Chemistry Formula Sheet - Physical Chemistry

1. Atomic Structure

Bohr’s Model

• Energy of electron: $E_n = -\frac{13.6}{n^2} eV$
• Radius of orbit: $r_n = 0.529n^2$ Å
• Frequency of radiation: $\nu = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$

de Broglie and Heisenberg

• de Broglie wavelength: $\lambda = \frac{h}{mv}$
• Heisenberg uncertainty principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

2. Chemical Bonding

Bond Parameters

• Bond order: $\text{Bond order} = \frac{\text{Bonding electrons} - \text{Anti-bonding electrons}}{2}$
• Dipole moment: $\mu = \delta \times d$
• Lattice energy (Born-Haber cycle): $U = \Delta H_f - \Delta H_{sub} - \frac{1}{2}\Delta H_{diss} - IE - EA$

3. Thermodynamics

Basic Concepts

• First law of thermodynamics: $\Delta U = q + w$
• Work done: $w = -P_{ext}\Delta V$
• Enthalpy change: $\Delta H = \Delta U + \Delta n_g RT$
• Heat capacity: $C = \frac{q}{\Delta T}$

Entropy and Free Energy

• Entropy change: $\Delta S = \frac{q_{rev}}{T}$
• Gibbs free energy: $\Delta G = \Delta H - T\Delta S$
• Gibbs-Helmholtz equation: $\Delta G = \Delta G^{\circ} + RT\ln Q$
• Equilibrium constant: $\Delta G^{\circ} = -RT\ln K$

4. Chemical Equilibrium

Equilibrium Constant

• Law of mass action: $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Relation between K_p and K_c: $K_p = K_c(RT)^{\Delta n}$
• Reaction quotient: $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Acid-Base Equilibrium

• pH: $pH = -\log[H^+]$
• pOH: $pOH = -\log[OH^-]$
• Water dissociation: $K_w = [H^+][OH^-] = 10^{-14}$ (at 25°C)
• Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]}$

5. Chemical Kinetics

Rate of Reaction

• Rate law: Rate = $k[A]^m[B]^n$
• Rate constant for different orders:
  • Zero order: $[A]_t = [A]_0 - kt$
  • First order: $\ln\frac{[A]_t}{[A]_0} = -kt$ or $[A]_t = [A]_0 e^{-kt}$
  • Second order: $\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt$

Arrhenius Equation

• Temperature dependence: $k = A e^{-E_a/RT}$
• Modified form: $\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

6. Solutions

Concentration Terms

• Molarity: $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$
• Molality: $m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}$
• Mole fraction: $x_1 = \frac{n_1}{n_1 + n_2}$
• Mass percent: $% = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100$

Colligative Properties

• Raoult’s law: $P = x_A P_A^{\circ} + x_B P_B^{\circ}$
• Elevation of boiling point: $\Delta T_b = K_b \times m$
• Depression of freezing point: $\Delta T_f = K_f \times m$
• Osmotic pressure: $\pi = iMRT$ (van’t Hoff equation)

7. Electrochemistry

Electrochemical Cells

• Nernst equation: $E = E^{\circ} - \frac{RT}{nF}\ln Q$
• At 25°C: $E = E^{\circ} - \frac{0.0591}{n}\log Q$
• Gibbs free energy: $\Delta G = -nFE$

Conductance

• Specific conductance: $\kappa = \frac{1}{R} \times \frac{l}{A}$
• Molar conductance: $\Lambda_m = \frac{\kappa \times 1000}{c}$
• Kohlrausch’s law: $\Lambda_m^{\infty} = \lambda_+^{\infty} + \lambda_-^{\infty}$

8. Surface Chemistry

Adsorption

• Freundlich isotherm: $\frac{x}{m} = kp^{1/n}$
• Langmuir isotherm: $\frac{x}{m} = \frac{ap}{1 + bp}$

Colloids

• Hardy-Schulze rule: Coagulation power $\propto \frac{1}{\text{hydratation number}}$

This formula sheet covers essential physical chemistry formulas for JEE and NEET preparation. Use this for quick revision during your study sessions.