Physical Chemistry Formulas

01 Solutions 7 marks

Mole Fraction

xA = nA / (nA + nB)

xA + xB = 1. Dimensionless. Used in Raoult's law.

Raoult's Law

pA = xA × p°A ; pTotal = pA + pB

Valid for ideal solutions. p°A = vapour pressure of pure A.

Relative Lowering of Vapour Pressure

ΔP/P° = (p°A − pA)/p°A = xB

xB = mole fraction of solute. ΔP/P° is a colligative property.

Elevation of Boiling Point

ΔTb = Kb × m Kb: K·kg·mol⁻¹

Kb = ebullioscopic constant (water: 0.52). m = molality (mol/kg solvent).

Depression of Freezing Point

ΔTf = Kf × m Kf: K·kg·mol⁻¹

Kf = cryoscopic constant (water: 1.86). Used to find molar mass.

Osmotic Pressure

π = CRT = (n/V)RT π = iCRT [for electrolytes] π: bar or atm

Van't Hoff equation. C = molarity (mol/L). R = 0.083 L·bar·mol⁻¹·K⁻¹ (NCERT). i = van't Hoff factor; use for electrolytes (NaCl: i≈2, MgCl₂: i≈3).

Molar Mass from Colligative Properties

M = (Kb × w × 1000) / (ΔTb × W)

w = mass of solute (g), W = mass of solvent (g). Also works with Kf/ΔTf.

van't Hoff Factor

i = observed colligative property / theoretical value i = 1 + (n−1)α [dissociation] i = 1 − (1 − 1/n)α [association]

n = particles formed; α = degree of dissociation/association. i > 1 for dissociation, i < 1 for association.

02 Electrochemistry 9 marks

Standard Cell EMF

E°cell = E°cathode − E°anode

Cathode = reduction (+ve electrode). Anode = oxidation (−ve electrode).

Nernst Equation

E = E° − (RT/nF) ln Q E = E° − (0.0591/n) log Q [at 25°C]

n = electrons transferred; F = 96500 C/mol; Q = reaction quotient.

Gibbs Energy & EMF

ΔG° = −nFE°cell log K = nE° / 0.0591

Spontaneous if E°cell > 0 (ΔG° < 0). K = equilibrium constant.

Molar Conductivity

Λm = κ × 1000 / M S·cm²·mol⁻¹

κ = conductivity (S/cm); M = molarity (mol/L). Λm increases as dilution increases.

Kohlrausch's Law

Λ°m = Σν₊λ°₊ + Σν₋λ°₋ Λm = Λ°m − b√c [strong electrolytes]

λ° = limiting molar conductivity of individual ions. Used to find Λ°m of weak electrolytes.

Faraday's First Law

m = ZIt = (M / nF) × It m: grams

Z = electrochemical equivalent = M/(nF). I = current (A); t = time (s).

Faraday's Second Law

m₁/m₂ = E₁/E₂

E = equivalent weight = M/n. Same charge deposits masses in ratio of equivalent weights.

Key Constants

F = 96500 C mol⁻¹ RT/F = 0.02569 V [at 25°C]

1 Faraday = charge on 1 mole of electrons. 2.303RT/F = 0.0591 V at 298 K.

03 Chemical Kinetics 7 marks

Rate of Reaction

r = −(1/a) d[A]/dt = +(1/b) d[B]/dt

For aA → bB. Rate is always positive. Units: mol L⁻¹ s⁻¹.

Rate Law

r = k [A]^m [B]^n

m, n = orders (determined experimentally, not from stoichiometry). Overall order = m + n.

Units of Rate Constant k

k: (mol L⁻¹)^(1−n) s⁻¹

Zero order: mol L⁻¹ s⁻¹. First order: s⁻¹. Second order: L mol⁻¹ s⁻¹.

Zero Order Integrated Rate Law

[A] = [A]₀ − kt t½ = [A]₀ / 2k

Plot [A] vs t → straight line (slope = −k). Half-life depends on initial concentration.

First Order Integrated Rate Law

k = (2.303/t) log ([A]₀/[A]) t½ = 0.693/k

Plot ln[A] vs t → straight line (slope = −k). Half-life INDEPENDENT of [A]₀.

Arrhenius Equation

k = A e^(−Ea/RT) log(k₂/k₁) = (Ea/2.303R) × (T₂−T₁)/(T₁T₂) Ea: J mol⁻¹

A = frequency factor. R = 8.314 J mol⁻¹ K⁻¹. Plot log k vs 1/T → slope = −Ea/2.303R.

Effect of Temperature

rate doubles for every 10°C rise

Temperature coefficient ≈ 2. Catalyst lowers Ea without changing ΔH.

Physical Chemistry Formula Reference

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