Ionic Equilibrium in Solution — Revision Notes

⚡ 30-Second Revision

Electrolytes — Strong ($\alpha \approx 1$), Weak ($0 < \alpha < 1$).
Ostwald's Dilution Law — $\alpha = \sqrt{K_a/C}$ (for weak acid).
Ionic Product of Water — $K_w = [H^+][OH^-] = 1.0 \times 10^{-14}$ at $25^circ C$.
pH Scale — $pH = -log[H^+]$, $pOH = -log[OH^-]$, $pH + pOH = 14$.
Acid/Base Strength — $K_a$ (acid), $K_b$ (base). Larger $K_a$/$K_b$ = stronger. $pK_a = -logK_a$, $pK_b = -logK_b$. Smaller $pK_a$/$pK_b$ = stronger.
Conjugate Pair — $K_a \times K_b = K_w$ or $pK_a + pK_b = pK_w$.
Salt Hydrolysis

- SA+SB: Neutral - SA+WB: Acidic ($K_h = K_w/K_b$) - WA+SB: Basic ($K_h = K_w/K_a$) - WA+WB: pH depends on $K_a$ vs $K_b$.

Buffer Solutions — Weak acid/conjugate base OR Weak base/conjugate acid.
Henderson-Hasselbalch — $pH = pK_a + log_{10}\frac{[Salt]}{[Acid]}$ (acidic buffer).
Solubility Product — For $A_xB_y$, $K_{sp} = [A^{y+}]^x[B^{x-}]^y$.
Common Ion Effect — Decreases solubility of sparingly soluble salt.
Precipitation — Occurs if $Q_{sp} > K_{sp}$.

2-Minute Revision

Ionic equilibrium describes the dynamic balance of ions and undissociated molecules in electrolyte solutions. Strong electrolytes dissociate completely, while weak electrolytes establish equilibrium, quantified by the degree of dissociation ($alpha$) and governed by Ostwald's Dilution Law.

Water's autoionization gives rise to the ionic product ($K_w = 10^{-14}$ at $25^circ C$) and the pH scale ($pH = -log[H^+]$), where $pH+pOH=14$. Acid and base strengths are measured by $K_a$ and $K_b$ (or $pK_a$ and $pK_b$), with the crucial relationship $K_a \times K_b = K_w$ for conjugate pairs.

Salts can hydrolyze, affecting solution pH depending on the strengths of their parent acid and base. Buffer solutions, mixtures of weak acid/base and their conjugates, resist pH changes, with their pH calculated using the Henderson-Hasselbalch equation.

Finally, sparingly soluble salts establish solubility equilibrium, characterized by the solubility product ($K_{sp}$), which is used to calculate molar solubility ($S$) and predict precipitation. The common ion effect reduces the solubility of such salts.

5-Minute Revision

Ionic equilibrium is the study of reactions involving ions in solution, specifically the dynamic balance between dissociated ions and undissociated molecules. This is particularly relevant for weak electrolytes (weak acids, weak bases), which only partially ionize. The **degree of dissociation ($alpha$) quantifies this extent, and Ostwald's Dilution Law** states that $\alpha$ increases with dilution.

Water's autoionization ($H_2O \rightleftharpoons H^+ + OH^-$) is fundamental, yielding the **ionic product of water ($K_w = [H^+][OH^-]$)**, which is $1.0 \times 10^{-14}$ at $25^circ C$. This forms the basis of the pH scale ($pH = -log[H^+]$), where $pH+pOH=14$. Solutions are acidic ($pH<7$), neutral ($pH=7$), or basic ($pH>7$) at $25^circ C$.

Acids and bases are defined by Arrhenius (H+/OH- producers), Brønsted-Lowry (proton donors/acceptors), and Lewis (electron pair acceptors/donors). Their strengths are quantified by **acid dissociation constant ($K_a$) and base dissociation constant ($K_b$)**. A larger $K_a$ means a stronger acid, and a larger $K_b$ means a stronger base. For a conjugate acid-base pair, a critical relationship exists: $K_a \times K_b = K_w$, or in logarithmic form, $pK_a + pK_b = pK_w = 14$.

Salt hydrolysis occurs when ions from a salt react with water, altering the solution's pH. Salts of strong acid-strong base are neutral. Salts of strong acid-weak base are acidic (e.g., $NH_4Cl$). Salts of weak acid-strong base are basic (e.g., $CH_3COONa$). Salts of weak acid-weak base have a pH determined by the relative strengths of the acid and base ($pH = 7 + \frac{1}{2}pK_a - \frac{1}{2}pK_b$).

Buffer solutions resist pH changes upon addition of small amounts of acid or base. They consist of a weak acid and its conjugate base (acidic buffer) or a weak base and its conjugate acid (basic buffer). Their pH can be calculated using the Henderson-Hasselbalch equation: $pH = pK_a + log_{10}\frac{[Salt]}{[Acid]}$ for acidic buffers.

Solubility equilibrium deals with sparingly soluble salts. For a salt $A_xB_y$, the **solubility product constant ($K_{sp}$)** is $K_{sp} = [A^{y+}]^x[B^{x-}]^y$. This constant relates to the **molar solubility ($S$)** of the salt (e.g., $K_{sp}=S^2$ for $AB$, $K_{sp}=4S^3$ for $AB_2$). The common ion effect reduces the solubility of a sparingly soluble salt when a common ion is added. Precipitation occurs if the **ionic product ($Q_{sp}$)** exceeds $K_{sp}$.

Worked Example: Calculate the pH of a $0.01,\text{M}$ $NH_4OH$ solution if $K_b = 1.8 \times 10^{-5}$.

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$NH_4OH \rightleftharpoons NH_4^+ + OH^-$
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Initial: $0.01$, $0$, $0$.
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Equilibrium: $0.01-x$, $x$, $x$.
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$K_b = \frac{x^2}{0.01-x} \approx \frac{x^2}{0.01} = 1.8 \times 10^{-5}$.
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$x^2 = 1.8 \times 10^{-7} \implies x = [OH^-] = \sqrt{1.8 \times 10^{-7}} = 4.24 \times 10^{-4},\text{M}$.
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$pOH = -log(4.24 \times 10^{-4}) = 4 - log(4.24) = 4 - 0.627 = 3.373$.
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$pH = 14 - pOH = 14 - 3.373 = 10.627$.

Prelims Revision Notes

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Electrolytes — Substances producing ions in solution. Strong (complete dissociation, e.g., HCl, NaOH, NaCl). Weak (partial dissociation, equilibrium, e.g., $CH_3COOH$, $NH_4OH$).
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Degree of Dissociation ($alpha$) — Fraction dissociated. For weak electrolytes, $\alpha = \sqrt{K/C}$ (Ostwald's Dilution Law). $\alpha$ increases with dilution.
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Ionic Product of Water ($K_w$) — $H_2O \rightleftharpoons H^+ + OH^-$. $K_w = [H^+][OH^-]$. At $25^circ C$, $K_w = 1.0 \times 10^{-14}$. $K_w$ increases with temperature.
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pH Scale — $pH = -log[H^+]$, $pOH = -log[OH^-]$. $pH + pOH = 14$ at $25^circ C$. Acidic ($pH<7$), Neutral ($pH=7$), Basic ($pH>7$).
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Acid-Base Theories

* Arrhenius: Acid ($H^+$ producer), Base ($OH^-$ producer). * Brønsted-Lowry: Acid (proton donor), Base (proton acceptor). Conjugate acid-base pairs (e.g., $HCl/Cl^-$). * Lewis: Acid (electron pair acceptor), Base (electron pair donor).

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Acid/Base Dissociation Constants — $K_a = \frac{[H^+][A^-]}{[HA]}$, $K_b = \frac{[B^+][OH^-]}{[BOH]}$. $pK_a = -logK_a$, $pK_b = -logK_b$. Stronger acid = larger $K_a$ (smaller $pK_a$). Stronger base = larger $K_b$ (smaller $pK_b$).
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Conjugate Pair Relationship — For a conjugate acid-base pair, $K_a \times K_b = K_w$ or $pK_a + pK_b = pK_w = 14$.
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Salt Hydrolysis — Reaction of salt ions with water to produce acidity or basicity.

* SA+SB (e.g., NaCl): No hydrolysis, $pH=7$. * **SA+WB (e.g., $NH_4Cl$)**: Cation hydrolysis ($NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+$), acidic solution, $pH < 7$. $K_h = K_w/K_b$. * **WA+SB (e.g., $CH_3COONa$)**: Anion hydrolysis ($CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$), basic solution, $pH > 7$. $K_h = K_w/K_a$. * **WA+WB (e.g., $CH_3COONH_4$)**: Both hydrolyze. $pH = 7 + \frac{1}{2}pK_a - \frac{1}{2}pK_b$.

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Buffer Solutions — Resist pH change.

* Acidic Buffer: Weak acid + its conjugate base (e.g., $CH_3COOH/CH_3COONa$). $pH = pK_a + log_{10}\frac{[Salt]}{[Acid]}$. * Basic Buffer: Weak base + its conjugate acid (e.g., $NH_4OH/NH_4Cl$). $pOH = pK_b + log_{10}\frac{[Salt]}{[Base]}$.

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Solubility Product ($K_{sp}$) — For sparingly soluble salt $A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$, $K_{sp} = [A^{y+}]^x[B^{x-}]^y$.

* **Molar Solubility ($S$)**: For $AB$, $K_{sp}=S^2$. For $AB_2$, $K_{sp}=4S^3$. For $A_2B_3$, $K_{sp}=108S^5$.

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Common Ion Effect — Decreases solubility of a sparingly soluble salt by adding a common ion.
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Precipitation Condition — Compare Ionic Product ($Q_{sp}$) with $K_{sp}$. If $Q_{sp} > K_{sp}$, precipitation occurs.

Vyyuha Quick Recall

Please Help All Boys Solve Buffer Solubility Equations:

PH: $pH = -log[H^+]$
Henderson-Hasselbalch: $pH = pK_a + log\frac{[Salt]}{[Acid]}$
Acid-Base Conjugates: $K_a \times K_b = K_w$
Buffer Action: Resists pH changes
Salt Hydrolysis: Determines pH of salt solutions
Basic/Acidic: $pH<7$ (acidic), $pH>7$ (basic)
Solubility Product: $K_{sp}$ for sparingly soluble salts
Equilibrium: Dynamic balance in weak electrolytes