Acids, Bases, Buffers, and Titrations

Bronsted-Lowry Acids and Bases

The Bronsted-Lowry definition — the one that matters most on the MCAT — defines an acid as a proton (H⁺) donor and a base as a proton acceptor. When an acid HA donates its proton to water, it forms the conjugate base A⁻ and the hydronium ion H₃O⁺: HA + H₂O ⇌ A⁻ + H₃O⁺. The acid and its conjugate base differ by exactly one proton and together form a conjugate acid-base pair (HA/A⁻). The strength of an acid is measured by how completely it transfers its proton to water. Strong acids (HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄, HClO₃) dissociate completely — the equilibrium lies so far to the right that Ka is effectively infinite. Weak acids (essentially every other acid you'll encounter, including carboxylic acids, ammonium ions, and HF) establish a measurable equilibrium with their conjugate base. The Lewis definition broadens the concept: a Lewis acid is an electron-pair acceptor (e.g., BF₃, AlCl₃, transition-metal cations), and a Lewis base is an electron-pair donor (e.g., NH₃, H₂O, Cl⁻). The MCAT typically frames questions in Bronsted-Lowry terms but may test Lewis concepts in the context of coordination complexes, electrophilic organic reactions, or enzymatic metal-ion catalysis.

Strong and Weak Acids and Bases

Strong acids and bases ionize completely in aqueous solution. The six strong acids universally accepted on the MCAT are HCl, HBr, HI, HNO₃, H₂SO₄ (first proton only; HSO₄⁻ is weak with Ka ≈ 1.2 × 10⁻²), HClO₄, and HClO₃. Strong bases are Group 1 and Group 2 metal hydroxides: LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂. For a strong monoprotic acid at any analytically reasonable concentration, [H₃O⁺] equals the formal acid concentration. For a strong diprotic base like Ba(OH)₂, [OH⁻] = 2 × [Ba(OH)₂]. Weak acids and bases establish equilibrium. The acid dissociation constant Ka = [H₃O⁺][A⁻]/[HA] quantifies acid strength — larger Ka means stronger acid. The base dissociation constant Kb = [BH⁺][OH⁻]/[B] quantifies base strength. For a conjugate pair at 25°C, Ka × Kb = Kw = 1.0 × 10⁻¹⁴. This relationship means that the conjugate base of a strong acid (e.g., Cl⁻) is essentially neutral — it has no measurable tendency to accept a proton in water — while the conjugate base of a weak acid (e.g., CH₃COO⁻) is itself a weak base. The MCAT frequently exploits this: if you know an acid's Ka, you can calculate its conjugate base's Kb, and vice versa. Acid strength trends are rationalized by stability of the conjugate base: electron-withdrawing groups (electronegative atoms, resonance delocalization) stabilize A⁻ and increase acidity; electron-donating groups destabilize A⁻ and decrease acidity.

pH and pOH

pH is the negative base-10 logarithm of the hydronium ion concentration: pH = −log[H₃O⁺]. pOH = −log[OH⁻]. At 25°C, pH + pOH = 14.00 because Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴. Three categories define aqueous solutions: acidic (pH < 7, [H₃O⁺] > [OH⁻]), neutral (pH = 7, [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ M), and basic (pH > 7, [H₃O⁺] < [OH⁻]). The logarithmic scale means each unit change in pH represents a 10-fold change in [H₃O⁺]: a solution at pH 3 is ten times more acidic than one at pH 4 and one hundred times more acidic than one at pH 5. For strong monoprotic acids and bases, pH calculation is direct: pH = −log[H₃O⁺] where [H₃O⁺] equals the formal acid concentration (after accounting for any dilution). For weak acids, the approximation [H₃O⁺] ≈ √(Ka × [HA]₀) works when [HA]₀ is much larger than Ka and the percent ionization is below 5%. The complete quadratic equation must be used when this approximation fails (high dilution or Ka > 10⁻³). A common MCAT shortcut: for a weak acid with Ka = 10⁻ⁿ, the pH of a 1.0 M solution is approximately n/2; for a 0.01 M solution, it's approximately (n + 2)/2. The exam rewards approximate reasoning under time pressure.

Ka, Kb, and pKa

pKa = −log(Ka) is the acid-strength analog to pH. A lower pKa means a stronger acid — each unit decrease in pKa represents a 10-fold increase in acid strength. The pKa scale compresses the enormous range of Ka values (10⁻⁵⁰ for alkanes to ~10¹⁰ for magic acid) into a manageable range of numbers typically between −10 and 50. Key pKa values to internalize for the MCAT: strong mineral acids (pKa < 0), carboxylic acids (pKa ≈ 4-5), protonated amines / ammonium ions (pKa ≈ 9-10), water (pKa = 15.7), alcohols (pKa ≈ 16-18), alpha-hydrogens of carbonyls (pKa ≈ 20), terminal alkynes (pKa ≈ 25), and amines as acids (pKa ≈ 35-38). The pKa tells you the pH at which an acid is exactly 50% dissociated — at pH = pKa, [HA] = [A⁻]. This is the heart of buffer chemistry. When pH < pKa, the protonated form (HA) predominates; when pH > pKa, the deprotonated form (A⁻) predominates. The MCAT uses this logic constantly: at physiological pH 7.4, carboxylic acids (pKa ~4) are >99.9% deprotonated, while protonated amines (pKa ~9-10) are >97% protonated. For polyprotic acids like H₃PO₄, each successive proton has its own pKa (2.2, 7.2, 12.4), and the species distribution changes as pH rises — H₃PO₄ → H₂PO₄⁻ → HPO₄²⁻ → PO₄³⁻. At the midpoint of each transition (pH = pKaₙ), the two species bracketing that pKa are present in equal concentrations.

The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is the single most useful formula in MCAT acid-base chemistry: pH = pKa + log([A⁻]/[HA]). It is derived from the Ka expression by taking −log of both sides and rearranging. The equation tells you that when [A⁻] = [HA], pH = pKa — this is the midpoint of a buffer's effective range and the flattest part of a titration curve (the point of maximum buffering). When [A⁻] > [HA] (excess conjugate base), pH > pKa; when [HA] > [A⁻] (excess acid form), pH < pKa. The MCAT tests this equation in three primary ways: (1) calculating pH of a buffer given the pKa and the ratio of base to acid; (2) calculating the ratio of protonated to deprotonated forms at a given pH (relevant for amino acid side chains, drug absorption, and enzyme active sites); and (3) predicting how pH shifts when strong acid or base is added to a buffer — the equilibrium shifts to consume the added H⁺ or OH⁻, changing the [A⁻]/[HA] ratio slightly, which you plug back into HH to compute the new pH. A critical trap: the equation uses equilibrium concentrations, not initial concentrations, but for buffers where the common-ion effect dominates and dissociation is negligible, initial and equilibrium concentrations are essentially identical. The effective buffering range is approximately pKa ± 1 — outside this window, the ratio of conjugate forms is so lopsided (>10:1 or <1:10) that added acid or base overwhelms the buffer's capacity.

Buffers

A buffer is a solution that resists changes in pH upon addition of small amounts of strong acid or strong base. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid) in comparable concentrations. The buffer works by Le Chatelier's principle: added H⁺ reacts with the conjugate base A⁻ to form HA (shifting the equilibrium left), while added OH⁻ reacts with HA to form A⁻ and H₂O (shifting the equilibrium right). The buffer's capacity — how much acid or base it can absorb before the pH changes significantly — depends on two factors: the absolute concentration of the buffering species (more concentrated = higher capacity) and the ratio of [A⁻] to [HA] (capacity is maximized when the ratio is close to 1:1, i.e., when pH ≈ pKa). The MCAT's favorite buffer systems to test are: the bicarbonate buffer (H₂CO₃/HCO₃⁻, pKa₁ = 6.1, the primary blood buffer despite operating slightly outside its optimal range); the phosphate buffer (H₂PO₄⁻/HPO₄²⁻, pKa₂ = 7.2, important in intracellular fluid and renal tubular fluid); amino acid side chains (histidine's imidazole, pKa ≈ 6.0, critical in enzyme active sites and hemoglobin); and acetate buffer (CH₃COOH/CH₃COO⁻, pKa = 4.76, common in laboratory contexts). In the body, the bicarbonate system is coupled to respiration: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻. When metabolic acid builds up, ventilation increases to blow off CO₂, pulling the equilibrium left and consuming H⁺. Conversely, hypoventilation retains CO₂, pushing the equilibrium right and lowering pH — respiratory acidosis. This integration of chemical equilibrium with physiology is pure MCAT gold.

Titration Curves

A titration curve plots pH against the volume of titrant added. The shape of the curve reveals the nature of the analyte. Strong acid titrated with strong base: the curve starts at low pH, rises very gradually at first, then shoots nearly vertically at the equivalence point (pH = 7), where moles of OH⁻ added equal moles of H⁺ initially present. The inflection point is sharp and vertical. Weak acid titrated with strong base: the initial pH is higher than for a strong acid of the same concentration (because the weak acid only partially dissociates). The curve has several characteristic features: (1) a buffering region where pH rises gradually — at the half-equivalence point, pH = pKa of the weak acid, and [HA] = [A⁻]; (2) the equivalence point occurs at a pH > 7 because the conjugate base A⁻ hydrolyzes water to produce OH⁻ (A⁻ + H₂O ⇌ HA + OH⁻); (3) the post-equivalence pH approaches the pH of the excess strong base. For a weak base titrated with strong acid, the curve is the mirror image: equivalence point pH < 7 (conjugate acid BH⁺ donates H⁺ to water). Polyprotic acids (e.g., H₃PO₄, H₂CO₃, H₂SO₄) produce multiple equivalence points — one per acidic proton — with buffering regions centered on each pKa. The MCAT regularly tests your ability to: identify pKa from the half-equivalence point on a titration curve; determine the analyte's identity from the curve shape; select an appropriate indicator based on its pKa relative to the equivalence-point pH; and calculate the concentration of an unknown analyte from the equivalence-point volume. Indicators are themselves weak acids with different colors for HA and A⁻ forms; they must be chosen so their color-change pH range straddles the equivalence-point pH.

How it works

Every acid-base problem on the MCAT is a proton-transfer equilibrium problem. You start by identifying the species that can donate or accept protons in the system. For strong electrolytes, you assume full dissociation and calculate [H₃O⁺] or [OH⁻] directly. For weak electrolytes, you set up the Ka (or Kb) expression, determine whether to use the approximation [H₃O⁺] ≈ √(Ka × C₀) or the full quadratic, and solve. For buffers, the Henderson-Hasselbalch equation collapses the equilibrium calculation into a simple log ratio. For titrations, you track the stoichiometric consumption of the limiting reagent at each stage: before the equivalence point, you have a buffer of unreacted weak species plus its conjugate; at the equivalence point, the solution contains only the conjugate of the original analyte, which hydrolyzes water; after the equivalence point, excess strong titrant dictates the pH. The proton is a currency — track where it goes, and you always know the pH.

How it works

Every acid-base problem on the MCAT is a proton-transfer equilibrium problem. You start by identifying the species that can donate or accept protons in the system. For strong electrolytes, you assume full dissociation and calculate [H₃O⁺] or [OH⁻] directly. For weak electrolytes, you set up the Ka (or Kb) expression, determine whether to use the approximation [H₃O⁺] ≈ √(Ka × C₀) or the full quadratic, and solve. For buffers, the Henderson-Hasselbalch equation collapses the equilibrium calculation into a simple log ratio. For titrations, you track the stoichiometric consumption of the limiting reagent at each stage: before the equivalence point, you have a buffer of unreacted weak species plus its conjugate; at the equivalence point, the solution contains only the conjugate of the original analyte, which hydrolyzes water; after the equivalence point, excess strong titrant dictates the pH. The proton is a currency — track where it goes, and you always know the pH.

Comparisons

• C/P (Acid-base calculations): Ka, Kb, Kw, pH, pOH, and Henderson-Hasselbalch — the computational heart of the C/P section; expect at least one stand-alone question and one passage-based application.
• C/P (Titration curves and indicators): Reading equivalence points from titration curves; selecting indicators; comparing weak acid vs. strong acid titration shapes.
• B/B (Amino acid protonation): Histidine's pKa ~6.0 makes it the physiologically relevant buffer in enzyme active sites; Henderson-Hasselbalch tells you the charge state of any residue at any pH.
• B/B (Hemoglobin and Bohr effect): CO₂ + H₂O → H₂CO₃ → H⁺ + HCO₃⁻ lowers pH in tissues, shifting hemoglobin's O₂-binding curve right — a direct acid-base equilibrium consequence.
• B/B (Renal physiology): Kidney regulates blood pH via H⁺ secretion, HCO₃⁻ reabsorption, and phosphate/ammonia buffering in the distal tubule; metabolic acidosis/alkalosis concepts.
• B/B (Drug absorption): Weak acids (e.g., aspirin, pKa ~3.5) are protonated and uncharged in the stomach (pH ~2), favoring passive absorption; weak bases are protonated and trapped in the stomach but absorb in the intestine.
• P/S (Research methods): Buffer preparation for biochemical assays; pH-dependent protein stability; ion-exchange chromatography exploits charge differences governed by pH relative to pI.

Common confusions

• Confusing Kw's temperature dependence: Kw = 1.0 × 10⁻¹⁴ ONLY at 25°C. At higher temperatures, Kw increases (endothermic autoionization), so neutral pH shifts below 7. If a passage gives temperature other than 25°C, do NOT assume pH 7 is neutral without checking.
• Forgetting that the half-equivalence point equals pKa: the most common titration-curve question asks you to read pKa from the graph — it's the pH at the volume halfway to equivalence. If you read the equivalence-point pH instead, you will get the wrong answer.
• Applying the Henderson-Hasselbalch equation outside the buffering range: the HH equation always gives a number, but outside pKa ± 1 the buffer has negligible capacity and the calculation becomes inaccurate because you can no longer ignore water's autoionization.
• Assuming the equivalence point pH is always 7: strong acid + strong base → pH 7, but weak acid + strong base → pH > 7 (conjugate base hydrolyzes water), weak base + strong acid → pH < 7 (conjugate acid hydrolyzes). This is the single most-tested titration concept.
• Miscalculating [OH⁻] for Group 2 hydroxides: Ba(OH)₂ and Ca(OH)₂ are strong diprotic bases. [OH⁻] = 2 × [Ba(OH)₂]₀. Missing the factor of 2 leads to pH values that are off by ~0.3 units — enough to pick the wrong answer.
• Forgetting that polyprotic species distribution depends on pH: at any given pH, one of the pKas tells you which two forms are in equilibrium. For phosphoric acid: below pH 2.2 → H₃PO₄; between 2.2 and 7.2 → H₂PO₄⁻ dominant; between 7.2 and 12.4 → HPO₄²⁻ dominant; above 12.4 → PO₄³⁻ dominant.
• Treating the conjugate base of a strong acid as basic: Cl⁻, Br⁻, I⁻, NO₃⁻, ClO₄⁻, and HSO₄⁻ (technically, SO₄²⁻ is weakly basic) are neutral in water — they do not hydrolyze and do not affect pH. The MCAT will tempt you to include them in a net-ionic equation.
• Neglecting dilution effects when mixing solutions: when equal volumes of acid and base are mixed, concentrations are halved BEFORE you calculate pH. This is invisible if you jump straight to the stoichiometric calculation without accounting for the new total volume.

Quick review

• Bronsted-Lowry: acid = H⁺ donor, base = H⁺ acceptor. Conjugate pair differs by one H⁺.
• Six strong acids: HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄. Strong bases: Group 1/2 hydroxides.
• Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C. pH + pOH = 14.00 at 25°C only.
• Ka × Kb = Kw for conjugate pair. Stronger acid → weaker conjugate base.
• pH = −log[H₃O⁺]; pOH = −log[OH⁻]; pKa = −log(Ka). Each unit = 10× change.
• Weak acid approx: [H₃O⁺] ≈ √(Ka × C₀). Valid when C₀ >> Ka, ionization < 5%.
• HH equation: pH = pKa + log([A⁻]/[HA]). At half-equivalence: pH = pKa, [HA] = [A⁻].
• Buffering range: pKa ± 1. Capacity max when [A⁻] = [HA]. More concentrated = higher capacity.
• Titration: strong acid + strong base → eq pt pH 7. Weak acid + strong base → eq pt pH > 7.
• Polyprotic: H₃PO₄ pKa 2.2, 7.2, 12.4. One eq pt per proton. Buffer at each half-eq pt.
• Blood buffer: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻ (pKa 6.1). Respiration couples to pH.
• Indicator: pKa_indicator ≈ pH at equivalence point for sharp color change.