Weak acids and bases, Kw, pH and the solubility product
الأسبوع 14 · الباب الثالث (٥): تركيز أيوني الهيدرونيوم والهيدروكسيل للأحماض والقواعد الضعيفة وتأين الماء وحاصل الضرب الأيوني Kw وpH وpOH والذوبانية وحاصل الإذابة Ksp (أثقل أسبوع: ثلاثة دروس حسابية) · 3 دروس
3
Solubility and the solubility product
Chemistry Sec 3 Term 1, Chapter 3: pp. 71–77
GoalSay what a saturated solution is, write Ksp for a sparingly soluble salt, and convert between solubility and Ksp.
New words
saturated solution · a solution that holds the most solute it can at a given temperature, in equilibrium with the undissolved solidsolubility s · the concentration of the saturated solution, in mol/L (multiply by the molar mass for g/L)solubility product Ksp · the product of the ion concentrations, each raised to its coefficient, in a saturated solution
Explanation
At a fixed temperature a solid dissolves only up to a limit. At the limit the solution is saturated: some solid stays at the bottom and the dissolving and the crystallising go on at equal rates, a dynamic equilibrium. The solubility s is the concentration of the saturated solution, here in mol/L; multiply by the molar mass to get g/L. Salts differ greatly: potassium nitrate is very soluble, while PbBr₂ and CaF₂ are only sparingly soluble. For a sparingly soluble salt the law of mass action applies to the dissolving, for example CaF₂(s) ⇌ Ca²⁺ + 2F⁻, and the solid is left out, so Ksp = [Ca²⁺][F⁻]². In general Ksp is the product of the ion concentrations, each raised to its coefficient in the equation. Ksp is the standard name, because a solid is left out. For a salt AB, s mol/L gives [A⁺] = [B⁻] = s, so Ksp = s². For a salt AB₂, [A²⁺] = s but [B⁻] = 2s, so Ksp = s × (2s)² = 4s³. Watch three slips: mol/L against g/L, the factor 2s, and the solid appearing in Ksp.
Salt type
Dissolving
[A] and [B]
Ksp
AB
AB(s) ⇌ A⁺ + B⁻
s , s
s²
AB₂ (CaF₂)
CaF₂(s) ⇌ Ca²⁺ + 2F⁻
s , 2s
4s³
Worked examples
ƒSalt of type AB
Ksp = s² = (1.0 × 10⁻⁶)² = 1.0 × 10⁻¹²
A salt AB. An invented salt AB has a solubility s = 1.0 × 10⁻⁶ mol/L. Then [A⁺] = [B⁻] = 1.0 × 10⁻⁶, so Ksp = [A⁺][B⁻] = (1.0 × 10⁻⁶)² = 1.0 × 10⁻¹².
Ion
Concentration
Ca²⁺
s = 2.0 × 10⁻⁴ mol/L
F⁻
2s = 4.0 × 10⁻⁴ mol/L
A salt AB₂: CaF₂ with s = 2.0 × 10⁻⁴ mol/L. [Ca²⁺] = 2.0 × 10⁻⁴ and [F⁻] = 2 × 2.0 × 10⁻⁴ = 4.0 × 10⁻⁴. Ksp = [Ca²⁺][F⁻]² = 2.0 × 10⁻⁴ × (4.0 × 10⁻⁴)² = 2.0 × 10⁻⁴ × 1.6 × 10⁻⁷ = 3.2 × 10⁻¹¹. The short way gives the same: 4s³ = 4 × 8.0 × 10⁻¹² = 3.2 × 10⁻¹¹.
From Ksp to s, and to g/L. For CaF₂ with Ksp = 3.2 × 10⁻¹¹: 4s³ = 3.2 × 10⁻¹¹, so s³ = 8.0 × 10⁻¹² and s = 2.0 × 10⁻⁴ mol/L (because 2³ = 8 and (10⁻⁴)³ = 10⁻¹²). With Ca = 40 and F = 19, M(CaF₂) = 40 + 2 × 19 = 78 g/mol, so the solubility is 2.0 × 10⁻⁴ × 78 = 0.0156 g/L. Never mix the units: s is in mol/L inside Ksp, and g/L only at the end.
Class activity
How much salt dissolves, with a grown-up. Fill a clear cup with cool tap water. Stir in table salt one level teaspoon at a time, stirring well each time, and count the spoons. When some salt stays at the bottom however long you stir, the water is saturated: the extra stays solid. Do not drink it. Write the count, and say what you think happens at the bottom: dissolving and crystallising at the same speed. Table salt is much more soluble than the sparingly soluble salts of this lesson, so it only shows the idea of a saturated solution.
Practice
1
An invented salt AB has s = 3.0 × 10⁻⁵ mol/L. Find Ksp.
Ksp = s² = (3.0 × 10⁻⁵)² = 9.0 × 10⁻¹⁰.
2
An invented salt AB₂ has s = 1.0 × 10⁻⁴ mol/L. Find Ksp.
