Acid–Base Equilibria, pH Scales, and Neutralization (Comprehensive Study Notes)

Acid–Base Characterization Overview

  • Primary definition (Brønsted–Lowry focus)
    • Acids: species that donate H+\text{H}^+
    • Bases: species that accept H+\text{H}^+
  • Aqueous viewpoint (Arrhenius supplement)
    • Acidic solution ⇢ higher [H+][\text{H}^+] (or [H3O+][\text{H}_3\text{O}^+])
    • Basic solution ⇢ higher [OH−][\text{OH}^-]
  • Descriptive labels
    • “Strong / weak” ⇢ extent of dissociation (chemical behavior)
    • “Concentrated / dilute” ⇢ molar concentration (quantity)
    • MCAT expects you to separate these ideas explicitly.

Auto-ionization of Water (Self-Ionization)

  • Amphoteric nature: H2O\text{H}_2\text{O} acts as an acid in presence of a base and as a base in presence of an acid.
  • Reaction
    H<em>2O(l)+H</em>2O(l)⇌H3O+(aq)+OH−(aq)\text{H}<em>2\text{O}(l)+\text{H}</em>2\text{O}(l)\rightleftharpoons\text{H}_3\text{O}^+(aq)+\text{OH}^-(aq)
  • Key notes
    • One molecule donates a proton, the other accepts.
    • In many books the hydronium ion is written as H+\text{H}^+; remember the proton is never free in solution.
    • Reaction is reversible ⇢ equilibrium established in pure water.

Water Dissociation Constant KwK_w

  • Defined: K<em>w=[H</em>3O+][OH−]K<em>w=[\text{H}</em>3\text{O}^+][\text{OH}^-]
  • At 25 °C (298 K): Kw=1.0×10−14K_w=1.0\times10^{-14}
    • In pure water [H3O+]=[OH−]=1.0×10−7 M[\text{H}_3\text{O}^+]=[\text{OH}^-]=1.0\times10^{-7}\,\text{M}.
  • Non-neutral solutions
    • [H3O+]≠[OH−][\text{H}_3\text{O}^+]\neq[\text{OH}^-] but their product remains 10−1410^{-14} at 298 K.
  • Temperature dependence
    • Auto-ionization is endothermic → raising T increases KwK_w; lowering T decreases it.
    • Therefore pH = 7 is neutral only at 25 °C.

Le Châtelier’s Principle Applied to KwK_w

  • Adding strong acid (↑[H+][\text{H}^+])
    • System shifts toward reactants of auto-ionization.
    • [OH−][\text{OH}^-] drops until product equals new KwK_w.
  • Adding strong base (↑[OH−][\text{OH}^-])
    • System shifts toward products, replacing lost H+\text{H}^+.
    • [H+][\text{H}^+] decreases correspondingly.

p-Scales: pH and pOH

  • General p-definition: pX=−log⁡<em>10(X)=log⁡</em>10(1X)pX=-\log<em>{10}(X)=\log</em>{10}\left(\dfrac{1}{X}\right)
  • Formulas
    • pH=−log⁡[H+]=log⁡1[H+]\text{pH}=-\log[\text{H}^+]=\log\dfrac{1}{[\text{H}^+]}
    • pOH=−log⁡[OH−]=log⁡1[OH−]\text{pOH}=-\log[\text{OH}^-]=\log\dfrac{1}{[\text{OH}^-]}
  • Relationship at 25 °C
    pH+pOH=14\text{pH} + \text{pOH} = 14
  • Interpretation
    • pH < 7 (pOH > 7) ⇒ acidic.
    • pH > 7 (pOH < 7) ⇒ basic.
    • pH = 7 ⇒ neutral.
  • Logarithmic convenience
    • Reactivity correlates more directly with the log of [H+][\text{H}^+] rather than the linear value.

Quick Logarithmic Estimation Tricks (MCAT Friendly)

  • For values exactly 10−m10^{-m}
    • [H+]=10−3 M⇒pH=3[\text{H}^+]=10^{-3}\,\text{M} \Rightarrow \text{pH}=3.
  • For numbers in scientific notation n×10−mn\times10^{-m} with 1<n<10
    • p(value)≈m−0.0np\text{(value)} \approx m-0.0n
      (slide decimal of n one place → treat as subtraction factor)
  • Example
    • K<em>a=1.8×10−5⇒pK</em>a≈5−0.18=4.82K<em>a=1.8\times10^{-5}\Rightarrow pK</em>a\approx5-0.18=4.82
      (actual 4.74; good to within ≈0.1 unit)
  • Mental boundary: MCAT rarely needs full calculator logs—use approximation + answer-choice elimination.

Strong Acids and Bases

  • Definition: Complete dissociation in water → reaction “goes to completion.”
  • Common MCAT strong acids
    • HCl, HBr, HI, H<em>2SO</em>4, HNO<em>3, HClO</em>4\text{HCl},\ \text{HBr},\ \text{HI},\ \text{H}<em>2\text{SO}</em>4,\ \text{HNO}<em>3,\ \text{HClO}</em>4
  • Common MCAT strong bases
    • NaOH, KOH\text{NaOH},\ \text{KOH} (+ other Group 1 hydroxides)
  • Calculations
    • 1 M NaOH⇒[OH−]=1 M; [H+]=10−14 M; pH=141\,\text{M NaOH} \Rightarrow [\text{OH}^-]=1\,\text{M};\ [\text{H}^+]=10^{-14}\,\text{M};\ \text{pH}=14
  • Dilute strong acid/base caveat
    • If concentration ≲10−7 M10^{-7}\,\text{M}, auto-ionization of water is not negligible.
    • Example: 1×10−8 M HCl1\times10^{-8}\,\text{M HCl} yields pH ≈6.98, not 8.
    • Solve via quadratic on KwK_w if needed (but recognize conceptually on exam).
  • pH < 0 or > 14 possible
    • Very concentrated strong acids/bases push scale beyond “traditional” limits (e.g., 10 M HClO4\text{HClO}_4 → pH = –1).

Weak Acids and Bases

  • Partial dissociation ⇢ equilibrium established.
  • Weak acid (monoprotic) general reactionHA(aq)+H<em>2O(l)⇌H</em>3O+(aq)+A−(aq)\text{HA}(aq)+\text{H}<em>2\text{O}(l)\rightleftharpoons\text{H}</em>3\text{O}^+(aq)+\text{A}^-(aq)
    • Acid dissociation constant
      K<em>a=[H</em>3O+][A−][HA]K<em>a=\dfrac{[\text{H}</em>3\text{O}^+][\text{A}^-]}{[\text{HA}]}
  • Weak base (Arrhenius monovalent)BOH(aq)⇌B+(aq)+OH−(aq)\text{BOH}(aq)\rightleftharpoons\text{B}^+(aq)+\text{OH}^-(aq)
    • Base dissociation constant
      Kb=[B+][OH−][BOH]K_b=\dfrac{[\text{B}^+][\text{OH}^-]}{[\text{BOH}]}
  • Rules of thumb
    • K<em>a<1K<em>a<1 ⇒ weak acid; Kb<1 ⇒ weak base.
    • MCAT molecular weak bases are usually amines.
  • Approximation criteria
    • If K<em>aK<em>a (or K</em>bK</em>b) ≤ 10−410^{-4} and starting concentration ≥100× larger, you can assume x ≪ initial (5 % rule).
  • Worked example (acetic acid)
    • Given: [CH<em>3COOH]</em>0=2.0 M, Ka=1.8×10−5[\text{CH}<em>3\text{COOH}]</em>0=2.0\,\text{M},\ K_a=1.8\times10^{-5}
    • Set x=[H3O+]≈6×10−3 Mx=[\text{H}_3\text{O}^+]\approx6\times10^{-3}\,\text{M}.
    • Validate x/2.0<0.05 ⇒ assumption fine.

Conjugate Acid–Base Pairs & K<em>aK</em>b=KwK<em>aK</em>b=K_w

  • Definitions
    • Conjugate acid: base + H+\text{H}^+
    • Conjugate base: acid – H+\text{H}^+
  • Linked equilibria
    • For any conjugate pair
      K<em>a(acid)×K</em>b(conj. base)=Kw=1.0×10−14K<em>a(\text{acid})\times K</em>b(\text{conj. base})=K_w=1.0\times10^{-14} (at 25 °C)
  • Implications
    • Strong acid (large K<em>aK<em>a) ⇒ very weak conjugate base (small K</em>bK</em>b) → often termed inert.
    • Similarly, strong base ⇢ inert conjugate acid.
    • Weak acid ⇔ weak conjugate base; relative magnitudes dictate buffer behavior and solution pH.
  • Bicarbonate example
    • HCO<em>3−\text{HCO}<em>3^- (weak acid) ⇌ CO</em>32−\text{CO}</em>3^{2-} (weak base) + H+\text{H}^+
    • Two opposing equilibria balance in bicarbonate buffer (vital in blood chemistry; see Biology Ch 6).
  • Inductive & structural effects
    • Electronegative atoms near acidic proton withdraw e⁻ density, weaken H–A bond → stronger acid.

Practical Calculation Strategies (Ka / Kb Problems)

  • ICE tables + approximation most common procedure.
  • Steps
    1. Write balanced equilibrium.
    2. Establish Initial, Change, Equilibrium concentrations.
    3. Insert into K<em>aK<em>a or K</em>bK</em>b expression.
    4. If ratio Kinitial conc.≤10−2\dfrac{K}{\text{initial conc.}}\le10^{-2}, drop “–x” in denominator.
    5. Solve simplified algebra (usually x2=K×initialx^2=K\times\text{initial} ⇒ x=K×M0x=\sqrt{K\times M_0}).
  • Error estimation rule: assumption valid if error <5 %; MCAT almost always designs numbers accordingly.

Neutralization & Salt Formation

  • General net
    AOH+HB→AB+H2O\text{AOH}+\text{HB}\rightarrow \text{AB}+\text{H}_2\text{O} (if both strong)
    (may differ when weak species not hydroxides)
  • Four combinations
    1. Strong acid + strong base → neutral salt + water (pH ≈ 7)
    2. Strong acid + weak base → acidic salt (pH < 7); no water if base not hydroxide.
    3. Weak acid + strong base → basic salt + water (pH > 7).
    4. Weak acid + weak base → pH depends on relative K<em>aK<em>a vs K</em>bK</em>b.
  • Illustrative reactions
    • HCl+NaOH→NaCl+H2O\text{HCl}+\text{NaOH}\rightarrow\text{NaCl}+\text{H}_2\text{O} (neutral)
    • HCl+NH<em>3→NH</em>4++Cl−\text{HCl}+\text{NH}<em>3\rightarrow\text{NH}</em>4^++\text{Cl}^- then NH<em>4++H</em>2O→NH<em>3+H</em>3O+\text{NH}<em>4^++\text{H}</em>2\text{O}\rightarrow\text{NH}<em>3+\text{H}</em>3\text{O}^+ (acidic)
    • CH<em>3COOH+NaOH→Na++CH</em>3COO−+H<em>2O\text{CH}<em>3\text{COOH}+\text{NaOH}\rightarrow\text{Na}^++\text{CH}</em>3\text{COO}^-+\text{H}<em>2\text{O}; CH</em>3COO−+H<em>2O→CH</em>3COOH+OH−\text{CH}</em>3\text{COO}^-+\text{H}<em>2\text{O}\rightarrow\text{CH}</em>3\text{COOH}+\text{OH}^- (basic)
  • Hydrolysis: reverse of neutralization; ions react with water to regenerate acid/base.

Biological / Real-World Connections

  • Peptide bond formation
    • Carboxylic acid (acid) + amine (base) ⇢ amide (peptide) + H2O\text{H}_2\text{O}; classified as a condensation/neutralization reaction.
  • Buffer systems (bicarbonate, phosphate, proteins) rely on weak acid/conjugate base pairs governed by same Ka–Kb logic.

MCAT Test-Day Strategy & Ethical Note

  • Focus on conceptual reasoning + approximations, not heavy calculator math.
  • Always check for special cases (very dilute strong acid/base; temperatures ≠25 °C).
  • Use dimensional analysis & intuition to catch impossible results (e.g., acidic solution with pH > 7).
  • Ethical practice: understand underlying chemistry to apply safely in lab/clinical settings—misestimating pH can harm biological samples or patients.