Physical Chemistry Formula Sheet & Quick Revision Guide - NDA

1. Quantum Chemistry & Atomic Structure

Atomic structure forms the baseline of physical chemistry questions in the NDA General Ability Test (GAT). Candidates must memorize Planck's relation, de Broglie matter waves, and Heisenberg's uncertainty relation.

Key Formulas

• Planck's Quantum Law: Expresses energy quantization for photons: \[E = h u = \frac{hc}{\lambda}\]
• De Broglie Wavelength: Relates matter wave characteristics to particle momentum: \[\lambda = \frac{h}{p} = \frac{h}{mv}\]
• Heisenberg Uncertainty Principle: Imposes fundamental limits on precision: \[\Delta x \cdot \Delta p_x \ge \frac{\hbar}{2}\]
• Time-Independent Schrödinger Equation: The foundational wave equation for quantum systems: \[\hat{H}\psi = E\psi\]

2. Thermodynamics & Thermochemistry

Thermodynamics analyzes energy transformations, work done by physical systems, and spontaneity conditions governing chemical processes.

Core Equations & Principles

• First Law of Thermodynamics: Statement of conservation of energy: \[\Delta U = q + w\]
• Expansion Work: Work performed during gas expansion/compression: \[w = -\int P_{ext} dV\]
• Enthalpy Relation: Heat content at constant pressure: \[H = U + PV\]
• Entropy Change: Measure of molecular disorder or randomness: \[\Delta S = \int \frac{dq_{rev}}{T}\]
• Gibbs Free Energy: Criteria for thermodynamic stability: \[G = H - TS\]
• Criterion for Spontaneity: A process is spontaneous at constant temperature and pressure if: \[\Delta G_{T,P} < 0\]
• Gibbs-Helmholtz Equation: Describes variation of Gibbs free energy with temperature: \[(\frac{\partial (G/T)}{\partial T})_P = -\frac{H}{T^2}\]

3. Chemical Kinetics

Chemical kinetics evaluates the rates of chemical reactions, reaction mechanisms, and temperature dependencies.

Rate Expressions & Integrated Laws

• Differential Rate Law: Explicit dependence on reactant concentrations: \[\text{Rate} = k[A]^x[B]^y\]
• Arrhenius Temperature Dependence: Quantifies activation energy barriers: \[k = A e^{-E_a / RT}\]
• Integrated Rate Laws:
  • Zero Order: \([A]_t = -kt + [A]_0\)
  • First Order: \(\ln[A]_t = -kt + \ln[A]_0\)
  • Second Order: \(\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}\)
• First-Order Half-Life: Concentration-independent half-life expression: \[t_{1/2} = \frac{\ln 2}{k}\]

4. Electrochemistry

Electrochemistry focuses on the interconversion between chemical energy and electrical energy within electrochemical cells.

Essential Relationships

• Standard Cell Potential: EMF derived from half-cell reduction potentials: \[E_{cell} = E_{cathode} - E_{anode}\]
• Gibbs Free Energy and Cell EMF: Relationship connecting electrochemistry to thermodynamics: \[\Delta G = -nFE_{cell}\]
• Nernst Equation: Cell potential dependence under non-standard conditions: \[E = E^0 - \frac{RT}{nF} \ln Q\]
• Kohlrausch's Law of Independent Migration: Calculation of limiting molar conductivity: \[\Lambda_m^0 = u_+ \lambda_+^0 + u_- \lambda_-^0\]

5. Solutions & Colligative Properties

Colligative properties depend on the number of solute particles relative to the total number of solvent particles present.

Formulas & Laws

• Raoult's Law: Partial vapor pressure of solvent over liquid mixture: \[P_A = X_A P_A^0\]
• Elevation in Boiling Point: Boiling point elevation using van 't Hoff factor \(i\): \[\Delta T_b = i K_b m\]
• Freezing Point Depression: Cryoscopic constant equation: \[\Delta T_f = i K_f m\]
• Osmotic Pressure: Pressure exerted across a semipermeable membrane: \[\Pi = iCRT\]

6. NDA PYQ & Exam Pattern Analysis

An in-depth analysis of past UPSC NDA question papers highlights consistent weightage assigned to conceptual physical chemistry problems:

• NTA / UPSC Exam Pattern: Direct formula-based numerical questions appear alongside conceptual statements on spontaneity (\(\Delta G < 0\)), order vs. molecularity, and Faraday laws.
• Chapter Weightage: Atomic Structure and Thermodynamics account for ~40% of chemistry marks in the NDA GAT section. Electrochemistry and Solutions constitute another 30%.
• High-Yield Shortcuts: Memorize direct conversion values for Planck's constant \(h\), Faraday's constant \(F = 96500\text{ C/mol}\), and gas constant \(R = 8.314\text{ J/mol K}\).

7. Structural & Spatial Understanding

Physical chemistry principles frequently overlap with organic structural properties. For instance, consider aromatic substitution patterns and spatial orientation during reactions.

Evaluate the spatial arrangement of the following target aromatic derivative formed via electro-chemical or chemical oxidation pathways:

Note: Visualizing 2D and 3D molecular structures enhances understanding of dipole moments, boiling point trends, and intermolecular forces across different physical states.

8. People Also Ask (FAQs)