Maharashtra State Board · Class 12 · Chemistry · Chapter 3

Ionic Equilibria — Formula Sheet

Board Formulas

16 formulas

1.Degree of Dissociation
$α = \frac{moles of electrolyte dissociated}{total moles of electrolyte dissolved}$
α ≈ 1 for strong electrolytes and α ≪ 1 for weak electrolytes. Percent dissociation = 100α. No unit.
2.Ostwald's Dilution Law (weak acid)★
$K_{a} = \frac{α ^{2} c}{1 - α} \approx α^{2} c \Rightarrow α = \frac{K _{a}}{c}$
$K_{a}$ : Acid dissociation (ionisation) constant · $α$ : Degree of dissociation · $c$ : Initial molar concentration of the acid (mol L⁻¹)
For a weak monobasic acid HA. The approximation 1 − α ≈ 1 is valid only when α is small. α increases as the solution is diluted (c decreases). Not applicable to strong electrolytes.
3.Ostwald's Dilution Law (weak base)
$K_{b} = \frac{α ^{2} c}{1 - α} \approx α^{2} c \Rightarrow α = \frac{K _{b}}{c}$
For a weak base BOH such as NH₄OH: BOH ⇌ B⁺ + OH⁻. The algebra is the same as for a weak acid.
4.Hydronium Ion Concentration of a Weak Acid★
$[H_{3} O^{+}] = α c = K_{a} c$
Substitute α = √(Ka/c) into [H₃O⁺] = αc. Then pH = −log₁₀[H₃O⁺].
5.Hydroxide Ion Concentration of a Weak Base
$[OH^{-}] = α c = K_{b} c$
Find pOH from [OH⁻] first, then pH = 14 − pOH at 298 K.
6.Ionic Product of Water
$K_{w} = [H_{3} O^{+}] [OH^{-}] = 1.0 \times 1 0^{- 14} at 298 K$
Holds for pure water and every aqueous solution. In pure water at 298 K, [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M. Kw increases with temperature.
7.pH and pOH★
$pH = - lo g_{10} [H_{3} O^{+}], pOH = - lo g_{10} [OH^{-}]$
For a strong acid, [H₃O⁺] = c × number of H⁺ released (0.01 M HCl gives pH 2). For a strong base, [OH⁻] = c × number of OH⁻ released (Ba(OH)₂ gives 2c).
8.Relation between pH and pOH
$pH + pOH = p K_{w} = 14 (298 K)$
Obtained by taking −log₁₀ of both sides of Kw. At 298 K: pH < 7 acidic, pH = 7 neutral, pH > 7 basic.
9.pKa and pKb
$p K_{a} = - lo g_{10} K_{a}, p K_{b} = - lo g_{10} K_{b}$
The smaller the pKa, the stronger the acid; the smaller the pKb, the stronger the base.
10.Hydrolysis of Salts — Nature of the Solution
$NaCl: pH = 7, CH_{3} COONa: pH > 7, NH_{4} Cl: pH < 7$
Strong acid + strong base salt (NaCl): no hydrolysis, neutral. Weak acid + strong base salt (CH₃COONa): the anion hydrolyses, CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻, basic. Strong acid + weak base salt (NH₄Cl): the cation hydrolyses, NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺, acidic. pH values are for 298 K.
11.Salt of a Weak Acid and a Weak Base
$K_{a} > K_{b} : acidic; K_{a} < K_{b} : basic; K_{a} = K_{b} : neutral$
Both ions hydrolyse, so the relative strengths of the parent acid and base decide. CH₃COONH₄ is nearly neutral because Ka of CH₃COOH and Kb of NH₄OH are both about 1.8 × 10⁻⁵.
12.Henderson–Hasselbalch Equation (acidic buffer)★
$pH = p K_{a} + lo g_{10} \frac{[ salt ]}{[ acid ]}$
For a weak acid with its salt of a strong base (e.g. CH₃COOH + CH₃COONa). When [salt] = [acid], pH = pKa.
13.Henderson–Hasselbalch Equation (basic buffer)
$pOH = p K_{b} + lo g_{10} \frac{[ salt ]}{[ base ]}$
For a weak base with its salt of a strong acid (e.g. NH₄OH + NH₄Cl). Convert to pH = 14 − pOH at 298 K.
14.Solubility Product
$A_{x} B_{y} (s) ⇌ x A^{y +} (a q) + y B^{x -} (a q), K_{s p} = [A^{y +}]^{x} [B^{x -}]^{y}$
Product of the molar concentrations of the ions in a saturated solution, each raised to its coefficient. The solid does not appear. Ksp of a salt changes only with temperature.
15.Relation between Ksp and Molar Solubility★
$K_{s p} = x^{x} y^{y} S^{x + y}$
$K_{s p}$ : Solubility product · $S$ : Molar solubility (mol L⁻¹) · $x, y$ : Numbers of cations and anions in the formula AxBy
S in mol L⁻¹ (divide g L⁻¹ by molar mass). AB (AgCl, BaSO₄): Ksp = S². AB₂ or A₂B (CaF₂, PbI₂, Ag₂CrO₄): Ksp = 4S³. AB₃ (Fe(OH)₃): Ksp = 27S⁴. A₃B₂ (Ca₃(PO₄)₂): Ksp = 108S⁵.
16.Condition for Precipitation
$IP > K_{s p} : precipitate; IP = K_{s p} : saturated; IP < K_{s p} : unsaturated$
Ionic product (IP) has the same form as Ksp but uses the actual concentrations after mixing; mixing equal volumes halves each concentration. Adding a common ion raises IP, so solubility decreases (common ion effect).