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Química Geral · Acid–base and solubility equilibria

pH de ácidos fracos, bases fracas e sais

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O que você vai aprender

  • Interconvert pH, pOH, [H₃O⁺] and [OH⁻] at 25 °C and calculate the pH of strong acid and strong base solutions.
  • Write Ka and Kb expressions and find the pH of a weak acid or weak base with an ICE table, checking the 5 % approximation and solving the quadratic when it fails.
  • Calculate percent ionization and explain why it rises when a weak acid is diluted.
  • Use Ka·Kb = Kw to decide whether a salt solution is acidic, basic or neutral and to calculate its pH.
  • Treat a polyprotic acid through its first ionization and recognize that [A²⁻] ≈ Ka2 in a solution of H₂A alone.

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pH, pOH and strong acids and bases

pH = −log[H₃O⁺] and pOH = −log[OH⁻]. Water autoionizes, and at 25 °C Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14.00. Each pH unit is a factor of 10 in [H₃O⁺]. A solution is neutral when [H₃O⁺] = [OH⁻]; that happens at pH 7.00 only at 25 °C, because Kw grows with temperature. Strong acids (HCl, HBr, HI, HNO₃ (drawn), HClO₄ and the first proton of H₂SO₄) and strong bases (the group 1 hydroxides and Ca(OH)₂, Sr(OH)₂, Ba(OH)₂) ionize completely, so their concentrations give [H₃O⁺] or [OH⁻] directly. Example: 0.0040 M HClO₄ has [H₃O⁺] = 0.0040 M, pH = 2.40, and [OH⁻] = 1.0 × 10⁻¹⁴/0.0040 = 2.5 × 10⁻¹² M. 0.0020 M KOH has pOH = 2.70 and pH = 14.00 − 2.70 = 11.30.

Weak acids and bases: Ka, Kb and the ICE table

A weak acid transfers a proton to water only partly: HA + H₂O ⇌ H₃O⁺ + A⁻, Ka = [H₃O⁺][A⁻]/[HA], and pKa = −log Ka. A weak base takes a proton from water: B + H₂O ⇌ BH⁺ + OH⁻, Kb = [BH⁺][OH⁻]/[B]. Water is the solvent and is left out of both expressions. For a solution of HA at concentration C, the ICE table gives Ka = x²/(C − x) with x = [H₃O⁺]. Assume x is small, drop it from C − x, so x = √(Ka·C), and then check that x is less than 5 % of C. Example: 0.10 M HOCl (Ka = 3.0 × 10⁻⁸, drawn) gives x = √(3.0 × 10⁻⁹) = 5.5 × 10⁻⁵ M, only 0.055 % of C, and pH = 4.26. When the check fails, solve x² + Ka·x − Ka·C = 0. For 0.10 M CH₃NH₂ (Kb = 4.4 × 10⁻⁴) the shortcut gives 6.6 × 10⁻³ M, 6.6 % of C, so use the quadratic: x = [−Kb + √(Kb² + 4Kb·C)]/2 = 6.4 × 10⁻³ M = [OH⁻], pOH = 2.19 and pH = 11.81. In most weak acid and weak base solutions the un-ionized molecule is the main solute species; only very dilute solutions of the stronger weak acids, such as 0.0010 M HF (about 55 % ionized), break this pattern.

Proton transfer to and from water

Each of these equilibria is a single proton transfer with water. In HF + H₂O ⇌ H₃O⁺ + F⁻ (drawn), a lone pair on the water oxygen bonds to the hydrogen of HF and the H–F bonding pair stays on fluorine as fluoride. Water is the base and HF the acid; H₃O⁺/H₂O and HF/F⁻ are the conjugate pairs. A basic anion reverses the roles: in OCl⁻ + H₂O ⇌ HOCl + OH⁻ an oxygen lone pair of hypochlorite takes a proton from water and the O–H bonding pair stays on the water oxygen as hydroxide. Both proton transfers are fast in each direction, so Ka or Kb simply measures where the balance lies.

Percent ionization and dilution

Percent ionization = x/C × 100. Under the 5 % approximation it equals 100·√(Ka/C), so diluting a weak acid 100-fold raises its percent ionization about tenfold even though [H₃O⁺] falls. The reason is Le Châtelier: dilution lowers every dissolved concentration by the same factor, and because the right side has two dissolved particles and the left side one, Q = [H₃O⁺][A⁻]/[HA] drops below Ka and more acid ionizes. Example: HOCl is 0.055 % ionized at 0.10 M and 0.55 % at 0.0010 M; its pH rises only from 4.26 to 5.26 over that 100-fold dilution. A strong acid behaves differently: its pH rises by one unit for every tenfold dilution, while a weak acid's pH rises by only about half a unit.

Conjugate pairs and salts: Ka·Kb = Kw

For any conjugate pair Ka·Kb = Kw, so pKa + pKb = 14.00 at 25 °C: the stronger an acid, the weaker its conjugate base. To predict the pH of a salt, look at each ion. Conjugate bases of strong acids (Cl⁻, Br⁻, I⁻, NO₃⁻, ClO₄⁻) and the cations of strong bases (Li⁺, Na⁺, K⁺, Ca²⁺, Ba²⁺) do not react with water. Anions of weak acids (F⁻, CH₃COO⁻, CN⁻, OCl⁻) are weak bases and make the solution basic. NH₄⁺ and small, highly charged hydrated metal ions such as Al³⁺ and Fe³⁺ are weak acids. When both ions react, compare Ka of the cation with Kb of the anion. Example: for 0.10 M NH₄Cl (drawn), Ka(NH₄⁺) = 1.0 × 10⁻¹⁴/1.8 × 10⁻⁵ = 5.6 × 10⁻¹⁰, [H₃O⁺] = √(5.6 × 10⁻¹¹) = 7.5 × 10⁻⁶ M and pH = 5.13.

Polyprotic acids

A polyprotic acid gives up its protons one at a time, and Ka1 ≫ Ka2 because the second proton must leave a negatively charged ion. When Ka1 is much larger than Ka2, the pH of a solution of H₂A alone comes from the first ionization only. The first step also makes [HA⁻] ≈ [H₃O⁺], so in Ka2 = [H₃O⁺][A²⁻]/[HA⁻] the two cancel and [A²⁻] ≈ Ka2, whatever the starting concentration. Example: 0.10 M carbonic acid (drawn; Ka1 = 4.3 × 10⁻⁷, Ka2 = 5.6 × 10⁻¹¹) has [H₃O⁺] = √(4.3 × 10⁻⁸) = 2.1 × 10⁻⁴ M, pH = 3.68, and [CO₃²⁻] ≈ 5.6 × 10⁻¹¹ M. Sulfuric acid is the exception: its first proton is strong and Ka2 = 1.2 × 10⁻² is large enough that the second step adds a measurable amount of H₃O⁺, which needs its own quadratic.

What to carry forward

Convert freely between pH, pOH, [H₃O⁺] and [OH⁻] with Kw = 1.0 × 10⁻¹⁴ at 25 °C. Strong acids and bases ionize completely. For a weak acid or base, write the ICE table, try x = √(K·C), check the 5 % rule and fall back on the quadratic. Percent ionization rises on dilution. Ka·Kb = Kw tells you how strongly a salt's ions react with water. In a polyprotic acid the first ionization sets the pH and [A²⁻] ≈ Ka2.

Problemas de prática (40)

Praticar é grátis com uma conta.

Desenhe o mecanismo 2

Weak acids and bases

  • Hydrofluoric acid gives a proton to waterDraw the proton transfer from HF to water with curved arrows and use Ka to judge how far it goes.

Salts and Ka·Kb = Kw

  • Hypochlorite ion takes a proton from waterDraw the proton transfer from water to hypochlorite that makes bleach solutions basic, and calculate Kb of hypochlorite from Ka of hypochlorous acid.

Preveja o produto 4

Weak acids and bases

  • What is really in ammonia solution?Predict the most abundant solute species in a weak-base solution from the size of Kb.
  • Write Kb for methylamineWrite the base-ionization constant expression for a weak base reacting with water.

Salts and Ka·Kb = Kw

  • When both ions react with waterPredict whether a salt of a weak acid and a weak base is acidic or basic by comparing the cation's Ka with the anion's Kb.

Percent ionization and dilution

  • Diluting acetic acid 100-foldPredict how percent ionization and pH change when a weak acid is diluted 100-fold.

Classificar 2

Salts and Ka·Kb = Kw

  • Which salt makes water basic?Classify salts as acidic, basic or neutral by identifying which ion reacts with water.

pH, pOH and strong acids and bases

  • Spot the all-strong listClassify common acids as strong or weak in water from the standard list of strong acids.

Comparar 4

Polyprotic acids

  • Phosphate species in phosphoric acidRank the concentrations of the species in a polyprotic acid solution from its stepwise Ka values.

Weak acids and bases

  • Rank acids given Ka or pKaRank weak acids by strength when some are given as Ka and others as pKa.

pH, pOH and strong acids and bases

  • Rank solutions given in mixed unitsRank solutions described by pH, pOH, [H₃O⁺] or [OH⁻] by converting each to a common pH scale.

Salts and Ka·Kb = Kw

  • Rank salt solutions by pHRank salt solutions by pH by comparing the Ka or Kb of the ion that reacts with water.

Calcular 17

Polyprotic acids

  • How much ascorbate dianion is present?Find the concentration of the fully deprotonated anion of a diprotic acid using [A²⁻] ≈ Ka2.
  • pH of a vitamin C solutionCalculate the pH of a diprotic acid from its first ionization when Ka1 ≫ Ka2.
  • pH of 0.10 M phosphoric acidSolve the quadratic for the first ionization of a polyprotic acid whose Ka1 is too large for the 5 % approximation.
  • pH of 0.010 M sulfuric acidCalculate the pH of dilute sulfuric acid by combining a complete first ionization with an equilibrium second ionization.

pH, pOH and strong acids and bases

  • pH of diluted nitric acidCombine a dilution with complete ionization to find the pH of a strong acid.
  • Hydroxide concentration from pHConvert a measured pH into the hydroxide-ion concentration of a basic solution.
  • pH from a hydroxide concentrationConvert a hydroxide-ion concentration into pH through pOH and Kw.

Percent ionization and dilution

  • Percent ionization after dilutionScale percent ionization with the inverse square root of concentration when a weak acid is diluted.
  • Percent ionization from pHCalculate the percent ionization of a weak acid from its concentration and measured pH.
  • How much benzoic acid ionizes?Calculate the percent ionization of a weak acid from Ka and its concentration.

Salts and Ka·Kb = Kw

  • pH of 0.20 M ammonium chlorideCalculate the pH of an ammonium salt solution from Kb of ammonia via Ka = Kw/Kb.
  • pH of 0.10 M sodium fluorideCalculate the pH of a solution of a weak acid's sodium salt using Kb = Kw/Ka.
  • pKa of the methylammonium ionUse pKa + pKb = 14.00 to find the pKa of a weak base's conjugate acid.

Weak acids and bases

  • pH of 0.20 M formic acidCalculate the pH of a weak acid with the square-root approximation and confirm it with the 5 % rule.
  • When the 5 % rule fails: dilute methylamineRecognize when the 5 % approximation fails for a weak base and solve the quadratic for its pH.
  • pH of 0.20 M pyridineCalculate the pH of a very weak base solution from Kb, converting through pOH.
  • pKa from a measured pHWork back from the measured pH of a weak acid solution to its Ka and pKa.

Encontre o erro 3

Polyprotic acids

  • Does more carbonic acid mean more carbonate?Diagnose the error of assuming that the doubly deprotonated anion scales with the concentration of a diprotic acid.

Weak acids and bases

  • Find the flaw in a weak-acid pHDiagnose an invalid use of the square-root approximation for a dilute weak acid.

pH, pOH and strong acids and bases

  • Is warm pure water acidic?Diagnose the error of equating pH 7 with neutrality at a temperature other than 25 °C.

Interprete as evidências 1

  • Read dilution data to tell strong from weakInterpret how pH responds to tenfold dilution to identify a strong acid and a weak acid.

Trabalhe de trás para frente 2

Weak acids and bases

  • How concentrated must the HF be?Work backwards from a target pH to the initial concentration of a weak acid.

Salts and Ka·Kb = Kw

  • pKa from the pH of a salt solutionWork back from the pH of a sodium salt solution to the pKa of the parent weak acid.

Planeje uma síntese 1

  • Pick a salt for a pH near 9Plan which salt to dissolve to reach a target pH window by estimating each salt solution's pH from Ka or Kb.

Explique por quê 4

Salts and Ka·Kb = Kw

  • Why aluminium nitrate is acidicExplain the acidity of a solution of a small, highly charged metal cation through proton loss from a coordinated water molecule.

pH, pOH and strong acids and bases

  • Same concentration, different pHExplain the pH difference between equal concentrations of a strong and a weak acid by the extent of proton transfer to water.

Percent ionization and dilution

  • Why dilution helps a weak acid ionizeExplain the rise in percent ionization on dilution by comparing the reaction quotient with Ka.

Polyprotic acids

  • Why the second proton is harder to removeExplain why successive acid-dissociation constants of a polyprotic acid decrease.

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