14Ionic equilibrium

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ELECTROLYTES
▢ Electrolyte: Substance which in solution or fused/molten state conducts electricity and simultaneously undergoes chemical decomposition.
▢ Non-electrolyte: Substance which in solution or molten state does not conduct electricity.
▢ Examples of Non-electrolytes:
    ◉ _*type: bullet
  1. Organic compounds
  2. Pure water
  3. \(C_6H*{12}O_6\) → not electrolyte because no ions with water

Table 1: Strong vs weak electrolytes

Type
Dissociation
\(\alpha\)
Strong electrolyte
Almost complete ionisation in aqueous solution
\(\alpha \approx 1\)
Weak electrolyte
Poor / partial ionisation in aqueous solution
\(\alpha < 1\)
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ARRHENIUS THEORY OF ELECTROLYTIC DISSOCIATION
▢ Postulates:
  • •
    Electrolyte molecules in aqueous solution undergo spontaneous dissociation.
  • •
    Positive ions + negative ions formed.
  • •
    \(NaOH \rightarrow Na^+ + OH^-\)
  • •
    \(KCl \rightarrow K^+ + Cl^-\)
▢ Degree of Ionisation:
❖ Definition: Fraction of total electrolyte molecules dissociated into ions.
❖ Formula: \(\alpha = \dfrac{\text{Number of dissociated molecules}}{\text{Total molecules of electrolyte before dissociation}}\)
❖ Dilution Effect: Dilution \(\uparrow\) → \(\alpha\uparrow\); infinite dilution → \(\alpha \rightarrow 1\)
▢ Ionic Equilibrium:
  • •
    Moderate concentration → equilibrium between ions and undissociated molecules
  • •
    \(NaOH \rightleftharpoons Na^+ + OH^-\)
  • •
    \(KCl \rightleftharpoons K^+ + Cl^-\)
  • •
    \(Al_2(SO_4)_3 \rightleftharpoons 2Al^{3+} + 3SO_4^{2-}\)
📚
FACTORS AFFECTING DEGREE OF IONISATION

Table 1: Factors

Factor
Effect
Nature of electrolyte
Strong electrolyte: \(\alpha\approx1\); weak electrolyte: \(\alpha<1\)
Nature of solvent
Higher dielectric constant → higher ionising power
Water
Most powerful ionising solvent
Concentration
\(\alpha \propto \dfrac{1}{\text{concentration}}\)
Amount of solute
\(\alpha \propto \dfrac{1}{\text{amount of solute in given volume / wt. solution}}\)
Dilution
\(\alpha \propto\) dilution; dissociation increases with dilution [MOE Model]
Amount of solvent
\(\alpha \propto\) amount of solvent
Temperature
\(\alpha\) increases with rise in temperature; \(\alpha \propto T\)
Common ion
Presence of common ion decreases ionisation
▢ Common Ion Examples:
  • •
    Ionisation of \(CH_3COOH\) suppressed by \(HCl\) due to common \(H^+\)
  • •
    \(HCl\) gas through saturated \(NaCl\) solution → solubility of \(NaCl\) decreases
  • •
    Purification of \(NaCl\) by \(HCl\) uses common ion effect [MOE 2052]
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OSTWALD'S DILUTION LAW
▢ Concept:
  • •
    Weak electrolytes not completely dissociated.
  • •
    Equilibrium exists between ions and undissociated molecules.
  • •
    Equilibrium = ionic equilibrium.
  • •
    Applicable only to weak electrolytes.
  • •
    Fails for strong electrolytes.
▢ For Weak Electrolyte \(AB\):
❖ Reaction: \(AB \rightleftharpoons A^+ + B^-\)

Table 1: Concentration setup

State
\(AB\)
\(A^+\)
\(B^-\)
Initial
\(c\)
0
0
Equilibrium
\(c-c\alpha=c(1-\alpha)\)
\(c\alpha\)
\(c\alpha\)
❖ Formulae:
  • •
    \(K = \dfrac{[A^+][B^-]}{[AB]}\)
  • •
    \(K = \dfrac{c\alpha \times c\alpha}{c(1-\alpha)}\)
  • •
    \(K = \dfrac{c\alpha^2}{1-\alpha}\)
▢ If 1 Mole in \(V\) L:
  • •
    \(c = \dfrac{1}{V}\)
  • •
    \(K = \dfrac{\alpha^2}{(1-\alpha)V}\)
▢ For Weak Electrolyte, \(\alpha\) Very Small:
  • •
    \(1-\alpha \approx 1\)
  • •
    \(K = c\alpha^2\)
  • •
    \(K = \dfrac{\alpha^2}{V}\)
  • •
    \(\alpha = \sqrt{\dfrac{K}{c}}\)
  • •
    \(\alpha = \sqrt{VK}\)
  • •
    \(\alpha \propto \dfrac{1}{\sqrt{c}}\)
  • •
    \(\alpha \propto \sqrt{V}\)
📚
DISSOCIATION OF ACID IN WATER
▢ Reaction: \(HA \rightleftharpoons H^+ + A^-\)
▢ Dissociation Constant:
  • •
    \(K_a = \dfrac{[H^+][A^-]}{[HA]}\)
  • •
    \(K_a\) = characteristic constant of acid \(HA\)
  • •
    Greater \(K_a\) → greater \([H^+]\) → stronger acid

Table 1: Weak acid setup

State
\(HA\)
\(H^+\)
\(A^-\)
Initial
\(c\)
0
0
Equilibrium
\(c(1-\alpha)\)
\(c\alpha\)
\(c\alpha\)
▢ Formulae:
  • •
    \(K_a = \dfrac{c\alpha^2}{1-\alpha}\)
  • •
    For weak acid: \(1-\alpha \approx 1\)
  • •
    \(K_a = c\alpha^2\)
  • •
    \(\alpha = \sqrt{\dfrac{K_a}{c}}\)
  • •
    \([H^+] = c\alpha = \sqrt{cK_a}\)
  • •
    \(pH = -\log[H_3O^+]\)
  • •
    \(pH = -\log(cK_a)^{1/2}\)
  • •
    \(pH = \dfrac{1}{2}(-\log c - \log K_a)\)
📚
POLYBASIC ACIDS
▢ Concept:
  • •
    Complete ionisation in several steps.
  • •
    Number of ionisation steps = number of replaceable hydrogen atoms.
  • •
    Each step has definite ionisation constant.
  • •
    Number of constants = number of replaceable hydrogen atoms.
▢ Example: Orthophosphoric Acid:
  • •
    \(H_3PO_4 \rightleftharpoons H^+ + H_2PO_4^-\) ; \(K_1\)
  • •
    \(H_2PO_4^- \rightleftharpoons H^+ + HPO_4^{2-}\) ; \(K_2\)
  • •
    \(HPO_4^{2-} \rightleftharpoons H^+ + PO_4^{3-}\) ; \(K_3\)
  • •
    \(K_1 > K_2 > K_3\)
  • •
    \(K = K_1 \times K_2 \times K_3\)
Diprotic acid
For any diprotic acid \(H_2X\), \(K_1 > K_2\).
📚
DISSOCIATION OF BASE IN WATER
▢ Reaction: \(BOH \rightleftharpoons B^+ + OH^-\)

Table 1: Weak base setup

State
\(BOH\)
\(B^+\)
\(OH^-\)
Initial
\(c\)
0
0
Equilibrium
\(c(1-\alpha)\)
\(c\alpha\)
\(c\alpha\)
▢ Formulae:
  • •
    \(K_b = \dfrac{[B^+][OH^-]}{[BOH]}\)
  • •
    \(K_b = \dfrac{c\alpha^2}{1-\alpha}\)
  • •
    For weak base: \(1-\alpha \approx 1\)
  • •
    \(K_b = c\alpha^2\)
  • •
    \(\alpha = \sqrt{\dfrac{K_b}{c}}\)
  • •
    \([OH^-] = c\alpha = \sqrt{cK_b}\)
  • •
    \(pOH = -\log[OH^-]\)
  • •
    \(pOH = \dfrac{1}{2}(-\log c - \log K_b)\)
  • •
    \(pH = 14 - pOH\)
▢ Strength: Greater \(K_b\) → greater dissociation → stronger base.
📚
STRENGTH OF ACIDS AND BASES
▢ Acid Strength:
    ◉ **type: bullet
  1. Depends on number of free \(H^+\) ions in solution.
  2. Dilution increases ionisation → acid strength increases.
  3. At infinite dilution, ionisation of all acids is nearly complete.
  4. All acids are not equally strong at infinite dilution.
  5. \(HCl\), \(H_2SO_4\) ionise fully at all dilutions → strong acids.
  6. Acetic acid ionises to lesser extent → weak acid.
▢ Relative Strength:
    ◉ **type: bullet
  1. \(\dfrac{\alpha_1}{\alpha_2} = \sqrt{\dfrac{K*{a1}}{K*{a2}}}\)
  2. \(\dfrac{\text{Strength of HA}}{\text{Strength of HB}} = \sqrt{\dfrac{K*{HA}}{K*{HB}}}\)
▢ Leveling Effect: Strength of all strong acids in water becomes equal to strength of \(H_3O^+\).
▢ Acid Strength in Glacial Acetic Acid: \(HClO_4 > HI > HBr > H_2SO_4 > HCl > HNO_3 > H_3O^+ > H_3PO_4 > HF > CH_3COOH > H_2CO_3 > H_2S > HCN\)
▢ Base Strength:
    ◉ **type: bullet
  1. \(\dfrac{\alpha_1}{\alpha_2} = \sqrt{\dfrac{K*{b1}}{K*{b2}}}\)
  2. \(CsOH\) = strongest base known
Important
  • •
    \(HClO_4\) = strongest acid known
  • •
    \(HCN\) = weakest hydracid known
📚
DISSOCIATION OF WATER / IONIC PRODUCT OF WATER
▢ Water: Ampholyte: acts as acid by donating \(H^+\); acts as base by accepting \(H^+\).
▢ Reaction: \(H_2O \rightleftharpoons H^+ + OH^-\)
▢ Equilibrium Expression:
  • •
    \(K = \dfrac{[H^+][OH^-]}{[H_2O]}\)
  • •
    Undissociated water concentration nearly constant: \(55.5\,mol\,L^{-1}\)
  • •
    \(K_w = [H^+][OH^-]\)
▢ At \(25^\circ C\):
  • •
    \(K_w = 1\times10^{-14}\,mol^2L^{-2}\) [MOE 2062]
  • •
    Pure water: \([H^+] = [OH^-] = 1\times10^{-7}\,M\)
  • •
    Only \(10^{-7}\) mole of water in ionic form out of approximately \(55.5\) mole

Table 1: Nature of solution

Condition
Nature
\([H^+] = [OH^-]\)
Neutral
\([H^+] > [OH^-]\)
Acidic
\([H^+] < [OH^-]\)
Basic
▢ Temperature Effect:
  • •
    \(K_w\) increases with temperature.
  • •
    In pure water, \([H^+]\) and \([OH^-]\) remain equal.
  • •
    At \(0^\circ C\): \(K_w \approx 10^{-15}\), \([H^+] = [OH^-] = 10^{-7.5}\), neutral pH = 7.5
  • •
    At \(25^\circ C\): neutral pH = 7.0
  • •
    At \(60^\circ C\): \(K_w \approx 10^{-13}\), neutral pH = 6.5
  • •
    pH scale at \(60^\circ C\): 0 to 13
  • •
    pH decreases with increase in temperature.
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HYDROGEN AND HYDROXYL ION CONCENTRATION
▢ Strong Acids / Bases:
  • •
    Complete ionisation.
  • •
    \([H^+] =\) normality of acid
  • •
    \([OH^-] =\) normality of base
  • •
    \([H^+] = \text{molarity} \times \text{basicity}\)
  • •
    \([OH^-] = \text{molarity} \times \text{acidity}\)
▢ Weak Acids / Bases:
  • •
    \([H^+] = \sqrt{K_a c}\)
  • •
    \([H^+] = c\alpha\)
  • •
    \([OH^-] = \sqrt{K_b c}\)
  • •
    \([OH^-] = c\alpha\)
▢ Using Normality and Degree of Ionisation:
  • •
    \([H^+] = N\alpha\)
  • •
    \([OH^-] = N\alpha\)
📚
PH SCALE
▢ Introduced By: Sorensen
▢ Basis: Ionic product of water.
▢ Definitions:
  • •
    \([H^+] = 10^{-pH}\)
  • •
    \(pH = -\log[H^+]\)
  • •
    \(pH = \log\dfrac{1}{[H^+]}\)

Table 1: pH, pOH and ion concentration

Parameter
Acidic
Basic
Neutral
\([H^+]\) mol/L
\(>10^{-7}\)
\(<10^{-7}\)
\(=10^{-7}\)
pH
\(<7\)
\(>7\)
\(=7\)
\([OH^-]\) mol/L
\(<10^{-7}\)
\(>10^{-7}\)
\(=10^{-7}\)
pOH
\(>7\)
\(<7\)
\(=7\)
▢ Important Points:
  • •
    Neutral pure water at \(25^\circ C\): pH = 7
  • •
    Acidic solution: pH < 7
  • •
    Alkaline solution: pH > 7
  • •
    \(K_w\) changes with temperature → pH also changes with temperature
  • •
    Heating water → dissociation increases; pH decreases
  • •
    Boiling water pH = 6.5625 but neutral
  • •
    10-fold increase in \([H^+]\) decreases pH by 1 unit
  • •
    pH 5 to pH 2 → \([H^+]\) increases \(10^3\) times
  • •
    100-fold decrease in \([H^+]\
Q1.
pH of 10-12 M HCl is
📅MOE Model
Q2.
The pH value of a solution of NaOH is 10. Assuming complete dissociation, the concentration of OH- ion is
📅MOE 2062
Q3.
Why is precipitate of AgCl obtained when a drop of AgNO3 is added to aqueous NaCl solution?
📅MOE 2062
Q4.
Ionic product of water is
📅MOE 2060
Q5.
pH of 0.02 M NaOH is
📅MOE 2063
Q6.
pH of 50 cc of 0.01 N HCl is decreased by
Q7.
4 ml of 0.5 N HCl is mixed with 1 ml of 2 N KOH. The pH of resulting solution is
📅MOE 2056
Q8.
Solubility of AB2 is x. Then the solubility product will be
📅IOM 2007
Q9.
The solubility product of a sparingly soluble salt AB2 is 1.08 × 10-23 at 25°C. Its molar solubility is
📅IOM 1996
Q10.
pH of a solution containing 2 g of sodium hydroxide per litre of water will be
📅IOM 2005
Q11.
The highest pH value is shown by 0.1 M
📅IOM 2008•MOE 2065
Q12.
pH of 0.1% solution of NaOH is