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Química Geral · Exam review

Tampões, titulações e solubilidade

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O que você vai aprender

  • Calculate buffer pH with the Henderson–Hasselbalch equation, doing the strong acid or strong base stoichiometry first, and design a buffer of given pH and capacity.
  • Locate every region of a titration curve, calculate its pH, choose an indicator and extract Ka, concentration or molar mass from titration data.
  • Convert between Ksp and molar solubility for salts of any formula and predict precipitation by comparing Q with Ksp after mixing.
  • Predict how common ions, pH and complex formation change solubility, and plan selective precipitations and separations.

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Buffers: stoichiometry first, then Henderson–Hasselbalch

A buffer holds a weak acid HA and its conjugate base A⁻ in comparable amounts, and pH = pKa + log(n(A⁻)/n(HA)). Because both species share one volume, moles can replace concentrations. When a strong acid or base is added, first let it react completely: H₃O⁺ converts A⁻ into HA, and OH⁻ converts HA into A⁻. Only then apply the equation. Worked example (pKa 4.76): 1.00 L holding 0.100 mol HA and 0.080 mol A⁻ has pH 4.76 + log(0.080/0.100) = 4.66. Adding 0.020 mol HCl leaves 0.120 mol HA and 0.060 mol A⁻, so pH = 4.76 + log 0.50 = 4.46. A buffer also forms when a weak acid is partly neutralized by a strong base, or a weak base partly by a strong acid, as long as some of the weak species is left over. Lactic acid and lactate (drawn, pKa 3.86) are a typical pair. Traps: a 1 : 1 mole ratio of weak base and strong acid gives only the conjugate acid, not a buffer. A buffer works best within about one pH unit of its pKa. Its capacity grows with the amounts of HA and A⁻, so dilution barely changes the pH but lowers the capacity.

Reading a titration curve

Before doing any arithmetic, decide which region of the curve you are in. Worked example: 20.0 mL of 0.100 M formic acid (Ka 1.8 × 10⁻⁴, pKa 3.74) is titrated with 0.100 M NaOH, so the equivalence point is at 20.0 mL. Start: a weak acid alone, [H₃O⁺] = √(Ka·C) = 4.2 × 10⁻³ M, pH 2.37. Buffer region: after 5.0 mL, n(HCOO⁻)/n(HCOOH) = 0.50/1.50, so pH = 3.745 − 0.477 = 3.27 (keep the unrounded pKa, 3.745, in the arithmetic). Half-equivalence (10.0 mL): pH = pKa = 3.74. Equivalence: only formate is left, at 2.00 mmol/40.0 mL = 0.0500 M, so it must be diluted to the total volume. Kb = Kw/Ka = 5.6 × 10⁻¹¹, [OH⁻] = √(Kb·C) = 1.7 × 10⁻⁶ M, and pH = 8.22. After equivalence: the excess OH⁻ sets the pH. At 25.0 mL it is 0.50 mmol/45.0 mL = 0.0111 M, so pH = 12.05. A weak base titrated with a strong acid gives the mirror image: the curve starts basic, pH = pKa of the conjugate acid at half-equivalence, and the equivalence point is acidic. Only strong acid–strong base titrations have pH 7.00 at equivalence. A diprotic acid needs two moles of NaOH per mole of acid when both protons are titrated.

Indicators and two-step curves

An indicator HIn changes colour over roughly pKa(HIn) ± 1. Choose one whose colour-change range lies on the steep part of the curve around the equivalence pH: phenolphthalein (8.2–10.0) for a weak acid with a strong base, methyl red (4.4–6.2) for a weak base with a strong acid, and almost any of these for a strong acid with a strong base. An indicator that changes inside the buffer region stops the titration early. The pH there changes slowly with volume, so the error is large, not small. A polyprotic system gives one equivalence point per proton when the pKa values are several units apart. Carbonate (drawn) titrated with HCl reaches HCO₃⁻ at the first equivalence point, where pH ≈ ½(6.35 + 10.33) = 8.34. It reaches H₂CO₃ (dissolved CO₂) at the second, where the pH is about 4. Halfway to each equivalence point the pH equals the corresponding pKa. A mixture of a strong and a weak acid also shows two equivalence points: the strong acid is neutralized first, and the volume between the two jumps measures the weak acid.

Ksp, molar solubility and Q

When a salt dissolves into a cations and b anions per formula unit, Ksp = [cation]ᵃ[anion]ᵇ, and each ion concentration is the stoichiometric multiple of the molar solubility s. For a 1 : 1 salt Ksp = s², and for a 1 : 2 or 2 : 1 salt Ksp = (s)(2s)² = 4s³. Worked example: PbI₂ with Ksp = 9.8 × 10⁻⁹ has s = (Ksp/4)^⅓ = 1.35 × 10⁻³ M, and [I⁻] = 2s. Compare solubilities through s, never through Ksp, when the formulas differ. To predict precipitation, first dilute each ion to the mixed volume, then compute Q with the same exponents as Ksp. If Q > Ksp a solid forms, if Q = Ksp the solution is saturated, and if Q < Ksp nothing forms. When a precipitate does form from a large excess, let the reaction go essentially to completion, then let the leftover ions set the dissolved amount. Ksp changes only with temperature; adding more solid does not change the concentrations in a saturated solution. The ideal-solution treatment used throughout ignores activity effects, which are large in concentrated salt solutions.

Common ions, pH and complex ions

A common ion lowers solubility. PbI₂ in 0.10 M KI has s = Ksp/(0.10)² = 9.8 × 10⁻⁷ M, more than a thousand times less than in water. Remember to square the common-ion concentration when its exponent is 2. A salt whose anion is a base dissolves better in acid: H₃O⁺ converts F⁻ into HF, CO₃²⁻ into HCO₃⁻ and H₂CO₃, and OH⁻ into water, so Q drops below Ksp and more solid dissolves. Anions of strong acids (Cl⁻, Br⁻, I⁻) are not protonated and are unaffected. Sulfate (pKa of HSO₄⁻ 1.99) is protonated only in fairly strong acid, and even at pH 1 BaSO₄ becomes only about three times more soluble. For a hydroxide held in a buffer, [OH⁻] = Kw/[H₃O⁺] and s = Ksp/[OH⁻]ⁿ, so lowering the pH by one unit raises s a hundredfold for M(OH)₂ and a thousandfold for M(OH)₃. An NH₃/NH₄⁺ buffer can hold [OH⁻] low enough to keep Mg(OH)₂ from forming. A Lewis base ligand bound to a metal ion (Lewis acid) forms a complex ion such as [Ag(NH₃)₂]⁺ or [Cu(NH₃)₄]²⁺, with formation constant Kf. Complexation removes the free metal ion, so a precipitate can dissolve. The overall constant is K = Ksp × Kf; for AgCl in ammonia K = 1.8 × 10⁻¹⁰ × 1.7 × 10⁷ = 3.1 × 10⁻³. A large Kf alone does not guarantee dissolution.

Selective precipitation

When a precipitating ion is added slowly to a mixture, each solid begins to form when its own Q reaches its Ksp. The solid needing the lowest concentration of added ion appears first. Calculate that onset concentration for each salt. For salts of different formula this concentration, not the Ksp value, decides the order. Worked example: with 0.010 M Cl⁻ and 0.010 M I⁻, AgI starts at [Ag⁺] = 8.3 × 10⁻¹⁷/0.010 = 8.3 × 10⁻¹⁵ M and AgCl at 1.8 × 10⁻¹⁰/0.010 = 1.8 × 10⁻⁸ M. When AgCl just starts, [I⁻] = 8.3 × 10⁻¹⁷/1.8 × 10⁻⁸ = 4.6 × 10⁻⁹ M, so the iodide has been removed almost completely. Hydroxides are separated the same way by controlling pH. Ammonia separates ions that form ammine complexes (Ag⁺, Cu²⁺, Zn²⁺, Ni²⁺) from those that only precipitate as hydroxides (Fe³⁺, Al³⁺). Amphoteric hydroxides such as Zn(OH)₂ and Al(OH)₃ redissolve in excess NaOH.

What to carry forward

Work every problem in the same order: do the stoichiometry of any strong acid, strong base or precipitation reaction first, decide which species remain, then choose the equilibrium. That is Henderson–Hasselbalch for a weak acid with its conjugate base, √(K·C) for a lone weak acid or base, Ksp for a saturated solution, or Ksp × Kf for dissolution by complexation. Dilute to the final volume before you compute Q or pH. Compare solubilities and precipitation order through molar solubilities and onset concentrations, never through raw Ksp values of salts with different formulas.

Problemas de prática (40)

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Preveja o produto 4

Titration curves and indicators

  • Two endpoints for sodium carbonatePredict the major species, pH and suitable indicator at each equivalence point of a dibasic anion titrated with strong acid.

Selective precipitation and complex ions

  • Which chromate appears first?Predict which of two 1 : 1 salts precipitates first when their common ion is added slowly.

Buffers and Henderson–Hasselbalch

  • Phosphoric acid meets phosphatePredict the species and pH formed when a polyprotic acid is mixed with its fully deprotonated anion.

Ksp, common ions and pH

  • Will silver sulfate precipitate?Predict precipitation on mixing two solutions by diluting first and computing Q with the correct exponents.

Classificar 3

Titration curves and indicators

  • Identify the titration from its curveClassify a titration as strong or weak, acid or base, from its starting, half-equivalence and equivalence pH values.

Buffers and Henderson–Hasselbalch

  • Which methylamine mixture buffers?Decide which mixtures of a weak base with strong acid, strong base or its salt leave a conjugate pair in comparable amounts.

Selective precipitation and complex ions

  • Roles in the tetraamminezinc(II) ionClassify the metal ion and ligand in complex-ion formation as Lewis acid and Lewis base and find the complex's charge.

Comparar 4

Ksp, common ions and pH

  • Which saturated solution has more iodate?Compare ion concentrations in saturated solutions of salts with different formulas and similar Ksp.
  • Manganese(II) hydroxide in four liquidsRank the solubility of a metal hydroxide in pure water, buffers and strong base by computing each value.

Selective precipitation and complex ions

  • Order of lead(II) precipitatesOrder the precipitation of salts of mixed formula types from their onset concentrations rather than raw Ksp values.

Buffers and Henderson–Hasselbalch

  • Rank four buffers by pHRank buffers by pH when both the pKa and the base-to-acid ratio differ.

Calcular 14

Selective precipitation and complex ions

  • How much bromide can ammoniacal silver tolerate?Combine Kf and Ksp to find the largest anion concentration a complexed metal solution tolerates without precipitating.
  • Free Cu²⁺ in ammoniaCalculate the free metal-ion concentration from Kf, the complex concentration and the free ligand concentration.
  • How cleanly does chromate separate lead from barium?Calculate the percentage of the first ion still dissolved when the second ion just begins to precipitate.
  • Solubility of AgCl in aqueous ammoniaCalculate the molar solubility of a salt dissolved by complex formation using K = Ksp × Kf.

Ksp, common ions and pH

  • How much calcium sulfate precipitates?Calculate how much of a moderately soluble salt precipitates when leftover dissolved ions cannot be neglected.
  • Lead(II) bromide in sodium bromideCalculate the molar solubility of a 1 : 2 salt in a solution of its common anion.
  • Ksp of lead(II) fluoride from its solubilityCalculate Ksp of a 1 : 2 salt from its measured solubility in grams per litre.
  • Molar solubility of strontium fluorideCalculate the molar solubility of a 1 : 2 salt in pure water from its Ksp.

Buffers and Henderson–Hasselbalch

  • Sodium carbonate plus excess acidCalculate the pH after a strong acid protonates a dibasic anion past its first equivalence point.
  • pH of a lactic acid–lactate bufferCalculate the pH of a buffer from the concentrations of a weak acid and its conjugate base.
  • Methylamine buffer after HClCalculate the pH of a weak-base buffer after a strong acid has reacted with its base component.

Titration curves and indicators

  • Hypochlorous acid partway to equivalenceCalculate the pH in the buffer region of a weak acid titration at a point other than half-equivalence.
  • pH at the equivalence point of nitrous acidCalculate the equivalence-point pH of a weak acid titration, including dilution by the titrant.
  • Equivalence volume for sulfuric acidCalculate the equivalence-point volume for a diprotic acid whose two protons are titrated together.

Encontre o erro 3

Buffers and Henderson–Hasselbalch

  • A buffer that is not a bufferFind the error when equal moles of a weak acid and a strong base are mixed and treated as a buffer.

Selective precipitation and complex ions

  • A large Kf is not enoughDiagnose the error in predicting complete dissolution of a precipitate from Kf alone.

Titration curves and indicators

  • Wrong indicator for acetic acidDiagnose the size and direction of the error when an indicator changes colour inside the buffer region.

Interprete as evidências 4

Selective precipitation and complex ions

  • Identify the cations from three testsInterpret precipitation and complex-formation tests to decide which cations an unknown contains.

Titration curves and indicators

  • Molar mass of a diprotic acidUse a titration endpoint and the acid's proticity to find the molar mass of an unknown acid.
  • A curve with two jumpsInterpret a two-jump titration curve of a strong and weak acid mixture to find the pH at a chosen volume.

Ksp, common ions and pH

  • Ksp of Ca(OH)₂ by titrationInterpret titration data for a saturated hydroxide solution to obtain its Ksp.

Trabalhe de trás para frente 2

Buffers and Henderson–Hasselbalch

  • Ratio in a nitrite bufferWork backwards from a measured buffer pH to the base-to-acid ratio it contains.

Titration curves and indicators

  • pKa from the equivalence-point pHWork backwards from the measured equivalence-point pH of a weak acid titration to the acid's pKa.

Planeje uma síntese 5

Ksp, common ions and pH

  • Ammonium chloride keeps magnesium in solutionUse a weak-base buffer to set the hydroxide concentration that keeps a metal hydroxide from precipitating.

Buffers and Henderson–Hasselbalch

  • How concentrated must the buffer be?Find the smallest buffer concentration that keeps the pH within a set limit after a given dose of strong acid.
  • Making a lactate buffer with NaOHCalculate the volume of strong base that partly neutralizes a weak acid to give a buffer of target pH.

Selective precipitation and complex ions

  • Separate copper(II) from iron(III)Plan a one-reagent separation of two cations using complex formation by one of them.

Titration curves and indicators

  • Indicator for a methylamine titrationChoose the indicator whose colour-change range contains the equivalence pH of a weak base–strong acid titration.

Explique por quê 1

  • Why acid dissolves one barium saltExplain why acid dissolves a salt of a strongly basic anion but barely affects a salt of a very weakly basic anion.

Travou em tampões, titulações e solubilidade? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

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