Ionic Equilibrium Lecture Notes

Theories of Acids and Bases

  • Arrhenius Theory

    • Acids: Defined as substances which release H+H^+ ions in H2OH_2O.

    • Bases: Defined as substances which release OH−OH^- ions in H2OH_2O.

  • Bronsted-Lowry Theory

    • Acid: A substance that acts as an H+H^+ ion donor.

    • Base: A substance that acts as an H+H^+ ion acceptor.

    • Conjugate Base: Obtained by removing an H+H^+ ion from a given species (Given species−H+\text{Given species} - H^+).

    • Conjugate Acid: Obtained by adding an H+H^+ ion to a given species (Given species+H+\text{Given species} + H^+).

    • Conjugate Acid-Base Pair: A pair of species that differs by only one H+H^+ ion.

    • Amphiprotic Substances: Species that have the capacity to both donate and accept H+H^+ ions.

    • Aprotic Substances: Species that act as neither a donor nor an acceptor of H+H^+ ions.

  • Lewis Theory

    • Acid: An electron-pair (e−e^- pair) acceptor.

    • Base: An electron-pair (e−e^- pair) donor.

    • Relationship: All Bronsted bases are Lewis bases.

Ostwald's Dilution Law and the Ionic Product of Water

  • Ostwald's Dilution Law

    • This law is applicable only for weak electrolytes, specifically Weak Acids (W.A.) and Weak Bases (W.B.).

    • For a monobasic acid or a monoacidic base, the degree of dissociation (α\alpha) is expressed as:       α=KC\alpha = \sqrt{\frac{K}{C}}       α=K×V\alpha = \sqrt{K \times V}

    • As volume (VV) increases or concentration (CC) approaches zero (V,C→0V, C \rightarrow 0), the degree of dissociation approaches unity (α→1\alpha \rightarrow 1).

    • Where:

      • α\alpha = Degree of dissociation

      • nn = amount in moles

  • Ionic Product of Water (KwK_w)

    • Definition: The product of the molar concentrations of hydrogen and hydroxyl ions at any given temperature.       Kw=[H+][OH−]K_w = [H^+] [OH^-]

    • Temperature Dependence: As the temperature increases, the value of KwK_w also increases.

    • Value at 25∘C25^\circ C: Kw=1×10−14 mol2 dm−6K_w = 1 \times 10^{-14}\,mol^2\,dm^{-6}.

    • The variation of KwK_w with temperature is governed by the equation:       log⁡(Kw2Kw1)=ΔH2.303R[… ]\log\left(\frac{K_{w2}}{K_{w1}}\right) = \frac{\Delta H}{2.303 R} [\dots]       (Note: Specifically related to the thermodynamic temperature change and enthalpy of ionization).

The pH Concept and Scale

  • Fundamental Definitions

    • pH=−log⁡10[H+]pH = -\log_{10}[H^+]

    • pH=−log⁡10[H3O+]pH = -\log_{10}[H_3O^+]

    • [H+]=10−pH[H^+] = 10^{-pH}

    • pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]

    • [OH−]=10−pOH[OH^-] = 10^{-pOH}

  • pH Scale at 25∘C25^\circ C

    • Scale Range: 00 (Highly Acidic) to 1414 (Highly Basic).

    • Neutral Point: pH=7pH = 7.

    • Relation: pH+pOH=pKw=14pH + pOH = pK_w = 14.

    • For neutral water: [H+]=[OH−]=Kw[H^+] = [OH^-] = \sqrt{K_w}.

  • pH Calculations for Acids and Bases

    • Strong Acids: [H+]=[Acid]=Normality[H^+] = [\text{Acid}] = \text{Normality}.

    • Strong Bases: [OH−]=[Base]=Normality[OH^-] = [\text{Base}] = \text{Normality}.

    • Weak Acids:

      • [H+]=Cα[H^+] = C \alpha

      • [H+]=KaC[H^+] = \sqrt{K_a C}

      • pH=−log⁡10(KaC)pH = -\log_{10}(\sqrt{K_a C})

      • pH=12[pKa−log⁡10C]pH = \frac{1}{2} [pK_a - \log_{10} C]

    • Weak Bases:

      • [OH−]=Cα=KbC[OH^-] = C \alpha = \sqrt{K_b C}

      • pOH=12[pKb−log⁡10C]pOH = \frac{1}{2} [pK_b - \log_{10} C]

Relative Strengths and Mixtures

  • Comparison of Two Weak Acids

    • [H+]1[H+]2=C1α1C2α2=Ka1C1Ka2C2\frac{[H^+]_1}{[H^+]_2} = \frac{C_1 \alpha_1}{C_2 \alpha_2} = \sqrt{\frac{K_{a1} C_1}{K_{a2} C_2}}

  • Comparison of Two Weak Bases

    • [OH−]1[OH−]2=C1α1C2α2=Kb1C1Kb2C2\frac{[OH^-]_1}{[OH^-]_2} = \frac{C_1 \alpha_1}{C_2 \alpha_2} = \sqrt{\frac{K_{b1} C_1}{K_{b2} C_2}}

  • Mixing Strong Electrolytes

    • Two Strong Acids Mixed:       [H+]=N1V1+N2V2V1+V2[H^+] = \frac{N_1 V_1 + N_2 V_2}{V_1 + V_2}

    • Two Strong Bases Mixed:       [OH−]=N1V1+N2V2V1+V2[OH^-] = \frac{N_1 V_1 + N_2 V_2}{V_1 + V_2}

    • Strong Acid mixed with Strong Base:

      1. If NaVa=NbVbN_a V_a = N_b V_b: The solution is Neutral.

      2. If N_a V_a > N_b V_b: The solution is Acidic.            [H+]resultant=NaVa−NbVbVa+Vb[H^+]_{\text{resultant}} = \frac{N_a V_a - N_b V_b}{V_a + V_b}

      3. If N_a V_a < N_b V_b: The solution is Basic.            [OH−]resultant=NbVb−NaVaVa+Vb[OH^-]_{\text{resultant}} = \frac{N_b V_b - N_a V_a}{V_a + V_b}

  • Mixing Weak Electrolytes

    • Two Weak Acids Mixed:       [H+]=C1α1+C2α2[H^+] = C_1 \alpha_1 + C_2 \alpha_2       [H+]=Ka1C1+Ka2C2[H^+] = \sqrt{K_{a1} C_1 + K_{a2} C_2}

    • Two Weak Bases Mixed:       [OH−]=C1α1+C2α2[OH^-] = C_1 \alpha_1 + C_2 \alpha_2       [OH−]=Kb1C1+Kb2C2[OH^-] = \sqrt{K_{b1} C_1 + K_{b2} C_2}

    • Where C1C_1 and C2C_2 are the respective concentrations.

  • Conjugate Acid-Base Pair Relation

    • Ka×Kb=KwK_a \times K_b = K_w

    • pKa+pKb=pKwpK_a + pK_b = pK_w (Valid at any temperature).

Buffer Solutions

  • Classification of Buffers

    • Simple Buffer: Consists of salts of a Weak Acid (W.A.) and a Weak Base (W.B.).

    • Mixed Buffer:

      1. Acid Buffer: A mixture of a Weak Acid (W.A.) and its salt with a Strong Base (S.B.).

      2. Basic Buffer: A mixture of a Weak Base (W.B.) and its salt with a Strong Acid (S.A.).

  • Henderson's Equation for pH of Buffer Solutions

    • Acid Buffer: pH=pKa+log⁡10[Salt][Acid]pH = pK_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]}

    • Basic Buffer: pOH=pKb+log⁡10[Salt][Base]pOH = pK_b + \log_{10} \frac{[\text{Salt}]}{[\text{Base}]}

  • Buffer Capacity (ϕ\phi)

    • Definition: The number of moles of Strong Acid (S.A.) or Strong Base (S.B.) added to 1 dm3dm^3 of buffer to change the pH by one unit.       Buffer Capacity=no. of moles of S.A. (or) S.B. added to 1 litre bufferChange in pH\text{Buffer Capacity} = \frac{\text{no. of moles of S.A. (or) S.B. added to 1 litre buffer}}{\text{Change in pH}}

  • Maximum Buffer Capacity Condition

    • Acid Buffer: Maximum capacity occurs when pH=pKapH = pK_a or [Salt]=[Acid][\text{Salt}] = [\text{Acid}].

    • Base Buffer: Maximum capacity occurs when pOH=pKbpOH = pK_b or [Salt]=[Base][\text{Salt}] = [\text{Base}].

Salt Hydrolysis

  • Types of Salt Hydrolysis

    1. Salts of S.A. and S.B.: Do not undergo hydrolysis (pH=7pH = 7).

    2. Salts of S.A. and W.B.: Undergo Cationic Hydrolysis. The resulting solution is Acidic.

      • Kh=KwKbK_h = \frac{K_w}{K_b}

      • pH=7−12[pKb+log⁡10C]pH = 7 - \frac{1}{2} [pK_b + \log_{10} C] (at 25∘C25^\circ C)

      • h=KhC=KwKbCh = \sqrt{\frac{K_h}{C}} = \sqrt{\frac{K_w}{K_b C}}

      • Where CC = salt concentration.

    3. Salts of W.A. and S.B.: Undergo Anionic Hydrolysis. The resulting solution is Basic.

      • Kh=KwKaK_h = \frac{K_w}{K_a}

      • pH=7+12[pKa+log⁡10C]pH = 7 + \frac{1}{2} [pK_a + \log_{10} C]

      • h=KwKaCh = \sqrt{\frac{K_w}{K_a C}}

    4. Salts of W.A. and W.B.:

      • Kh=KwKaKbK_h = \frac{K_w}{K_a K_b}

      • pH=7+12[pKa−pKb]pH = 7 + \frac{1}{2} [pK_a - pK_b] (at 25∘C25^\circ C)

      • h=Kh1−h≈Khh = \sqrt{\frac{K_h}{1 - h}} \approx \sqrt{K_h}

      • Acidity/Basicity depends on relative constants:

        • If Ka=KbK_a = K_b: Solution is Neutral.

        • If K_a > K_b: Solution is Acidic.

        • If K_a < K_b: Solution is Basic.

  • pH of Amphiprotic/Amphoteric Salts

    • For salts like NaHCO3NaHCO_3, NaHSNaHS, NaH2PO4NaH_2PO_4:       pH=pK1+pK22pH = \frac{pK_1 + pK_2}{2}

    • For Na2HPO4Na_2HPO_4:       pH=pK2+pK32pH = \frac{pK_2 + pK_3}{2}

Indicators and Titrations

  • Theory of Indicators

    • Indicators are substances that signal the point of equivalence in a titration via color change.

    • Chemically, they are weak organic acids or bases.

    • They exhibit different colors in their ionized and unionized forms.

    • Acid Indicator Equation: pH=pKIn+log⁡10[In−][HIn]pH = pK_{In} + \log_{10} \frac{[In^-]}{[HIn]}

    • Basic Indicator Equation: pOH=pKIn+log⁡10[In+][InOH]pOH = pK_{In} + \log_{10} \frac{[In^+]}{[InOH]}

    • Color Change Range: An indicator changes color effectively when pH=pKInpH = pK_{In}. The detectable color range is:       Range=pKIn±1\text{Range} = pK_{In} \pm 1

  • Acid-Base Titration Curves

    1. Strong Acid (S.A.) vs Strong Base (S.B.): Vertical region lies in the pH range of 33 to 1010. Any indicator is suitable.

    2. Weak Acid (W.A.) vs Strong Base (S.B.): Vertical region lies in the pH range of 8.38.3 to 10.010.0. Phenolphthalein is suitable.

    3. Strong Acid (S.A.) vs Weak Base (W.B.): Vertical region lies in the pH range of 3.13.1 to 4.54.5. Methyl orange is suitable.

    4. Weak Acid (W.A.) vs Weak Base (W.B.): No sharp change in pH occurs. No single indicator is suitable.

Solubility and Solubility Product (KspK_{sp}"

  • Solubility Product Constant (KspK_{sp})

    • Applicable for sparingly soluble salts.

    • For a general salt AxBy⇌xAy++yBx−A_x B_y \rightleftharpoons xA^{y+} + yB^{x-}, where 'SS' is the solubility:       Ksp=(xS)x⋅(yS)y=xx⋅yy⋅Sx+yK_{sp} = (xS)^x \cdot (yS)^y = x^x \cdot y^y \cdot S^{x+y}

  • Ion Product (QQ)

    • Case 1: If Q=KspQ = K_{sp}, the solution is saturated.

    • Case 2: If Q < K_{sp}, the solution is unsaturated; no precipitation occurs.

    • Case 3: If Q > K_{sp}, the solution is supersaturated; precipitation takes place.

  • Factors Affecting Solubility

    • Common Ion Effect: The solubility of sparingly soluble salts decreases in the presence of a common ion.

      • Example: Solubility of AgClAgCl in NaClNaCl solution is less than its solubility in pure H2OH_2O (S_{AgCl} \text{ in } NaCl < S_{AgCl} \text{ in } H_2O).

    • Complex Formation: Solubility increases if the salt forms a soluble complex.

      • Example: Solubility of AgClAgCl in NH3NH_3 is greater than in pure H2OH_2O due to the formation of binary complex ions (S_{AgCl} \text{ in } NH_3 > S_{AgCl} \text{ in } H_2O).", "title": "Ionic Equilibrium Study Guide"}