscopy

Basic Concepts in Organic Chemistry and Stereochemistry

3 Topics

Electronic effects (resonance, inductive, hyperconjugation) and steric effects and its applications (acid/base property);

optical isomerism in compounds with and without any stereocenters (allenes, biphenyls);

conformation of acyclic systems (substituted ethane/n-propane/n-butane) and cyclic systems (mono- and di-substituted cyclohexanes).

Organic Reaction Mechanism and Synthetic Applications

6 Topics

Chemistry of reactive intermediates (carbocations, carbanions, free radicals, carbenes, nitrenes, benzynes etc.);

Hofmann-Curtius-Lossen rearrangement, Wolff rearrangement, Simmons-Smith reaction, Reimer-Tiemann reaction, Michael reaction, Darzens reaction, Wittig reaction and McMurry reaction;

Pinacol-pinacolone, Favorskii, benzilic acid rearrangement, dienone-phenol rearrangement, Baeyer-Villeger reaction;

oxidation and reduction reactions in organic chemistry

organometallic reagents in organic synthesis (Grignard, organolithium and organocopper); Diels-Alder, electrocyclic and sigmatropic reactions;

functional group inter-conversions and structural problems using chemical reactions

Qualitative Organic Analysis

2 Topics

Identification of functional groups by chemical tests

elementary UV, IR and 1H NMR spectroscopic techniques as tools for structural elucidation

Natural Products Chemistry

1 Topic

Chemistry of alkaloids, steroids, terpenes, carbohydrates, amino acids, peptides and nucleic acids

Aromatic and Heterocyclic Chemistry:

2 Topics

Monocyclic, bicyclic and tricyclic aromatic hydrocarbons, and monocyclic compounds with one hetero atom

synthesis, reactivity and properties

2 Topics

Periodic classification of elements and periodicity in properties

general methods of isolation and purification of elements

Chemical Bonding and Shapes of Compounds

6 Topics

Types of bonding; VSEPR theory and shapes of molecules

structure of NaCl, CsCl, diamond and graphite

Main Group Elements (s and p blocks)

2 Topics

General concepts on group relationships and gradation in properties

structure of electron deficient compounds involving main group elements

Transition Metals (d block):

3 Topics

Characteristics of 3d elements; oxide, hydroxide and salts of first row metals

coordination complexes

structure, isomerism, reaction mechanism and electronic spectra; VB, MO and Crystal Field theoretical approaches for structure, color and magnetic properties of metal complexes; organometallic compounds having ligands with back bonding capabilities such as metal carbonyls, carbenes, nitrosyls and metallocenes; homogenous catalysis

Bioinorganic Chemistry

3 Topics

Essentials and trace elements of life

basic reactions in the biological systems and the role of metal ions, especially Fe2+, Fe3+, Cu2+ and Zn2+

structure and function of hemoglobin and myoglobin and carbonic anhydrase

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