Types of Solids: Crystalline (definite geometry, sharp MP), Amorphous (irregular, gradual softening).
Unit Cells:
- Simple Cubic (SC): 1 atom/unit cell, $r = a/2$.
- Body-Centered Cubic (BCC): 2 atoms/unit cell, $r = \sqrt{3}a/4$.
- Face-Centered Cubic (FCC): 4 atoms/unit cell, $r = \sqrt{2}a/4$.
Packing Efficiency: SC (52.4%), BCC (68%), FCC/HCP (74%).
Density: $\rho = \frac{ZM}{a^3 N_A}$.
Voids: Tetrahedral (4 neighbors), Octahedral (6 neighbors).
Defects:
- Stoichiometric: Schottky (missing cation/anion), Frenkel (ion occupies interstitial site).
- Non-Stoichiometric: Metal excess/deficiency.
Magnetic Properties: Para-, Ferro-, Ferri-, Anti-ferromagnetism.

Concentration Terms:
- Molarity (M): moles of solute / volume of solution (L).
- Molality (m): moles of solute / mass of solvent (kg).
- Mole Fraction ($\chi$): moles of component / total moles.
- Mass %: (mass of component / total mass) $\times 100$.
Raoult's Law: $P_A = P_A^0 \chi_A$. For volatile components, $P_{total} = P_A^0 \chi_A + P_B^0 \chi_B$.
Colligative Properties: Depend on number of solute particles, not their nature.
- Relative Lowering of Vapor Pressure: $\frac{P_A^0 - P_A}{P_A^0} = \chi_B$.
- Elevation in Boiling Point: $\Delta T_b = K_b m$.
- Depression in Freezing Point: $\Delta T_f = K_f m$.
- Osmotic Pressure: $\Pi = iCRT$.
Van't Hoff Factor ($i$): For dissociation $i > 1$, for association $i < 1$.

Electrochemical Cell: Converts chemical energy to electrical energy.
Redox Reactions: Oxidation at anode, Reduction at cathode.
Electrode Potential: Tendency of an electrode to lose/gain electrons.
Standard Electrode Potential ($E^0$): Measured at 298 K, 1 atm, 1 M concentration.
Nernst Equation: $E_{cell} = E_{cell}^0 - \frac{RT}{nF} \ln Q$. At 298 K, $E_{cell} = E_{cell}^0 - \frac{0.0591}{n} \log Q$.
Gibbs Free Energy: $\Delta G^0 = -nFE_{cell}^0$.
Relation with Equilibrium Constant: $\Delta G^0 = -RT \ln K_{eq}$. $E_{cell}^0 = \frac{RT}{nF} \ln K_{eq}$.
Conductance: $G = \frac{1}{R}$. Unit: Siemens (S).
Conductivity ($\kappa$): $\kappa = G \times \frac{l}{A}$. Unit: S cm$^{-1}$.
Molar Conductivity ($\Lambda_m$): $\Lambda_m = \frac{\kappa \times 1000}{M}$. Unit: S cm$^2$ mol$^{-1}$.
Kohlrausch's Law: $\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0$.
Faraday's Laws of Electrolysis:
- First Law: $m \propto Q = It$.
- Second Law: $\frac{m_1}{m_2} = \frac{E_1}{E_2}$.

Rate of Reaction: Change in concentration of reactant/product per unit time.
Rate Law: Rate $= k[A]^x[B]^y$.
Order of Reaction: Sum of powers of concentration terms ($x+y$).
Molecularity: Number of reacting species in an elementary step.
Integrated Rate Laws:
- Zero Order: $[A]_t = [A]_0 - kt$.