General Chemistry Cheat Sheet - NDA

Welcome to the LibreTexts-style reference portal for National Defence Academy (NDA) General Chemistry preparation. This guide breaks down essential chemical principles, laws, equations, and problem-solving techniques tested heavily in the UPSC NDA written examination. Master these core topics to excel in the General Ability Test (GAT) paper.

1. Stoichiometry & Moles

Chapter Overview: Stoichiometry forms the quantitative backbone of chemistry. UPSC frequently tests mole calculations, concentration metrics, and gas laws in NDA.

• Mole Concept: Exactly \(1\text{ mol}\) contains \(6.022 \times 10^{23}\) elementary entities (Avogadro's number, \(N_A\)).
• Molar Mass (\(M\)): The mass of one mole of a substance expressed in \(\text{g/mol}\). Calculated via \(n = \frac{m}{M}\), where \(n\) is moles, \(m\) is mass, and \(M\) is molar mass.
• Concentration: Molarity is defined as moles of solute per liter of solution: \(M = \frac{n}{V} = \frac{\text{moles}}{\text{liters}}\).
• Ideal Gas Law: Relates pressure, volume, temperature, and moles via \(PV = nRT\), with universal gas constant \(R = 0.08206\text{ L}\cdot\text{atm}/(\text{mol}\cdot\text{K})\).

PYQ Analysis & Chapter Weightage: Expect 2 to 3 direct or application-based numerical questions per paper focusing on gas laws and mole fractions.

2. Atomic Structure

Chapter Overview: Understanding subatomic particles, wave-particle duality, and quantum mechanical models is crucial for predicting chemical behavior.

• Subatomic Particles: Protons (\(p^+\)), Neutrons (\(\varrho^0\)), and Electrons (\(e^-\)).
• Energy of Photon: Governed by Planck's equation and wave velocity: \[E = h u = \frac{hc}{\lambda}\] where Planck's constant \(h = 6.626 \times 10^{-34}\text{ J}\cdot\text{s}\).
• Quantum Numbers:
  • Principal quantum number (\(n = 1, 2, 3, \dots\)) determining shell size and energy.
  • Angular momentum quantum number (\(l = 0\) to \(n-1\)) defining subshell shape.
  • Magnetic quantum number (\(m_l = -l\) to \(+l\)) determining orbital orientation.
  • Spin quantum number (\(m_s = \pm \frac{1}{2}\)) denoting electron spin orientation.

NTA Pattern & Study Strategy: Memorize quantum number rules and photon energy relationships. Questions often test exceptions or maximum capacity formulas like \(2n^2\).

3. Thermochemistry

Chapter Overview: Thermochemistry studies energy changes during chemical reactions, establishing spontaneity and heat transfer properties.

• Enthalpy Change: \(\Delta H = H_{\text{products}} - H_{\text{reactants}}\)
• Heat Transfer: \(q = mc\Delta T\) where \(m\) is mass, \(c\) is specific heat capacity, and \(\Delta T\) is temperature change.
• Hess's Law: \(\Delta H_{\text{rxn}} = \sum \Delta H_f^{\circ}(\text{prod}) - \sum \Delta H_f^{\circ}(\text{react})\)
• Gibbs Free Energy: \(\Delta G = \Delta H - T\Delta S\)
• Spontaneity Criteria: \(\Delta G < 0\) indicates a spontaneous process, while \(\Delta G > 0\) represents a non-spontaneous process.

Chapter Weightage: Spontaneity conditions and Gibbs free energy calculations appear frequently in conceptual statements.

4. Chemical Equilibrium

Chapter Overview: Reversible reactions reach a dynamic balance characterized by equilibrium constants.

• Equilibrium Constant (\(K_c\)): For a general reversible reaction \(aA + bB leftharpoons cC + dD\): \[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\]
• Relationship with \(K_p\): \(K_p = K_c(RT)^{\Delta n}\)
• Reaction Quotient (\(Q\)):
  • \(Q < K\): Reaction shifts right toward products.
  • \(Q > K\): Reaction shifts left toward reactants.
  • \(Q = K\): System is at dynamic equilibrium.

5. Acids and Bases

Chapter Overview: Acid-base equilibria govern proton transfer processes, pH scales, and buffer solutions.

• pH and pOH: \[\text{pH} = -\log[H^+], \quad \text{pOH} = -\log[OH^-]\] \[\text{pH} + \text{pOH} = 14\]
• Acid Dissociation (\(K_a\)): \[K_a = \frac{[H^+][A^-]}{[HA]}, \quad \text{p}K_a = -\log K_a\]
• Buffer Solutions (Henderson-Hasselbalch): \[\text{pH} = \text{p}K_a + \log\bigl(\frac{[\text{Base}]}{[\text{Acid}]}\bigr)\]

6. Electrochemistry

Chapter Overview: Interconversion of chemical and electrical energy drives galvanic and electrolytic cells.

• Cell Potential: \(E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}\)
• Gibbs Energy & Cell Potential: \(\Delta G^{\circ} = -nFE^{\circ}_{\text{cell}}\) where Faraday constant \(F = 96485\text{ C/mol}\).
• Nernst Equation: \(E = E^{\circ} - \frac{RT}{nF} \ln Q\)

CC(=O)Oc1ccccc1C(=O)O

Frequently Asked Questions

Q1: What is the value of Avogadro's number used in NDA chemistry problems?
A1: It is standardly taken as \(6.022 \times 10^{23}\text{ particles/mol}\).

Q2: How do you determine if a chemical reaction is spontaneous?
A2: A reaction is spontaneous when the change in Gibbs free energy \(\Delta G < 0\) under constant temperature and pressure.

Q3: What does the Nernst equation calculate?
A3: The Nernst equation calculates the cell potential of an electrochemical cell under non-standard conditions.