Acid
In chemistry, an acid is defined as a molecular entity or chemical species capable of donating a hydron (proton, H⁺) or forming a covalent bond with an electron pair.[1] This encompasses the Brønsted-Lowry concept of proton donation and the Lewis concept of electron-pair acceptance, providing a unified framework for understanding acid behavior across various solvents and reaction conditions.[1] Acids are fundamental to numerous chemical processes, exhibiting properties such as a pH less than 7 in aqueous solutions, the ability to turn litmus paper red, and a sour taste in dilute forms./03:_Acid-Base_Chemistry/3.02:_Brnsted_and_Lewis_Acids_and_Bases) The concept of acids evolved through key theoretical advancements in the late 19th and early 20th centuries. In 1884, Svante Arrhenius proposed the first modern definition, describing acids as substances that increase the concentration of hydrogen ions (H⁺) when dissolved in water, laying the groundwork for understanding ionization in aqueous solutions./03:_Acid-Base_Chemistry/3.02:_Brnsted_and_Lewis_Acids_and_Bases) This Arrhenius model was expanded in 1923 by Johannes Brønsted and Thomas Lowry, who redefined acids as proton (H⁺) donors in any acid-base reaction, independent of the solvent and applicable to a broader range of chemical systems./03:_Acid-Base_Chemistry/3.02:_Brnsted_and_Lewis_Acids_and_Bases) Concurrently, Gilbert N. Lewis introduced a more general perspective in 1923, classifying acids as electron-pair acceptors, which extended the theory to non-protonic reactions and coordination chemistry./03:_Acid-Base_Chemistry/3.02:_Brnsted_and_Lewis_Acids_and_Bases) These definitions—Arrhenius, Brønsted-Lowry, and Lewis—remain central to contemporary acid-base chemistry, with the IUPAC Gold Book integrating them into its current nomenclature.[1] Acids are classified by their strength, source, and structure, influencing their reactivity and applications. Strong acids, such as hydrochloric acid (HCl) and sulfuric acid (H₂SO₄), fully dissociate in water to yield H⁺ ions, resulting in high conductivity and corrosive properties./05:_Molecules_and_Compounds/5.09:_Naming_Acids) In contrast, weak acids like acetic acid (CH₃COOH) partially dissociate, establishing equilibrium with their conjugate bases and exhibiting milder effects./05:_Molecules_and_Compounds/5.09:_Naming_Acids) Structurally, acids include binary acids (e.g., HF, HCl), which consist of hydrogen bonded to a nonmetal; oxyacids (e.g., HNO₃, H₂SO₄), containing oxygen; and organic acids (e.g., citric acid, formic acid), typically featuring a carboxyl group (-COOH) and prevalent in biological systems.[2] Common examples also encompass carbonic acid (H₂CO₃) from dissolved CO₂ and phosphoric acid (H₃PO₄) used in food additives. Beyond fundamental reactions like neutralization with bases to form salts and water, acids play pivotal roles in industry and daily life./07:_Acids_and_Bases/7.08:_Acids_and_Bases_in_Industry_and_in_Daily_Life) Sulfuric acid, the most industrially produced chemical worldwide, is essential for manufacturing fertilizers (e.g., phosphate-based), petroleum refining, metal extraction, and battery production, with global output of approximately 261 million metric tons annually as of 2024.[3] Hydrochloric acid is vital for steel pickling to remove rust and in pH adjustment for water treatment, while nitric acid supports explosives and fertilizer synthesis./07:_Acids_and_Bases/7.08:_Acids_and_Bases_in_Industry_and_in_Daily_Life) In biology and food science, organic acids like citric and lactic acid act as preservatives, flavor enhancers, and metabolic intermediates, underscoring acids' ubiquity in sustaining chemical equilibrium and enabling diverse technological advancements.[4]Definitions
Arrhenius Acids
The Arrhenius theory of acids, developed by Swedish chemist Svante Arrhenius in his 1884 doctoral dissertation, provided the first modern definition by linking acidic properties to the electrolytic dissociation of substances in water. This groundbreaking work explained how acids behave through the production of charged particles, earning Arrhenius the Nobel Prize in Chemistry in 1903 for his contributions to understanding electrolytes. According to the Arrhenius definition, an acid is a substance that increases the concentration of hydrogen ions (H⁺, often represented as the hydronium ion H₃O⁺ in modern notation) when dissolved in water. The general dissociation reaction for an Arrhenius acid can be expressed as: \text{HA(aq)} \rightarrow \text{H}^+(\text{aq}) + \text{A}^-(\text{aq}) This process occurs fully for strong acids and partially for weak acids, leading to observable properties like sour taste, reaction with metals, and neutralization with bases. Representative examples include hydrochloric acid (HCl), a strong acid that completely dissociates in water to produce H⁺ and Cl⁻ ions, and acetic acid (CH₃COOH), a weak acid that partially dissociates to yield H⁺ and CH₃COO⁻ ions. These dissociations directly contribute to the increased H⁺ concentration characteristic of acidic solutions. However, the Arrhenius definition is restricted to aqueous solutions and fails to account for acidic behavior in non-aqueous solvents or for substances that exhibit acidity without producing hydrogen ions, such as certain metal cations./07%3A_Acids_and_Bases/7.02%3A_Acids_and_Bases) Later theories, like Brønsted-Lowry, expanded on this by focusing on proton transfer in various media./07%3A_Acids_and_Bases/7.02%3A_Acids_and_Bases)Brønsted–Lowry Acids
The Brønsted–Lowry theory defines an acid as a substance that donates a proton (H⁺ ion) to another substance, termed a base, which accepts the proton. This proton-transfer mechanism forms the core of acid-base reactions under this framework, expanding applicability beyond aqueous solutions to any medium where proton donation occurs. The theory was independently proposed in 1923 by Danish chemist Johannes Nicolaus Brønsted and British chemist Thomas Martin Lowry, providing a broader perspective than earlier models by emphasizing relative proton affinity rather than specific ion production./Acids_and_Bases/Acid/Bronsted_Concept_of_Acids_and_Bases) In a Brønsted–Lowry acid-base reaction, the acid (HA) donates a proton to the base (B), yielding the conjugate base (A⁻) and conjugate acid (HB⁺). This process is reversible and represented by the general equilibrium: \ce{HA + B ⇌ A^- + HB^+} The conjugate acid-base pair consists of species differing by one proton, such as HA and A⁻, where the strength of the acid inversely relates to the strength of its conjugate base. This theory generalizes proton dissociation in water as a specific case of broader proton transfer./Acids_and_Bases/Acid/Bronsted_Concept_of_Acids_and_Bases) Certain substances exhibit amphoterism, acting as both Brønsted–Lowry acids and bases depending on the reaction conditions, due to their ability to either donate or accept protons. The bicarbonate ion (HCO₃⁻) is a classic example of an amphoteric species. As a base, it accepts a proton from water: \ce{HCO3^- + H2O ⇌ H2CO3 + OH^-} As an acid, it donates a proton to water: \ce{HCO3^- + H2O ⇌ CO3^{2-} + H3O^+} These reactions highlight bicarbonate's role in buffering systems, such as in biological fluids.[5] Representative examples illustrate proton donation in non-aqueous or varied contexts. The ammonium ion (NH₄⁺) functions as a Brønsted–Lowry acid by transferring a proton to the hydroxide ion: \ce{NH4^+ + OH^- ⇌ NH3 + H2O} Here, NH₄⁺ is the acid, OH⁻ is the base, NH₃ is the conjugate base, and H₂O is the conjugate acid. Similarly, the hydrogen sulfate ion (HSO₄⁻) demonstrates amphoterism: it acts as an acid by donating a proton to water to form sulfate and hydronium ions (\ce{HSO4^- + H2O ⇌ SO4^{2-} + H3O^+}), or as a base by accepting a proton to form sulfuric acid (\ce{HSO4^- + H2O ⇌ H2SO4 + OH^-}), though the latter is less common.-plus-oh-(aq)-greater-nh3(aq)-plus-h2o(l)-is-nh4plus-a-bronsted-lowry-acid-a-bronsted-lowry-base-or-neither/) The Brønsted–Lowry framework ties directly to acid strength through the acid dissociation constant (K_a), which quantifies the equilibrium position of proton donation for weak acids in solution: K_a = \frac{[A^-][\ce{H^+}]}{[HA]} A larger K_a indicates a stronger tendency to donate protons, reflecting greater acid strength within this theory. This equilibrium expression underpins quantitative analysis of conjugate pair behaviors.[6]Lewis Acids
In 1923, Gilbert N. Lewis proposed a general theory of acid-base reactions that defines a Lewis acid as any species capable of accepting an electron pair from a Lewis base to form a coordinate covalent bond, broadening the scope beyond proton transfer mechanisms.[7] This definition emphasizes the role of electron deficiency in the acid, allowing it to complete its valence shell through donation from a base.[8] The general reaction can be represented as: \text{A (acceptor)} + :\text{B (donor)} \rightarrow \text{A}–\text{B} where A is the Lewis acid and :B denotes the lone pair on the base.[9] A classic example is the reaction between boron trifluoride (BF₃) and ammonia (NH₃), where the electron-deficient boron atom in BF₃ accepts the lone pair from nitrogen in NH₃ to form the adduct F₃B–NH₃.[10] Another prominent application occurs in organic synthesis, such as Friedel-Crafts alkylation reactions, where aluminum chloride (AlCl₃) acts as a Lewis acid by coordinating with the halogen of an alkyl halide to generate a carbocation electrophile.[11] Lewis acids play crucial roles in catalysis, particularly in biological systems where metal ions like Zn²⁺ function as electron-pair acceptors to activate substrates. For instance, in the enzyme carbonic anhydrase, Zn²⁺ coordinates with water to facilitate its deprotonation, enhancing the hydration of carbon dioxide.[12] This definition extends to non-protonic species, including metal cations such as Fe³⁺, which accept electron pairs from ligands due to their high charge density, and carbocations like (CH₃)₃C⁺, which seek stabilization through electron donation.[13] Protonic acids represent a subset of Lewis acids, as the H⁺ ion itself acts as an electron-pair acceptor.[14]Properties
Dissociation and Equilibrium
In aqueous solutions, acids dissociate by ionizing to produce hydrogen ions (H⁺) and their conjugate bases, as originally conceptualized in the Arrhenius definition of acids. For a general acid HA, this process is represented as HA ⇌ H⁺ + A⁻, where the extent of ionization determines whether the acid is strong or weak. Strong acids, such as hydrochloric acid (HCl), undergo complete dissociation in water, meaning nearly 100% of the molecules ionize to form H⁺ and Cl⁻ ions, with no significant equilibrium established. In contrast, weak acids partially ionize, resulting in an equilibrium mixture of undissociated HA, H⁺, and A⁻.[15][16][17] The equilibrium for weak acid dissociation is quantified by the acid dissociation constant, K_a, defined as K_a = \frac{[H^+][A^-]}{[HA]}, where the concentrations are those at equilibrium and activities are approximated by concentrations in dilute solutions. This constant reflects the position of the equilibrium; a smaller K_a indicates less dissociation and a weaker tendency to produce H⁺. For example, acetic acid (CH₃COOH) has K_a \approx 1.8 \times 10^{-5} at 25°C, meaning only a small fraction ionizes in typical solutions. Pure water also exhibits a related autoionization equilibrium: \ce{H2O ⇌ H^+ + OH^-}, governed by the ion product constant K_w = [H^+][OH^-] = 1.0 \times 10^{-14} at 25°C, which establishes a baseline concentration of H⁺ and OH⁻ ions even in neutral conditions.[18][19][20] The hydrogen ion concentration from weak acid dissociation can be approximated for initial calculations when the acid concentration C is much greater than the dissociated amount, yielding [H^+] \approx \sqrt{K_a \cdot C}; this simplification assumes [H⁺] = [A⁻] and negligible change in [HA] from the initial value, valid for moderately dilute solutions where dissociation is less than 5%. External factors influence this equilibrium per Le Châtelier's principle: dilution decreases concentrations of all species, shifting the equilibrium toward greater dissociation to restore balance, thereby increasing the percent ionization. Temperature changes alter K_a itself, as acid dissociation is typically endothermic; higher temperatures favor the forward reaction, increasing K_a and [H⁺].[21][22][23]Acid Strength
Acid strength quantifies the extent to which an acid donates a proton (H⁺) in solution, primarily measured by the acid dissociation constant K_a, defined for the equilibrium \ce{HA ⇌ H+ + A-} as K_a = \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}. The pKa value, given by \mathrm{p}K_a = -\log_{10} K_a, provides a convenient scale where a lower pKa corresponds to a stronger acid due to greater proton donation tendency.[24] In aqueous solutions, acids are classified as strong if they fully dissociate (pKa < 0), such as hydrochloric acid (HCl, pKa ≈ -7), which exists entirely as \ce{H+} and \ce{Cl-}. Weak acids, with pKa > 0, partially dissociate; for example, hydrofluoric acid (HF, pKa = 3.17) ionizes only to a limited extent due to the strong H–F bond and poor stabilization of the \ce{F-} conjugate base.[25][26] Several factors influence acid strength by affecting the stability of the conjugate base or the ease of proton release. Bond strength plays a key role: weaker H–A bonds favor stronger acids, as seen in the hydrogen halides where HF (strong H–F bond) is much weaker than HI (weaker H–I bond, pKa ≈ -9). Inductive effects from electron-withdrawing groups, such as halogens on a carbon chain, stabilize the negative charge on the conjugate base by withdrawing electron density, increasing acidity (e.g., chloroacetic acid is stronger than acetic acid). Resonance stabilization is particularly effective, delocalizing the conjugate base charge over multiple atoms, as in carboxylic acids where the acetate ion's charge spreads across two oxygen atoms, making them more acidic than alcohols.[27][27][27] For polyprotic acids, which can donate multiple protons, successive pKa values increase because each subsequent conjugate base is less willing to lose a proton; for sulfuric acid (H₂SO₄), pKa₁ ≈ -3 (strong first dissociation to \ce{HSO4-}) while pKa₂ ≈ 2 (weaker second dissociation to \ce{SO4^2-}).[28] In non-aqueous solvents, which are less basic than water, acid strengths can differ markedly due to reduced leveling effects; for instance, in acetic acid, the order reverses from aqueous behavior, with HCl weaker than HBr (and HI strongest) as the solvent's lower proton-accepting ability allows differentiation based on inherent bond polarities and conjugate base solvation.[29] Superacids, developed in the mid-20th century, exceed the strength of concentrated sulfuric acid (H₀ ≈ -12, where H₀ is the Hammett acidity function extending pH for highly acidic media); the "magic acid" system of fluorosulfuric acid (HSO₃F) with antimony pentafluoride (SbF₅) achieves H₀ < -20, enabling protonation of weak bases like hydrocarbons.[30][31]Nomenclature
The nomenclature of acids has evolved from early trivial names based on sensory properties or origins, such as "vinegar" for acetic acid, to systematic conventions established in the late 18th and 19th centuries by chemists like Antoine Lavoisier and Jöns Jacob Berzelius, who emphasized compositional elements, with the International Union of Pure and Applied Chemistry (IUPAC) formalizing rules in the 20th century to promote precision and universality.[32][33] This shift addressed ambiguities in pre-modern naming, where acids were often described by their sources or effects rather than structure, leading to the adoption of substitutive and additive methods that reflect molecular composition.[33] For inorganic acids, binary acids—those composed of hydrogen and a single nonmetal—are named using the prefix "hydro-" followed by the stem of the nonmetal and the suffix "-ic acid," as in hydrochloric acid for HCl.[33] Oxyacids, which include oxygen, follow traditional naming based on the corresponding oxyanion: the suffix "-ic acid" denotes the anion with more oxygen or higher oxidation state (e.g., sulfuric acid for H₂SO₄, derived from sulfate), while "-ous acid" indicates fewer oxygen atoms or lower oxidation state (e.g., sulfurous acid for H₂SO₃, from sulfite); additional prefixes like "per-" (highest oxygen, as in perchloric acid, HClO₄) and "hypo-" (lowest, as in hypochlorous acid, HClO) refine these distinctions.[33] IUPAC also endorses additive nomenclature for clarity, listing ligands alphabetically around the central atom (e.g., tetraoxidosulfuric acid for H₂SO₄), though traditional names remain widely retained.[33] Organic acids employ substitutive nomenclature, prioritizing the principal functional group as the suffix. Carboxylic acids, featuring the -COOH group, are named by identifying the longest carbon chain including the carboxyl carbon and appending "-oic acid," with the chain numbered from the carboxyl group; for instance, CH₃COOH is ethanoic acid (preferred IUPAC name, or PIN), though the retained common name acetic acid is acceptable in general use.[34] Sulfonic acids, with the -SO₃H group, similarly use the suffix "-sulfonic acid" attached to the parent hydrocarbon chain or ring, such as methanesulfonic acid for CH₃SO₃H or benzenesulfonic acid for C₆H₅SO₃H.[34] Polyprotic acids, capable of donating multiple protons, extend these rules to their anions through "hydrogen" prefixes indicating remaining ionizable hydrogens, as seen in dihydrogen phosphate for H₂PO₄⁻ (from phosphoric acid, H₃PO₄) or hydrogen phosphate for HPO₄²⁻; this convention treats partial deprotonation systematically while aligning with oxyanion naming patterns.[35] Overall, IUPAC distinguishes preferred systematic names (e.g., ethanoic acid) from retained trivial ones (e.g., acetic acid) to balance innovation with established terminology, ensuring nomenclature supports both educational and practical applications without implying acid strength differences solely through naming conventions.[34][33]Chemical Behavior
Monoprotic and Polyprotic Acids
Monoprotic acids are those capable of donating a single proton (H⁺) per molecule in aqueous solution, resulting in a single acid dissociation equilibrium characterized by one acid dissociation constant, K<sub>a</sub>.[36] Representative examples include hydrochloric acid (HCl), a strong monoprotic acid that fully dissociates, and acetic acid (CH₃COOH), a weak monoprotic acid with K<sub>a</sub> ≈ 1.8 × 10<sup>−5</sup>.[36] In contrast, polyprotic acids can donate more than one proton per molecule through successive dissociation steps. Diprotic acids, such as sulfuric acid (H₂SO₄), release two protons, while triprotic acids like phosphoric acid (H₃PO₄) release three.[37] For a generic diprotic acid denoted as H₂A, the stepwise dissociation equilibria are: \ce{H2A ⇌ H+ + HA-} \quad K_{a1} = \frac{[\ce{H+}][\ce{HA-}]}{[\ce{H2A}]} \ce{HA- ⇌ H+ + A^{2-}} \quad K_{a2} = \frac{[\ce{H+}][\ce{A^{2-}}]}{[\ce{HA-}]} Triprotic acids follow analogous stepwise processes for each proton.[36] The acid dissociation constants for successive steps decrease markedly (K<sub>a1</sub> ≫ K<sub>a2</sub> ≫ K<sub>a3</sub>), so pK<sub>a1</sub> < pK<sub>a2</sub> < pK<sub>a3</sub>; this occurs because each subsequent proton is removed from an increasingly negatively charged anion, which experiences greater electrostatic repulsion and holds the proton more tightly.[38] For sulfuric acid, for instance, K<sub>a1</sub> = 1.0 × 10<sup>3</sup> while K<sub>a2</sub> = 1.2 × 10<sup>−2</sup>, and for phosphoric acid, K<sub>a1</sub> = 7.1 × 10<sup>−3</sup>, K<sub>a2</sub> = 6.3 × 10<sup>−8</sup>, and K<sub>a3</sub> = 4.2 × 10<sup>−13</sup>.[37] The relative concentrations of the various species from a polyprotic acid in solution depend on the pH, with predominance shifting across the pK<sub>a</sub> values. For phosphoric acid, the dihydrogen phosphate species (H₂PO₄⁻) predominates in solutions with pH between approximately 2 and 7, the range spanning its first and second pK<sub>a</sub> values (2.1 and 7.2).[37] A key biological example is carbonic acid (H₂CO₃), a diprotic acid formed from CO₂ and H₂O in blood, where the bicarbonate ion (HCO₃⁻) is the dominant species at physiological pH (around 7.4), contributing to the bicarbonate buffer system that stabilizes blood pH between 7.35 and 7.45.[39]Neutralization Reactions
Neutralization reactions occur when an acid reacts with a base to form a salt and water, involving the combination of hydrogen ions (H⁺) from the acid and hydroxide ions (OH⁻) from the base to produce water.[40] The general equation for such a reaction is represented as HA + BOH → BA + H₂O, where HA is the acid, BOH is the base, BA is the salt, and H₂O is water.[40] These reactions are typically exothermic, particularly for pairs of strong acids and strong bases, where the heat of neutralization is approximately -57 kJ/mol at 25°C, reflecting the formation of water from fully dissociated ions.[40] The stoichiometry of neutralization reactions depends on the number of ionizable protons in the acid and hydroxide groups in the base. For monoprotic acids, such as hydrochloric acid (HCl), the reaction follows a 1:1 molar ratio with a monohydroxy base like sodium hydroxide (NaOH): HCl + NaOH → NaCl + H₂O.[40] Polyprotic acids require multiple equivalents of base; for example, sulfuric acid (H₂SO₄), a diprotic acid, reacts with two moles of NaOH: H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O.[40] The salts formed in neutralization reactions derive their properties from the strengths of the parent acid and base, specifically their conjugate pairs. Salts from strong acids and strong bases, such as NaCl from HCl and NaOH, are neutral with a pH of 7 in aqueous solution.[40] In contrast, salts from strong acids and weak bases, like ammonium chloride (NH₄Cl) from HCl and NH₃, are acidic (pH < 7) due to the hydrolysis of the conjugate acid of the weak base.[41] Representative examples illustrate these principles. The reaction of HCl with NaOH produces NaCl and water, a classic strong acid-strong base neutralization.[40] Historically, neutralization has been applied in soap production through saponification, where fatty acids from animal fats or vegetable oils react with lye (NaOH) to form soap salts and glycerol.[42]Weak Acid–Weak Base Equilibria
The reaction between a weak acid (HA) and a weak base (B) proceeds incompletely, establishing an equilibrium described by the equation: HA + B \rightleftharpoons A^- + HB^+ The equilibrium constant K for this reaction is given by K = \frac{K_a K_b}{K_w}, where K_a is the acid dissociation constant of HA, K_b is the base dissociation constant of B, and K_w is the ion product of water. This relationship arises because the forward reaction involves proton transfer from HA to B, with the position of equilibrium favoring the side containing the weaker acid and the weaker base (i.e., the side where the pK_a of the acid is higher and the pK_b of the base is lower).[43][44] Such equilibria form the basis of buffer solutions, which are mixtures of a weak acid and its conjugate base (or a weak base and its conjugate acid) that resist changes in pH upon addition of small amounts of strong acid or base. For instance, a buffer can be prepared by mixing acetic acid (CH₃COOH) with its conjugate base acetate (CH₃COO⁻), maintaining a stable pH through the reversible proton exchange. The pH of an acidic buffer is calculated using the Henderson-Hasselbalch equation: \text{pH} = \text{p}K_a + \log_{10} \frac{[A^-]}{[HA]} This equation, derived from the K_a expression, allows prediction of buffer pH based on the ratio of conjugate base to acid concentrations, assuming activity coefficients near unity.[45] A practical example is the mixture of acetic acid and ammonia (NH₃), where the equilibrium produces acetate and ammonium ions (NH₄⁺), creating a buffer system effective around neutral pH. In biological contexts, the bicarbonate buffer system—comprising carbonic acid (H₂CO₃) and bicarbonate (HCO₃⁻)—maintains blood pH near 7.4 by buffering metabolic acids and CO₂-derived protons. Buffers are most effective within approximately pK_a ± 1 unit, where the concentrations of the acid and conjugate base are within a 10:1 ratio, maximizing resistance to pH shifts. Beyond this range, buffering capacity diminishes significantly.[46]Measurement
Titration
Titration is an analytical technique used to determine the concentration of an acid by gradually adding a base of known concentration and monitoring the pH of the solution. The procedure typically involves placing a known volume of the acid solution in an Erlenmeyer flask and titrating it with the base from a burette, recording the pH after each incremental addition using a pH meter until the equivalence point is reached. This method relies on the neutralization reaction between the acid and base, allowing for precise quantification of the acid's molarity.[47] The resulting titration curve plots pH against the volume of base added, providing a visual representation of the reaction progress. For a strong acid titrated with a strong base, the curve is sigmoidal, characterized by a low initial pH, a gradual increase, and a sharp rise near the equivalence point due to excess base. In contrast, the curve for a weak acid titrated with a strong base features gentler slopes and plateaus, reflecting the buffering capacity of the system; the acid strength influences the curve's shape, with weaker acids producing less pronounced changes in pH. Buffer regions appear midway to the equivalence point, where the pH approximates the pK_a of the acid, as the solution contains roughly equal concentrations of the acid and its conjugate base, resisting pH changes.[48] The equivalence point occurs when the moles of acid equal the moles of base added for monoprotic acids, marking complete neutralization. For strong acid-strong base titrations, this point is at pH 7, as the resulting salt solution is neutral. In weak acid-strong base titrations, the equivalence point pH exceeds 7, typically around 8-9, because the conjugate base of the weak acid hydrolyzes to produce excess OH^-. For polyprotic acids such as H_2SO_4, the curve displays two distinct equivalence points corresponding to each proton donation, with inflection breaks at a low pH around 2–3 (first, forming HSO_4^-, determined by the pK_a of HSO_4^- ≈ 2) and pH 9 (second, forming SO_4^{2-}).[48][37] To calculate the volume of base required to reach the equivalence point for a monoprotic acid, use the formula: V_{\text{eq}} = \frac{C_{\text{acid}} \times V_{\text{acid}}}{C_{\text{base}}} where C_{\text{acid}} and C_{\text{base}} are the concentrations, and V_{\text{acid}} is the initial volume of acid; this assumes a 1:1 stoichiometry and follows from the equality of moles at equivalence. For polyprotic acids, the formula is adjusted by the number of equivalents, but the principle remains based on stoichiometric balance.[49]pH and Indicators
The concept of pH was introduced in 1909 by Danish biochemist Søren Peder Lauritz Sørensen while working at the Carlsberg Laboratory, providing a practical scale to quantify the acidity of solutions based on hydrogen ion activity.[50] Sørensen's innovation addressed the need for a logarithmic measure during biochemical research on enzyme activity in brewing.[51] pH is formally defined by the International Union of Pure and Applied Chemistry (IUPAC) as the negative base-10 logarithm of the activity of hydrogen ions in solution:\mathrm{pH} = -\log_{10} a(\mathrm{H^+})
where a(\mathrm{H^+}) represents the effective concentration accounting for non-ideal behavior.[52] In dilute aqueous solutions at 25°C, this approximates to \mathrm{pH} = -\log_{10} [\mathrm{H^+}], with the scale conventionally spanning 0 (highly acidic, [H⁺] = 1 M) to 14 (highly basic, [H⁺] = 10⁻¹⁴ M), and pH 7 indicating neutrality due to water's dissociation constant K_w = 10^{-14}.[52][53] Values below 0 or above 14 occur in concentrated strong acids or bases, but the 0–14 range applies to most aqueous systems under standard conditions.[53] Acid-base indicators are typically weak organic acids or bases that undergo a structural change, resulting in a visible color shift near their pKₐ value, allowing qualitative pH assessment.[54] The color transition occurs over a narrow pH interval (usually 1–2 units) where the indicator's protonated and deprotonated forms coexist in comparable amounts.[54] A common example is phenolphthalein, a weak acid with pKₐ ≈ 9.3, which remains colorless below pH 8.2 in its protonated form and turns pink above pH 10.0 in its deprotonated form due to extended conjugation in the basic state.[55][55] For precise quantitative measurement, glass pH electrodes are widely used, consisting of a thin, ion-selective glass membrane that develops a potential proportional to the external [H⁺] relative to an internal reference solution.[56] This potential adheres to the Nernst equation for the hydrogen ion half-cell:
E = E_0 - 0.059 \log_{10} a(\mathrm{H^+})
at 25°C, corresponding to a change of 59 mV per pH unit, with the electrode potential increasing by 59 mV as the pH decreases by one unit.[56] Despite their utility, pH measurements face limitations in non-aqueous solvents, where the absence of water alters ion activity and hydration, rendering standard scales and glass electrodes unreliable without solvent-specific calibrations or alternative probes.[57] Universal indicators, blends of multiple dyes such as methyl red, bromothymol blue, and thymol blue, overcome some precision needs by displaying a continuous color gradient across pH 1–14 (red for acidic, green for neutral, purple for basic), facilitating broad-range visual approximations without equipment.[58]