GATE Chemistry Physical Chemistry Syllabus

Physical Chemistry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Physical Chemistry in GATE Chemistry, not a summary of it.

1. 1

   Postulates of Quantum Mechanics

   4 topics

   • Operators
   • Time Dependent and Time Independent Schrödinger Equations
   • Born Interpretation
   • Dirac Bra-Ket Notation
2. 2

   Particle in a Box

   4 topics

   • Infinite and Finite Square Wells
   • Concept of Tunnelling
   • Particle in 1D, 2D and 3D-Box
   • Applications
3. 3

   Harmonic Oscillator

   2 topics

   • Harmonic and Anharmonic Potentials
   • Hermite Polynomials
4. 4

   Rotational Motion

   2 topics

   • Angular Momentum Operators
   • Rigid Rotor
5. 5

   Hydrogen and Hydrogen-like Atoms

   2 topics

   • Atomic Orbitals
   • Radial Distribution Function
6. 6

   Multi-electron Atoms

   4 topics

   • Orbital Approximation
   • Electron Spin
   • Pauli Exclusion Principle
   • Slater Determinants
7. 7

   Approximation Methods

   2 topics

   • Variation Method and Secular Determinants
   • First Order Perturbation Techniques
8. 8

   Atomic Units

   overview

   Examined as a single unit within Physical Chemistry — no further topic split in the official outline.

9. 9

   Molecular Structure and Chemical Bonding

   6 topics

   • Born-Oppenheimer Approximation
   • Valence Bond Theory and Linear Combination of Atomic Orbitals (LCAO-MO) Theory
   • Hybrid Orbitals
   • Applications of LCAO-MO Theory to H2+, H2
   • Orbital Theory (MOT) of Homo- and Heteronuclear Diatomic Molecules
   • Hückel Approximation and its Application to Annular π – Electron Systems
10. 10

    Group Theory

    5 topics

    • Symmetry Elements and Operations
    • Point Groups and Character Tables
    • Internal Coordinates and Vibrational Modes
    • Symmetry Adapted Linear Combination of Atomic Orbitals (LCAO-MO)
    • Construction of Hybrid Orbitals using Symmetry Aspects
11. 11

    Spectroscopy

    11 topics

    • Atomic Spectroscopy
    • Russell-Saunders Coupling
    • Term Symbols and Spectral Details
    • Origin of Selection Rules
    • Rotational, Vibrational, Electronic and Raman Spectroscopy of Diatomic and Polyatomic Molecules
    • Line Broadening
    • Einstein’s Coefficients
    • Relationship of Transition Moment Integral with Molar Extinction Coefficient and Oscillator Strength
    • Basic Principles of Nuclear Magnetic Resonance
    • Gyromagnetic Ratio
    • Chemical Shift, Nuclear Coupling
12. 12

    Equilibrium

    27 topics

    • Laws of Thermodynamics
    • Standard States
    • Thermochemistry
    • Thermodynamic Functions and their Relationships
    • Criteria of Spontaneity and Equilibrium
    • Absolute Entropy
    • Partial Molar Quantities
    • Thermodynamics of Mixing
    • Chemical Potential
    • Fugacity, Activity and Activity Coefficients
    • Ideal and Non-ideal Solutions
    • Raoult’s Law and Henry’s Law
    • Chemical Equilibria
    • Dependence of Equilibrium Constant on Temperature and Pressure
    • Ionic Mobility and Conductivity
    • Debye-Hückel Limiting Law
    • Debye-Hückel-Onsager Equation
    • Standard Electrode Potentials and Electrochemical Cells
    • Nernst Equation and its Application
    • Relationship between Electrode Potential and Thermodynamic Quantities
    • Potentiometric and Conduct Metric Titrations
    • Phase Rule
    • Clausius-Clapeyron Equation
    • Phase Diagram of One Component Systems: CO2, H2O, S
    • Phase Diagram of Two Component Systems: Liquid-Vapour, Liquid-Liquid, Solid-Liquid
    • Fractional Distillation
    • Azeotropes and Eutectics
13. 13

    Statistical Thermodynamics

    3 topics

    • Microcanonical, Canonical and Grand Canonical Ensembles
    • Boltzmann Distribution
    • Partition Functions and Thermodynamic Properties
14. 14

    Kinetics

    13 topics

    • Elementary, Parallel, Opposing and Consecutive Reactions
    • Steady State Approximation
    • Mechanisms of Complex Reactions
    • Unimolecular Reactions
    • Potential Energy Surfaces and Classical Trajectories
    • Concept of Saddle Points
    • Transition State Theory: Eyring Equation, Thermodynamic Aspects
    • Kinetics of Polymerization
    • Catalysis Concepts and Enzyme Catalysis
    • Kinetic Isotope Effects
    • Fast Reaction Kinetics: Relaxation and Flow Methods
    • Diffusion Controlled Reactions
    • Kinetics of Photochemical and Photophysical Processes
15. 15

    Surfaces and Interfaces

    6 topics

    • Physisorption and Chemisorption
    • Langmuir, Freundlich and Brunauer–Emmett–Teller (BET) Isotherms
    • Surface Catalysis: Langmuir-Hinshelwood Mechanism
    • Surface Tension, Viscosity
    • Self-assembly
    • Physical Chemistry of Colloids, Micelles and Macromolecules

Physical Chemistry flashcards for GATE Chemistry

19 of 50 cards from the Physical Chemistry deck — real questions with worked answers.

1. In quantum mechanics, what is an operator, and what defines an observable's operator?

   An operator is a mathematical instruction that acts on a function to produce another function. A physical observable is represented by a linear, Hermitian operator whose eigenvalues are the possible measurable (real) values.

2. Write the quantum-mechanical operators for position $x$ and linear momentum $p_x$ in one dimension.

   $$\hat{x} = x, \qquad \hat{p}_x = -i\hbar\frac{\partial}{\partial x}$$

3. State the commutator of position and momentum, $[\hat{x},\hat{p}_x]$.

   $$[\hat{x},\hat{p}_x] = i\hbar$$ Because it is nonzero, $x$ and $p_x$ cannot be measured simultaneously to arbitrary precision (Heisenberg uncertainty).

4. What does it mean for an operator $\hat{A}$ to be Hermitian, and why is it required?

   Hermitian means $\int \psi_i^{*}\hat{A}\psi_j\,d\tau = \left(\int \psi_j^{*}\hat{A}\psi_i\,d\tau\right)^{*}$. It guarantees real eigenvalues and orthogonal eigenfunctions, which is essential for physical observables.

5. Write the one-dimensional time-independent Schrödinger equation.

   $$\hat{H}\psi = E\psi \;\Rightarrow\; -\frac{\hbar^{2}}{2m}\frac{d^{2}\psi}{dx^{2}} + V(x)\psi = E\psi$$

6. Write the time-dependent Schrödinger equation.

   $$i\hbar\frac{\partial \Psi(x,t)}{\partial t} = \hat{H}\Psi(x,t) = \left[-\frac{\hbar^{2}}{2m}\frac{\partial^{2}}{\partial x^{2}} + V\right]\Psi(x,t)$$

7. For a time-independent potential, how does the full wavefunction depend on time?

   It separates as $\Psi(x,t) = \psi(x)\,e^{-iEt/\hbar}$. The state is stationary because $|\Psi|^{2} = |\psi|^{2}$ is time-independent.

8. State the Born interpretation of the wavefunction.

   $|\Psi(x,t)|^{2}\,dx$ is the probability of finding the particle between $x$ and $x+dx$. $\Psi$ itself is a probability amplitude; only $|\Psi|^{2}$ has physical (probability density) meaning.

9. What is the normalization condition for a wavefunction in one dimension?

   $$\int_{-\infty}^{\infty} |\Psi(x)|^{2}\,dx = 1$$ The total probability of finding the particle somewhere must equal 1.

10. List the conditions a physically acceptable wavefunction must satisfy.

    It must be single-valued, finite, continuous, and have a continuous first derivative; it must be normalizable (square-integrable). These follow from the Born interpretation.

11. In Dirac bra-ket notation, what do the ket $|\psi\rangle$ and bra $\langle\psi|$ represent?

    The ket $|\psi\rangle$ represents the state vector (wavefunction $\psi$); the bra $\langle\psi|$ is its conjugate (dual) vector, corresponding to $\psi^{*}$.

12. Express the overlap integral and an expectation value in Dirac notation.

    Overlap: $\langle\phi|\psi\rangle = \int \phi^{*}\psi\,d\tau$. Expectation value: $\langle \hat{A}\rangle = \dfrac{\langle\psi|\hat{A}|\psi\rangle}{\langle\psi|\psi\rangle}$, which equals $\langle\psi|\hat{A}|\psi\rangle$ for normalized $\psi$.

13. What is the orthonormality condition for a set of states $\{|n\rangle\}$ in bra-ket notation?

    $$\langle m|n\rangle = \delta_{mn}$$ where $\delta_{mn}=1$ if $m=n$ and $0$ otherwise.

14. Give the normalized energy eigenfunctions and energy levels of a particle in a 1D infinite square well of width $L$.

    $$\psi_n(x) = \sqrt{\frac{2}{L}}\sin\!\left(\frac{n\pi x}{L}\right), \qquad E_n = \frac{n^{2}h^{2}}{8mL^{2}}, \quad n=1,2,3,\dots$$

15. What is the zero-point energy of a particle in a 1D infinite square well, and why can't it be zero?

    The lowest energy is $E_1 = \dfrac{h^{2}}{8mL^{2}}$ ($n=1$). $n=0$ would make $\psi=0$ everywhere (no particle), and zero energy would violate the uncertainty principle.

16. How does a finite square well differ from an infinite square well regarding the wavefunction and energy levels?

    In a finite well the wavefunction penetrates (decays exponentially) into the barrier regions, energies are slightly lower than the infinite-well values, and only a finite number of bound states exist (plus possible continuum states above the well).

17. What is quantum mechanical tunnelling?

    Tunnelling is the penetration of a particle through a potential barrier higher than its energy—classically forbidden. The wavefunction decays exponentially inside the barrier but has nonzero amplitude beyond it, giving a finite transmission probability.

18. How does the tunnelling probability depend on particle mass, barrier width, and barrier height?

    Transmission $T \approx e^{-2\kappa a}$ with $\kappa = \dfrac{\sqrt{2m(V-E)}}{\hbar}$. Tunnelling decreases (exponentially) with greater mass $m$, wider barrier $a$, and higher barrier $(V-E)$.

19. Give the energy levels for a particle in a 2D box with sides $L_x$ and $L_y$.

    $$E_{n_x,n_y} = \frac{h^{2}}{8m}\left(\frac{n_x^{2}}{L_x^{2}} + \frac{n_y^{2}}{L_y^{2}}\right), \quad n_x,n_y = 1,2,\dots$$

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