5.2 Acid-Base Definitions, pH Scale, Titrations & Physiological Buffers

5.2 Acid-Base Definitions, pH Scale, Titrations & Physiological Buffers

Acid-base chemistry governs cellular metabolism and physiological homeostasis.

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Comparative Acid-Base Frameworks: Arrhenius, Brønsted-Lowry & Lewis

Acid-base chemistry spans three frameworks:

• Arrhenius: Restricted strictly to aqueous systems. Acids dissociate into $\text{H}^+$ ($\text{H}_3\text{O}^+$); bases dissociate into $\text{OH}^-$.
• Brønsted-Lowry: Based on proton transfer. An acid is a proton ($\text{H}^+$) donor; a base is a proton ($\text{H}^+$) acceptor. Proton transfer forms a conjugate acid-base pair differing by a single proton ($HA / A^-$ and $B / BH^+$).
• Lewis: Broadest model. An acid is an electron-pair acceptor (electrophile); a base is an electron-pair donor (nucleophile), forming coordinate covalent bonds (e.g., transition metal complexes $\text{Fe}^{2+} + \text{heme}$, and catalysts $\text{BF}_3, \text{AlCl}_3$).

Amphiprotic species can donate or accept protons ($\text{H}_2\text{O}$, $\text{HCO}_3^-$, $\text{H}_2\text{PO}_4^-$, and amino acids).

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Water Autoionization ($K_w$) and the Logarithmic pH Scale

Water autoionizes in an endothermic equilibrium:

$$2\text{H}_2\text{O}(l) \rightleftharpoons \text{H}_3\text{O}^+(aq) + \text{OH}^-(aq) \quad (\Delta H^\circ = +55.8\text{ kJ/mol})$$

At $25^\circ\text{C}$ ($298\text{ K}$), $K_w = [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}$, so $pH + pOH = 14.00$.

Physiological Temperature Dependence

Autoionization is endothermic; elevated temperature shifts equilibrium right. At body temperature ($37^\circ\text{C}$ or $310\text{ K}$), $K_w$ rises to $\approx 2.4 \times 10^{-14}$:

$$[\text{H}_3\text{O}^+]_{\text{neutral}} = \sqrt{2.4 \times 10^{-14}} \approx 1.55 \times 10^{-7}\text{ M} \implies pH_{\text{neutral}} \approx 6.81$$

Neutrality strictly denotes $[\text{H}_3\text{O}^+] = [\text{OH}^-]$, not a fixed pH of 7.00. Arterial blood at $37^\circ\text{C}$ (pH 7.40) has $[\text{H}^+] < [\text{OH}^-]$, rendering it mildly alkaline relative to physiological neutrality.

MCAT Log Estimation Shortcut

For $[\text{H}^+] = m \times 10^{-n}$ where $1 \le m < 10$:

$$pH = n - \log(m) \approx n - 0.m$$

Example: If $[\text{H}^+] = 4.0 \times 10^{-5}\text{ M} \implies pH \approx 5 - 0.40 = 4.60$ (exact: $5 - 0.60 = 4.40$).

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Strong vs. Weak Acids, Bases & Salt Hydrolysis

• Strong Acids: Ionize completely ($K_a \gg 1$): $\text{HCl}, \text{HBr}, \text{HI}, \text{HNO}_3, \text{HClO}_4, \text{HClO}_3, \text{H}_2\text{SO}_4$ (first proton). $[\text{H}^+] = [HA]_0$.
• Strong Bases: Dissociate completely: Group 1 hydroxides ($\text{LiOH}, \text{NaOH}, \text{KOH}$) and soluble Group 2 hydroxides ($\text{Ca(OH)}_2, \text{Sr(OH)}_2, \text{Ba(OH)}_2$). Note that $\text{Ca(OH)}_2$ yields $2\text{ moles of } \text{OH}^-$.
• Weak Acids and Bases: Ionize partially in equilibria ($K_a = [\text{H}_3\text{O}^+][A^-]/[HA]$ and $K_b = [BH^+][\text{OH}^-]/[B]$).
• Conjugate Relationship: $K_a \times K_b = K_w = 1.0 \times 10^{-14} \implies pK_a + pK_b = 14.00$ at $25^\circ\text{C}$. Stronger acids have weaker conjugate bases; strong acid conjugates possess negligible basicity. When ionization $< 5\%$, $[\text{H}^+] \approx \sqrt{K_a [HA]_0}$.

Polyprotic acids undergo stepwise deprotonations ($K_{a1} \gg K_{a2} \gg K_{a3}$) because removing a proton from an anion is electrostatically unfavorable. Solution pH is dictated by $K_{a1}$.

Salt Hydrolysis

Neutralization produces a salt whose hydrolysis determines pH:

• Strong Acid + Strong Base ($\text{NaCl}$): Neither ion hydrolyzes; $\mathbf{pH = 7.00}$.
• Strong Acid + Weak Base ($\text{NH}_4\text{Cl}$): Cation hydrolyzes ($\text{NH}_4^+ + \text{H}_2\text{O} \rightleftharpoons \text{NH}_3 + \text{H}_3\text{O}^+$); $\mathbf{pH < 7.00}$.
• Weak Acid + Strong Base ($\text{CH}_3\text{COONa}$): Anion hydrolyzes ($\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-$); $\mathbf{pH > 7.00}$.

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Titration Curves and Indicators

• Equivalence Point: Stoichiometric neutralization occurs ($n_{\text{acid}} = n_{\text{base}}$, $M_A V_A n_A = M_B V_B n_B$).
• Half-Equivalence Point: Exactly half the analyte is neutralized ($[HA] = [A^-]$). Here, $\mathbf{pH = pK_a}$, and buffer capacity is maximized.

Indicators are weak acids ($HIn \rightleftharpoons \text{H}^+ + In^-$) with distinct colors across $pK_{In} \pm 1$. An appropriate indicator has $pK_{In}$ within the steep equivalence inflection.

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Henderson-Hasselbalch Equation and Buffer Systems

A buffer contains a weak acid and its conjugate base (or a weak base and its conjugate acid), resisting pH changes. Buffer pH follows the Henderson-Hasselbalch equation:

$$pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right)$$

• When $[A^-] = [HA]$, $\log(1) = 0 \implies \mathbf{pH = pK_a}$.
• Effective buffering spans $\mathbf{pK_a \pm 1}$ (representing $[A^-]/[HA]$ ratios from $0.1$ to $10$).
• Buffer capacity scales directly with total buffer concentration $[HA] + [A^-]$. Diluting a buffer maintains the ratio and leaves pH unchanged, but decreases total buffer capacity.

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Physiological Buffer Systems and Clinical Disorders

Arterial blood pH is defended within the window of 7.35 to 7.45:

1. Bicarbonate Buffer System

The primary extracellular buffer in blood plasma operates as an open system:

$$\text{CO}_2(g) + \text{H}_2\text{O}(l) \overset{\text{Carbonic Anhydrase}}{\rightleftharpoons} \text{H}_2\text{CO}_3(aq) \rightleftharpoons \text{H}^+(aq) + \text{HCO}_3^-(aq)$$

With carbonic acid $pK_a = 6.10$, arterial pH 7.40 requires a $[\text{HCO}_3^-]:[\text{CO}_2]$ ratio of $\approx 20:1$ ($\log(20) = 1.30$). Pulmonary ventilation regulates volatile $\text{CO}_2$ within minutes, while kidneys regulate non-volatile $\text{HCO}_3^-$ over hours to days.

• Respiratory Acidosis: Hypoventilation (COPD) retains $\text{CO}_2$ ($P_{a\text{CO}_2} \uparrow, pH \downarrow$); compensated by renal $\text{HCO}_3^-$ retention.
• Respiratory Alkalosis: Hyperventilation blows off $\text{CO}_2$ ($P_{a\text{CO}_2} \downarrow, pH \uparrow$); compensated by renal $\text{HCO}_3^-$ excretion.
• Metabolic Acidosis: Ketoacidosis or diarrhea depletes $\text{HCO}_3^-$ ($[\text{HCO}_3^-] \downarrow, pH \downarrow$); compensated by hyperventilation (Kussmaul breathing).
• Metabolic Alkalosis: Vomiting ($\text{HCl}$ loss) increases $\text{HCO}_3^-$ ($[\text{HCO}_3^-] \uparrow, pH \uparrow$); compensated by hypoventilation.

2. Phosphate and Protein Buffers

The dihydrogen phosphate buffer ($\text{H}_2\text{PO}_4^- \rightleftharpoons \text{H}^+ + \text{HPO}_4^{2-}$, $pK_a = 6.80$) buffers intracellular cytoplasm and renal filtrate. Protein buffers—principally albumin and the histidine imidazole rings of hemoglobin ($pK_a \approx 6.5$)—buffer metabolic protons during tissue gas exchange (Bohr effect).