1. First Law in Chemistry & Work Calculations

First Law (IUPAC formulation): ΔU = q + w, where q is heat absorbed (+q) or evolved (-q) and w is work done ON system (+w) or BY system (-w). Pressure-Volume Work against constant external pressure P_ext: w = -P_ext ΔV = -P_ext (V2 - V1). Reversible Isothermal Expansion of ideal gas: w_rev = -2.303 n R T log10(V2 / V1) = -2.303 n R T log10(P1 / P2). In vacuum (free expansion, P_ext = 0): w = 0, so ΔU = 0 and ΔT = 0 for ideal gas.

2. Enthalpy (H), Heat Capacity & Hess's Law

Enthalpy: H = U + P V. For reactions involving gases: ΔH = ΔU + Δn_g R T, where Δn_g = (moles of gaseous products) - (moles of gaseous reactants). Heat capacity: at constant volume q_v = ΔU = n Cv ΔT; at constant pressure q_p = ΔH = n Cp ΔT. Kirchoff's Equations for temperature variation of reaction enthalpy: ΔH_T2 - ΔH_T1 = ΔCp (T2 - T1). Hess's Law of Constant Heat Summation: Total enthalpy change is identical whether a reaction occurs in one step or multiple steps: Δ_r H° = Σ Δ_f H°(products) - Σ Δ_f H°(reactants) = Σ Bond Energy(reactants) - Σ Bond Energy(products).

3. Entropy (S), Gibbs Free Energy (G) & Spontaneity

Entropy (measure of disorder): ΔS = q_rev / T. Second Law: For spontaneous process in isolated system: ΔS_total = ΔS_system + ΔS_surroundings > 0. Gibbs Free Energy: G = H - T S; at constant T and P: ΔG = ΔH - T ΔS. Spontaneity Criterion: (1) ΔG < 0: Process is spontaneous (exergonic); (2) ΔG = 0: System is in equilibrium; (3) ΔG > 0: Process is non-spontaneous (endergonic). Temperature dependence: (a) ΔH < 0, ΔS > 0: Spontaneous at ALL temperatures; (b) ΔH > 0, ΔS < 0: Non-spontaneous at all temperatures; (c) ΔH < 0, ΔS < 0: Spontaneous only at LOW temperatures (T < ΔH/ΔS); (d) ΔH > 0, ΔS > 0: Spontaneous only at HIGH temperatures (T > ΔH/ΔS).

4. Chemical Equilibrium: Kp, Kc & Reaction Quotient (Q)

For reversible reaction aA + bB ⇌ cC + dD: Equilibrium Constant Kc = ([C]^c [D]^d) / ([A]^a [B]^b); Kp = (P_C^c P_D^d) / (P_A^a P_B^b). Relation between Kp and Kc: Kp = Kc (R T)^Δn_g (where R = 0.0821 L·atm/(mol·K) and T in K). If Δn_g = 0: Kp = Kc (e.g., H2 + I2 ⇌ 2HI). Reaction Quotient Q: Has same mathematical form as K but evaluated at any arbitrary concentrations: (1) Q < K: Reaction proceeds in FORWARD direction; (2) Q = K: System is at EQUILIBRIUM; (3) Q > K: Reaction proceeds in BACKWARD direction. Standard Free Energy connection: ΔrG° = -R T ln K = -2.303 R T log10 K.

5. Le Chatelier's Principle Rules

When a dynamic equilibrium is subjected to stress (change in concentration, temperature, pressure, or volume), the system shifts in the direction that counteracts the applied stress: (1) Concentration: Adding reactant shifts equilibrium forward; adding product shifts backward; (2) Pressure: Increasing pressure shifts toward side with FEWER moles of gas (smaller Δn_g); if Δn_g = 0, pressure has no effect; (3) Temperature: Increasing temperature favors ENDOTHERMIC reaction (+ΔH); decreasing temperature favors EXOTHERMIC reaction (-ΔH); (4) Catalyst: Does NOT alter equilibrium position or K; merely speeds up attainment of equilibrium equally in both directions; (5) Inert Gas Addition: At constant volume: NO effect on equilibrium; at constant pressure: shifts toward side with GREATER number of gas moles.

6. Ionic Equilibrium: pH, Buffers & Henderson-Hasselbalch Equation

Ionic product of water at 298 K: Kw = [H+][OH-] = 1.0 × 10^-14 -> pH + pOH = 14. Weak Acid dissociation: Ka = (C α²) / (1 - α) ≈ C α² (Ostwald Dilution Law), so [H+] = √(Ka · C) and pH = (1/2) [pKa - log10 C]. Buffer Solutions (resist pH change): (1) Acidic Buffer (weak acid + its conjugate salt, e.g., CH3COOH + CH3COONa): Henderson-Hasselbalch Equation: pH = pKa + log10([Salt] / [Acid]); (2) Basic Buffer (weak base + its salt, e.g., NH4OH + NH4Cl): pOH = pKb + log10([Salt] / [Base]), with pH = 14 - pOH. Solubility Product (Ksp): For salt AxBy ⇌ x A^y+ + y B^x-: Ksp = (x·s)^x · (y·s)^y = x^x · y^y · s^(x+y). Precipitation condition: Ionic Product (IP) > Ksp.