Class 12 Chemistry — Mega Formula Sheet

Unit I

The Chemistry of Solutions

Raoult's Law & Vapour Pressure

Raoult's Law describes how the vapour pressure of an ideal solution depends on the mole fractions of its components. Solutions may exhibit positive or negative deviations from ideality.

p_A = p°_A × χ_A p_total = p°_A·χ_A + p°_B·χ_B (p° – p)/p° = χ_B [RLVP]

Ideal: ΔH_mix = 0, ΔV_mix = 0
+ve deviation: A–B weaker than A–A & B–B
–ve deviation: A–B stronger than A–A & B–B

Henry's Law — Gas Solubility

Henry's Law quantifies how gas dissolves in a liquid under pressure. Higher K_H means lower solubility at a given pressure. Gas solubility decreases with temperature as K_H increases.

p = K_H × χ K_H = p / χ S₁/S₂ = p₁/p₂ [at two pressures]

Applications: carbonated beverages, scuba diving physiology, dissolved oxygen in water bodies.

Colligative Properties

Depend Only on Number of Particles

Solubility Product (K_sp)

The solubility product links molar solubility to equilibrium concentrations of ions. Different ionic stoichiometries yield different expressions.

AB type: Ksp = S² AB₂ type: Ksp = 4S³ A₂B₃ type: Ksp = 108S⁵ A₃B₂ type: Ksp = 108S⁵

Azeotropes

Azeotropes are constant-boiling mixtures that cannot be separated by simple distillation. Their type is linked to the nature of deviation from Raoult's Law.

Minimum Boiling Azeotrope: +ve deviation (e.g., EtOH–H₂O 95.5%) BP < both components Maximum Boiling Azeotrope: –ve deviation (e.g., HNO₃–H₂O 68%) BP > both components

Unit II

Chemical Kinetics

Integrated Rate Equations

Zero Order

First Order

Second Order

Pseudo First Order

nth Order

ZERO ORDER

Zero Order Integrated Law

Rate = k[A]⁰ = k (constant) [A] = [A]₀ – kt k = ([A]₀ – [A]) / t t₁/₂ = [A]₀ / 2k ← depends on [A]₀ t_complete = [A]₀ / k ← time for complete reaction Graph: [A] vs t → straight line, slope = –k

Units of k: mol L⁻¹ s⁻¹ (M·s⁻¹). Rate is constant regardless of concentration.

FIRST ORDER

First Order Integrated Law

Rate = k[A] ln[A] = ln[A]₀ – kt [A] = [A]₀ · e^(–kt) k = (2.303/t) × log([A]₀/[A]) t₁/₂ = 0.693/k = ln2/k ← INDEPENDENT of [A]₀ After n half-lives: [A] = [A]₀ × (1/2)ⁿ Fraction remaining = (1/2)ⁿ Fraction decomposed = 1 – (1/2)ⁿ Key times: t₅₀% = 0.693/k t₇₅% = 2 × t₁/₂ t₉₀% = 2.303/k t₉₉% = 4.606/k t₉₉.₉% = 6.909/k Graphs: [A] vs t → exponential decay ln[A] vs t → slope = –k log[A] vs t → slope = –k/2.303

Units of k: s⁻¹. Most important order for CBSE — radioactivity, hydrolysis, inversions.

SECOND ORDER

Second Order Integrated Law

Type I: 2A → Products Rate = k[A]² 1/[A] = 1/[A]₀ + kt t₁/₂ = 1/(k[A]₀) ← depends on 1/[A]₀ Graph: 1/[A] vs t → slope = +k Type II: A + B → Products ([A]₀ ≠ [B]₀) k = [2.303/t([A]₀–[B]₀)] × log([B]₀[A]/[A]₀[B])

Units of k: L mol⁻¹ s⁻¹ (M⁻¹s⁻¹). Half-life inversely proportional to initial concentration.

PSEUDO FIRST ORDER

Pseudo First Order Reactions

For A + B → Products, where [B] >> [A]: Rate = k[A][B] ≈ k′[A] k′ = k[B] (pseudo first order rate constant) Example: CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH Rate = k[ester][H₂O] ≈ k′[ester] (since [H₂O] is in vast excess and stays constant)

The reaction behaves as first order because one reactant concentration remains effectively constant.

nth ORDER

General nth Order Formula

1/[A]^(n–1) – 1/[A]₀^(n–1) = (n–1)kt [n ≠ 1] t₁/₂ = (2^(n–1) – 1) / [(n–1) × k × [A]₀^(n–1)] t₁/₂ ∝ 1/[A]₀^(n–1) Summary: Zero: t₁/₂ ∝ [A]₀ k units: M·s⁻¹ First: t₁/₂ = const k units: s⁻¹ Second: t₁/₂ ∝ 1/[A]₀ k units: M⁻¹s⁻¹ nth: k units: M^(1–n)s⁻¹

Arrhenius Equation

k = A × e^(–Eₐ/RT) ln k = ln A – Eₐ/RT log k = log A – Eₐ/(2.303RT) Two-temperature form: log(k₂/k₁) = Eₐ(T₂–T₁) / (2.303·R·T₁T₂) Eₐ = –2.303R × slope (from graph)

The Arrhenius plot (log k vs 1/T) is a straight line. Its slope gives activation energy; the y-intercept gives the pre-exponential factor A. A catalyst lowers Eₐ without changing ΔH or equilibrium.

Quick Reference

Data Tables

TABLE 1 — Important Constants

Constant	Symbol	Value
Universal Gas Constant	R	8.314 J mol⁻¹ K⁻¹ = 0.0821 L·atm·mol⁻¹·K⁻¹ = 2 cal mol⁻¹ K⁻¹
Avogadro's Number	N_A	6.022 × 10²³ mol⁻¹
Boltzmann Constant	k_B	1.38 × 10⁻²³ J K⁻¹
Planck's Constant	h	6.626 × 10⁻³⁴ J·s
Standard Atmosphere	1 atm	101325 Pa = 101.325 kPa

TABLE 2 — Cryoscopic & Ebullioscopic Constants

Solvent	K_f (K·kg·mol⁻¹)	K_b (K·kg·mol⁻¹)	T_f (°C)	T_b (°C)
Water	1.86	0.52	0	100
Benzene	5.12	2.53	5.5	80.1
Chloroform	4.68	3.63	–63.5	61.2
Acetic Acid	3.90	3.07	16.6	118.1
Carbon Tetrachloride	29.8	5.03	–22.9	76.7
Camphor	40.0	5.61	178.4	207.4
Cyclohexane	20.0	2.79	6.5	80.7
Naphthalene	6.9	—	80.2	—
Nitrobenzene	7.0	5.24	5.7	210.8

TABLE 3 — Integrated Rate Law Summary

Order	Rate Law	Integrated Form	t₁/₂	Units of k
0	k	[A] = [A]₀ – kt	[A]₀/2k	M·s⁻¹
1	k[A]	ln[A] = ln[A]₀ – kt	0.693/k	s⁻¹
2	k[A]²	1/[A] = 1/[A]₀ + kt	1/(k[A]₀)	M⁻¹s⁻¹
n	k[A]ⁿ	Complex	(2^(n–1)–1)/[(n–1)k[A]₀^(n–1)]	M^(1–n)s⁻¹

TABLE 4 — Van't Hoff Factor for Common Electrolytes

Electrolyte	Type	Ions	Theoretical i (complete dissoc.)
NaCl	1:1	2	i = 2
CaCl₂	1:2	3	i = 3
Na₂SO₄	2:1	3	i = 3
AlCl₃	1:3	4	i = 4
Al₂(SO₄)₃	2:3	5	i = 5
CH₃COOH	Weak acid	—	1 < i < 2
Glucose	Non-electrolyte	—	i = 1
Acetic acid in benzene	Association	—	i < 1

TABLE 5 — % Completion for First Order Reactions

% Completion	Fraction Remaining	Formula
50%	1/2	t = 0.693/k = t₁/₂
75%	1/4	t = 2 × t₁/₂
87.5%	1/8	t = 3 × t₁/₂
90%	1/10	t = 2.303/k
93.75%	1/16	t = 4 × t₁/₂
99%	1/100	t = 4.606/k
99.9%	1/1000	t = 6.909/k

Mega Formula
Reference Sheet

The Chemistry of Solutions

Raoult's Law & Vapour Pressure

Henry's Law — Gas Solubility

Depend Only on Number of Particles

Solubility Product (K_sp)

Azeotropes

Chemical Kinetics

Rate Laws & Reaction Orders

Arrhenius Equation

Data Tables

Master Glossary

Tips & Mnemonics

Akshit Tyagi

Mega FormulaReference Sheet

The Chemistry of Solutions

Raoult's Law & Vapour Pressure

Henry's Law — Gas Solubility

Depend Only on Number of Particles

Solubility Product (Ksp)

Azeotropes

Chemical Kinetics

Rate Laws & Reaction Orders

Arrhenius Equation

Data Tables

Master Glossary

Tips & Mnemonics

Akshit Tyagi

Mega Formula
Reference Sheet

Solubility Product (K_sp)