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Química Geral · Acid–base and solubility equilibria

Equilíbrios de solubilidade e Ksp

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O que você vai aprender

  • Write the dissolution equation and Ksp expression of a sparingly soluble salt, omitting the solid.
  • Convert between molar solubility and Ksp for 1:1, 1:2 and 2:3 salts, and between molar and mass solubility.
  • Compare the solubilities of salts, using Ksp directly only when the formula types match and molar solubility otherwise.
  • Calculate the solubility of a salt in a solution that already contains one of its ions, and explain why a common ion lowers it.
  • Explain and calculate how pH changes the solubility of salts with basic anions such as hydroxide, fluoride, carbonate and phosphate.
  • Predict whether a precipitate forms by comparing the ion product Q, calculated after mixing, with Ksp.

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The solubility product

A sparingly soluble ionic solid in contact with its saturated solution sets up a dynamic equilibrium between the solid and its dissolved ions. For barium sulfate (drawn as its ions), BaSO₄(s) ⇌ Ba²⁺(aq) + SO₄²⁻(aq). The equilibrium constant is the solubility product, Ksp = [Ba²⁺][SO₄²⁻]. The pure solid is left out because its activity is 1, so adding more solid does not change the dissolved concentrations. Each ion concentration is raised to the power of its coefficient: for iron(III) hydroxide, Fe(OH)₃(s) ⇌ Fe³⁺ + 3 OH⁻ and Ksp = [Fe³⁺][OH⁻]³. Like every equilibrium constant, Ksp changes only with temperature. All Ksp values in this topic are for 25 °C, and solutions are treated as ideal.

Molar solubility and Ksp

The molar solubility s is the number of moles of the salt that dissolve per litre of saturated solution. Write each ion concentration in terms of s and substitute into Ksp. For a 1:1 salt such as AgCl, [Ag⁺] = [Cl⁻] = s, so Ksp = s² and s = √Ksp = √(1.8 × 10⁻¹⁰) = 1.34 × 10⁻⁵ M. For a 1:2 salt such as Mg(OH)₂, [Mg²⁺] = s and [OH⁻] = 2s, so Ksp = s(2s)² = 4s³ and s = (5.6 × 10⁻¹² ÷ 4)^⅓ = 1.12 × 10⁻⁴ M. For a 3:2 (or 2:3) salt such as Ca₃(PO₄)₂, [Ca²⁺] = 3s and [PO₄³⁻] = 2s, so Ksp = (3s)³(2s)² = 108s⁵. The coefficient appears twice: once as a multiplier inside the bracket and once as the exponent. To go from Ksp to grams per litre, multiply s by the molar mass; to go back, divide a mass solubility by the molar mass before substituting.

Comparing solubilities

For salts of the same formula type, the one with the smaller Ksp is less soluble: AgI (Ksp 8.5 × 10⁻¹⁷) is less soluble than AgCl (1.8 × 10⁻¹⁰). When the formula types differ, Ksp values cannot be compared directly, because Ksp is s² for one salt and 4s³ or 108s⁵ for another. Convert each Ksp to s first. AgCl has the larger Ksp (1.8 × 10⁻¹⁰ against 5.6 × 10⁻¹² for Mg(OH)₂), yet its molar solubility, 1.34 × 10⁻⁵ M, is lower than that of Mg(OH)₂, 1.12 × 10⁻⁴ M. For a very small Ksp, a higher power of s means a much larger s.

The common-ion effect

If the solution already contains one of the salt's ions, the dissolution equilibrium shifts to the left and less solid dissolves. Ksp is unchanged; only the way it is shared between the two ions changes. Worked example: AgCl in 0.10 M NaCl. Let s mol/L of AgCl dissolve, so [Ag⁺] = s and [Cl⁻] = 0.10 + s ≈ 0.10. Then s = Ksp/0.10 = 1.8 × 10⁻¹⁰ ÷ 0.10 = 1.8 × 10⁻⁹ M, about 7500 times less than in pure water. Check the approximation: s is negligible beside 0.10 M. If the salt's own contribution is not small (for example a fairly soluble salt in a dilute common-ion solution), keep it and solve the full equation. At the same concentration, a common ion that appears squared in Ksp suppresses the solubility more strongly than one that appears to the first power.

pH and salts of basic anions

If the anion is a base, acid removes it: F⁻ + H₃O⁺ → HF + H₂O (HF and F⁻ drawn), CO₃²⁻ + H₃O⁺ → HCO₃⁻ + H₂O, OH⁻ + H₃O⁺ → 2 H₂O. Lowering the anion concentration makes Q fall below Ksp, so more solid dissolves. Hydroxides, fluorides, carbonates, phosphates, oxalates and sulfides therefore become more soluble as the pH falls. Salts whose anion is the conjugate base of a strong acid (Cl⁻, Br⁻, I⁻, NO₃⁻) are essentially unaffected. For a hydroxide the effect follows directly from Ksp: at pH 9.00, [OH⁻] = 1.0 × 10⁻⁵ M, so the solubility of Mg(OH)₂ is 5.6 × 10⁻¹² ÷ (1.0 × 10⁻⁵)² = 0.056 M, 500 times its value in pure water. For a fluoride at a fixed pH, only the fraction Ka/(Ka + [H₃O⁺]) of the dissolved fluoride is present as F⁻, and that fraction enters Ksp.

Will a precipitate form?

The ion product Q has the same form as Ksp but uses the concentrations actually present. If Q < Ksp the solution is unsaturated and more solid can dissolve; if Q = Ksp it is saturated; if Q > Ksp it is supersaturated and the salt precipitates until Q falls to Ksp. When two solutions are mixed, first find each concentration in the combined volume. Worked example: 25.0 mL of 2.0 × 10⁻⁴ M AgNO₃ and 25.0 mL of 2.0 × 10⁻⁴ M NaCl give [Ag⁺] = [Cl⁻] = 1.0 × 10⁻⁴ M after mixing, so Q = 1.0 × 10⁻⁸ > 1.8 × 10⁻¹⁰ and AgCl precipitates. Only ions released by the dissolving salt carry its stoichiometric factor; an ion supplied by a soluble reagent such as AgNO₃ enters Q at its actual concentration. When precipitation occurs with one ion in excess, the minor ion is almost entirely removed. Find its final concentration from Ksp using the excess ion's concentration left after precipitation: for a 1:1 salt such as AgCl it is Ksp divided by that concentration, while an excess ion that appears squared in Ksp, such as Ag⁺ for Ag₂CrO₄, must be squared first.

What to carry forward

Write Ksp from the dissolution equation without the solid, express every ion as a multiple of s, and compare salts through s unless their formula types match. A common ion lowers solubility; acid raises the solubility of salts with basic anions. Compute Q from the concentrations after mixing: precipitation happens only when Q exceeds Ksp, and it continues until Q = Ksp.

Problemas de prática (40)

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Preveja o produto 4

Common-ion effect

  • More solid, same solutionPredict that adding more of the solid salt does not change the composition of a saturated solution.
  • Adding chloride to saturated AgClPredict how adding a common ion changes the solid and the ion concentrations in a saturated solution.

Predicting precipitation

  • When Q exceeds KspPredict that a supersaturated solution precipitates until the ion product falls to Ksp.
  • Excess silver, trace chloridePredict the final ion concentrations when a precipitate forms with one ion in large excess.

Classificar 5

Ksp and molar solubility

  • Ksp of iron(III) hydroxideWrite the solubility-product expression of a metal hydroxide whose formula contains three hydroxide ions.
  • Ksp of silver phosphate in terms of sExpress Ksp of a 3:1 salt in terms of its molar solubility.

Common-ion effect

  • Which liquid lowers the solubility of PbI₂?Identify which added substance lowers the molar solubility of a salt through a common ion.

Predicting precipitation

  • Unsaturated, saturated or supersaturated?Classify a solution as unsaturated, saturated or supersaturated by comparing Q with Ksp.

pH and solubility

  • A salt that ignores the pHClassify a salt as pH-insensitive when its anion is the conjugate base of a strong acid.

Comparar 6

Comparing solubilities

  • Rank five salts of different formula typesRank 1:1, 1:2, 2:1 and 3:2 salts by molar solubility after converting each Ksp to s.
  • Rank four sulfates by molar solubilityRank 1:1 salts by molar solubility using Ksp directly.
  • Smaller Ksp, more soluble?Compare a 1:1 salt and a 2:1 salt by converting each Ksp to molar solubility.
  • The least soluble silver halideCompare the molar solubilities of salts with the same formula type directly from their Ksp values.

Common-ion effect

  • AgCl in four liquidsRank the solubility of a salt in solutions with different common-ion concentrations, counting ions per formula unit.
  • Which common ion suppresses Ag₂CrO₄ more?Compare the common-ion effect of the squared ion and the first-power ion on a 2:1 salt.

Calcular 12

Common-ion effect

  • BaSO₄ in a sulfate solutionCalculate the molar solubility of a 1:1 salt in a solution of its anion.
  • PbCl₂ in dilute NaCl: when the shortcut failsSolve a common-ion problem exactly when the salt's own ions are not negligible beside the common ion.

Ksp and molar solubility

  • Molar solubility of BaSO₄Calculate the molar solubility of a 1:1 salt from its Ksp.
  • Molar solubility of Ca₃(PO₄)₂Calculate the molar solubility of a 3:2 salt from its Ksp using Ksp = 108s⁵.
  • Iodide in saturated PbI₂Calculate the concentration of the anion in a saturated solution of a 1:2 salt.

pH and solubility

  • CaF₂ at pH 2.00Calculate the solubility of a salt with a weakly basic anion at a fixed pH using the fraction of anion left unprotonated.
  • pH of saturated limewaterCalculate the pH of a saturated metal hydroxide solution from its Ksp.
  • Mg(OH)₂ in a pH 10 bufferCalculate the solubility of a metal hydroxide at a fixed pH from Ksp and Kw.

Predicting precipitation

  • Chloride left after precipitationCalculate the concentration of the minor ion remaining after a precipitation with one reagent in excess.
  • Q for lead(II) iodide after mixingCalculate the ion product after mixing unequal volumes and compare it with Ksp.
  • pH at which Mg(OH)₂ starts to precipitateFind the pH at which a metal hydroxide begins to precipitate from Q = Ksp.

Comparing solubilities

  • Same Ksp, different solubilityQuantify how much the formula type changes molar solubility for two salts with equal Ksp.

Encontre o erro 3

Common-ion effect

  • Find the error in a common-ion calculationDiagnose a common-ion calculation that forgets the stoichiometric factor on the ion released twice.

Predicting precipitation

  • A precipitation prediction gone wrongDiagnose the misuse of a dissolution stoichiometric factor when computing Q from ions supplied by soluble reagents.

Ksp and molar solubility

  • Where did the silver chromate calculation go wrong?Diagnose the use of the 1:1 square-root formula for a salt that releases three ions.

Interprete as evidências 2

Ksp and molar solubility

  • Ksp of PbCl₂ from a chloride analysisDeduce Ksp of a 1:2 salt from the measured concentration of one of its ions in a saturated solution.

pH and solubility

  • Reading solubility–pH dataInterpret how the solubilities of two salts vary with pH to decide which anion is basic.

Trabalhe de trás para frente 2

Ksp and molar solubility

  • Ksp of Mg(OH)₂ from a pH readingWork back from the pH of a saturated metal hydroxide solution to its Ksp.
  • Ksp of Ag₂CrO₄ from its mass solubilityWork back from a mass solubility in g/L to Ksp for a 2:1 salt.

Planeje uma síntese 1

  • Removing limescaleChoose a reagent that dissolves a carbonate deposit by protonating its basic anion.

Explique por quê 5

Ksp and molar solubility

  • Why barium sulfate is safe to swallowExplain from Ksp why a salt of a toxic ion can be safe when it is sparingly soluble and its anion is only very weakly basic.
  • What can change Ksp?Explain that Ksp depends only on temperature, not on the amounts of solid, water or common ions present.

pH and solubility

  • Why CaF₂ dissolves better in acidExplain how protonation of a basic anion increases the solubility of its salt.
  • Acid and tooth enamelExplain the dissolution of a mineral with basic anions when the pH falls.

Comparing solubilities

  • Why Ksp misleads across formula typesExplain why Ksp values rank solubility only for salts of the same formula type.

Travou em equilíbrios de solubilidade e Ksp? Escaneie o problema.

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