Acid-Base Chemistry — Apply acid–base concepts to evaluate pH, strength, equilibria, and reaction outcomes.

The classification of substances as acids or bases predates modern chemistry by millennia; alchemists recognized the sour taste of vinegar and the slippery feel of lye long before anyone proposed a molecular explanation. However, the transition from phenomenological description to quantitative theory required centuries of incremental insight. Understanding this intellectual trajectory is not merely historical trivia—it reveals why we define acids and bases the way we do, and it clarifies the scope and limitations of each definition you will encounter on the DAT.

These historical milestones converge on a central question the DAT expects you to answer fluently: given a reaction system, how do we identify the acid and the base, quantify the extent of proton transfer, compute pH, and predict the direction of equilibrium? The sections that follow build this competency from foundational definitions through quantitative problem-solving.

Three concentric definitions of acids and bases coexist in modern chemistry, each more general than the last. The DAT predominantly tests the Brønsted–Lowry framework for aqueous equilibria and pH calculations, but you must also recognize Lewis acid-base interactions—especially in the context of coordination compounds, electrophilic addition, and biological catalysis. The Arrhenius model, while narrower, still informs the language of strong acids dissociating completely in water.

The diagram above crystallizes a distinction the DAT tests repeatedly: for a strong acid such as HCl, HBr, HI, HNO₃, HClO₄, or H₂SO₄ (first proton), the equilibrium lies so far to the right that we treat dissociation as essentially 100%, meaning [H⁺] equals the formal concentration of the acid. For a weak acid (Kₐ ≪ 1), equilibrium favors the undissociated form HA, and we must solve the equilibrium expression—or use the simplifying approximation [H⁺] ≈ √(Kₐ × C₀)—to determine [H⁺]. This same logic applies symmetrically to strong and weak bases, substituting K_b and [OH⁻]. The pH is then obtained from pOH via pH + pOH = 14.00 at 25 °C.

These four expressions form the quantitative backbone of virtually every DAT acid-base problem. The pH definition and K_a expression are the most fundamental; the weak-acid approximation and Henderson–Hasselbalch equation are derived shortcuts that save time under exam conditions. Always verify that the assumptions underlying each shortcut hold—particularly the 5% criterion for the weak acid approximation and the requirement that buffer concentrations are large relative to the added strong acid or base for Henderson–Hasselbalch. Additionally, recall that for diprotic acids such as H₂SO₄ or H₂CO₃, each deprotonation step has its own Kₐ (Kₐ₁ ≫ Kₐ₂), and you typically treat each step independently when calculating pH.

A buffer solution resists changes in pH upon addition of small amounts of strong acid or strong base. Buffers consist of a weak acid and its conjugate base (e.g., CH₃COOH / CH₃COO⁻) or a weak base and its conjugate acid (e.g., NH₃ / NH₄⁺). The mechanism is straightforward: added H⁺ is consumed by A⁻ → HA, while added OH⁻ is consumed by HA → A⁻ + H₂O. Buffer capacity is greatest when [HA] ≈ [A⁻], i.e., pH ≈ pKₐ, and when the absolute concentrations of both species are high. The effective buffering range is typically pKₐ ± 1.

Several DAT-relevant features emerge from this titration curve. First, the initial pH is calculated using the weak acid approximation. Second, the buffer region (approximately the first half of the curve before the equivalence point) is where Henderson–Hasselbalch applies; pH changes slowly here because the buffer resists perturbation. Third, at the equivalence point, all HA has been converted to A⁻, and the pH is determined by the hydrolysis of this conjugate base: A⁻ + H₂O ⇌ HA + OH⁻. Because the conjugate base produces OH⁻, the equivalence-point pH of a weak acid/strong base titration is always above 7. Conversely, a weak base/strong acid titration has an equivalence-point pH below 7. These asymmetries dictate the choice of indicator: phenolphthalein (color change ≈ pH 8.2–10) for weak acid/strong base titrations, and methyl orange (≈ 3.1–4.4) for strong acid/weak base titrations.

While the DAT focuses on equilibrium calculations, higher-level reasoning connects molecular structure to acid strength—a topic that frequently appears in conceptual questions. Several structural factors determine how readily a molecule donates a proton: bond polarity, bond strength, electronegativity, resonance stabilization of the conjugate base, and inductive effects from nearby substituents. Understanding these factors lets you predict relative acid strengths without memorizing every Kₐ value.

These principles extend into organic chemistry and biochemistry. Amino acids, for instance, are polyprotic species whose side-chain pKₐ values depend on inductive and resonance effects, governing protein charge at physiological pH. On the DAT, recognizing that the stability of the conjugate base is the single most powerful predictor of acid strength can simplify ranking questions considerably. When in doubt, ask: how well is the negative charge on A⁻ stabilized by delocalization, induction, or orbital effects?