Chem Equil Homework Ksp Key

Ksp Problems - Set I 1. Write an equilibrium reaction representing each of the following saturated solutions: (a) barium fluoride BaF₂(s) ⇌ Ba²⁺(aq) + 2F⁻(aq) (b) magnesium hydroxide Mg(OH)₂(s) ⇌ Mg²⁺(aq) + 2OH⁻(aq) 2. Write the solubility product expression (Ksp) for the ionic compound AxBy. AxBy(s) ⇌ xAʸ⁺(aq) + yBˣ⁻(aq) Ksp = [Aʸ⁺]^x * [Bˣ⁻]^y 3. What is meant by the term molar solubility (s)? The molar solubility of a solution is the molarity of a solution when a solid has dissolved as much as it can. 4. Calculate the concentration of ions in the following saturated solutions: (a) [I⁻] in AgI with [Ag⁺] = 9.1 x 10⁻⁹ M. The Ksp of AgI is 8.3 x 10⁻¹⁷. [I⁻] = 9.1 x 10⁻⁹ M (b) [Al³⁺] in Al(OH)₃ with [OH⁻] = 2.9 x 10⁻⁹ M. (answer [Al³⁺] = 9.7 x 10⁻¹⁰ M) Al(OH)₃ ⇌ Al³⁺ + 3OH⁻ [Al³⁺] = (1/3)[OH⁻] = (1/3)(2.9 x 10⁻⁹) = 9.7 x 10⁻¹⁰ M 5. The molar solubility of Zn(OH)₂ is 1.67 x 10⁻⁵ M. What is its Ksp value? Start by writing an equilibrium equation that represents a saturated solution of zinc hydroxide. (1.88 x 10⁻¹⁵) Zn(OH)₂ ⇌ Zn²⁺ + 2OH⁻ Ksp = [Zn²⁺][OH⁻]² = (1.67 x 10⁻⁵)(3.34 x 10⁻⁵)² = 1.88 x 10⁻¹⁵ 6. If a saturated solution of zinc hydroxide has [OH⁻] = 0.02 M, what is the concentration of the zinc ion? (4.65 x 10⁻¹⁰ M) Zn(OH)₂ ⇌ Zn²⁺ + 2OH⁻ Ksp = [Zn²⁺][OH⁻]² 1.88 x 10⁻¹⁵ = [Zn²⁺](0.02)² [Zn²⁺] = 4.65 x 10⁻¹⁰ M 7. The molar solubility of calcium carbonate (CaCO₃) in pure water is 6.9 x 10⁻⁵ M. What is the Ksp? (4.8 x 10⁻⁹) CaCO₃ ⇌ Ca²⁺ + CO₃²⁻ Ksp = [Ca²⁺][CO₃²⁻] = (6.9 x 10⁻⁵)² = 4.8 x 10⁻⁹ 8. If [Pb²⁺] = 0.0012 M in a saturated solution of lead(II) iodide, calculate the Ksp. (6.9 x 10⁻⁹) PbI₂ ⇌ Pb²⁺ + 2I⁻ Ksp = [Pb²⁺][I⁻]² Ksp = (0.0012)(0.0024)² = 6.912 x 10⁻⁹ ≈ 6.9 x 10⁻⁹ 9. Given that the Ksp of silver chloride (AgCl) is 1.7 x 10⁻¹⁰, calculate its molar solubility in pure water. (1.3 x 10⁻⁵ M) AgCl ⇌ Ag⁺ + Cl⁻ Ksp = [Ag⁺][Cl⁻] 1.7 x 10⁻¹⁰ = (x)(x) x ≈ 1.3 x 10⁻⁵ M 10. Lead(II) chloride (PbCl₂), with a Ksp of 1.6 x 10⁻⁵, is among the more soluble of the salts considered "insoluble". What is its molar solubility in pure water? (0.016 M) PbCl₂ ⇌ Pb²⁺ + 2Cl⁻ Ksp = [Pb²⁺][Cl⁻]² 1.6 x 10⁻⁵ = x(2x)² 1.6 x 10⁻⁵ = 4x³ x ≈ 0.016 M 11. The molar solubility (s) of silver sulfide, Ag₂S, is 1.14 x 10⁻¹⁷ mol/L. What is the Ksp of Ag₂S? (5.9 x 10⁻⁵¹) Ag₂S ⇌ 2Ag⁺ + S²⁻ Ksp = [Ag⁺]²[S²⁻] Ksp = (2.28 x 10⁻¹⁷)²(1.14 x 10⁻¹⁷) = 5.9 x 10⁻⁵¹ 12. 100 liters of saturated cadmium sulfide, CdS, is evaporated to dryness. How many grams of solid CdS can be recovered upon evaporation? The Ksp of CdS is 8.0 x 10⁻²⁸. (4.09 x 10⁻¹⁰ g) CdS ⇌ Cd²⁺ + S²⁻ Ksp = [Cd²⁺][S²⁻] 8.0 x 10⁻²⁸ = x² x = 2.83 x 10⁻¹⁴ mol/L (100 L)(2.83 x 10⁻¹⁴ mol/L)(144.48 g/mol) = 4.09 x 10⁻¹⁰ g 13. The solubility of an ionic compound M₂X₃ (molar mass = 288 g/mol) is 3.6 x 10⁻¹⁷ g/L. What is the Ksp for the compound? (3.3 x 10⁻⁹³) 3.6 x 10⁻¹⁷ g/L / 288 g/mol = 1.25 x 10⁻¹⁹ M Ksp = [M³⁺]²[X³⁻]³ = (2.5 x 10⁻¹⁹)²(3.75 x 10⁻¹⁹)³ ≈ 3.30 x 10⁻⁹³ Ksp Problems - Set II - predicting precipitation 1. How can we predict whether a precipitate will form when two aqueous ionic solutions are mixed? If IP > Ksp, a precipitate will form. If IP < Ksp, it will continue to dissolve (no precipitate). 2. The Ksp of silver chloride (AgCl) is 1.7 x 10⁻¹⁰. If 60 mL of 0.002M NaCl are added to 40 mL of 3.0 x 10⁻⁵M AgNO₃: a) What is [Ag⁺]? 3.0 x 10⁻⁵ M (0.04 L) = 1.2 x 10⁻⁶ mol / 0.1 L = 1.2 x 10⁻⁵ M b) What is [Cl⁻]? 0.002 M (0.06 L) = 1.2 x 10⁻⁴ mol / 0.1 L = 1.2 x 10⁻³ M c) Will a precipitate form? (yes, IP > Ksp) IP = [Ag⁺][Cl⁻] = (1.2 x 10⁻⁵)(1.2 x 10⁻³) = 1.4 x 10⁻⁸ IP > Ksp so yes, precipitate will form. 3. Will lead(II) chloride (PbCl₂), with a Ksp of 1.6 x 10⁻⁵, precipitate if 15 mL of 0.0003M Pb(NO₃)₂ are combined with 25 mL of 0.04M CaCl₂? a) What is [Pb²⁺]? 0.0003 M (0.015 L) = 0.0000045 mol / 0.04 L = 0.000113 M b) What is [Cl⁻]? CaCl₂ → Ca²⁺ + 2Cl⁻ 0.04 M (0.025 L) = 0.001 mol / 0.04 L = 0.05 M c) Will a precipitate form? (no, IP < Ksp) IP = [Pb²⁺][Cl⁻]² = (0.000113)(0.05)² = 2.83 x 10⁻⁷ No, IP < Ksp. 4. A sample of 20 ml of 0.10 M Ba²⁺ is added to 50 ml of 0.10 M CO₃²⁻. Will BaCO₃ solid form? The Ksp of BaCO₃ is 8.1 x 10⁻⁹. a) What is [Ba²⁺]? (1 M)(0.02 L) = 0.02 mol / 0.07 L = 0.029 M b) What is [CO₃²⁻]? (1 M)(0.05 L) = 0.05 mol / 0.07 L = 0.071 M c) Will a precipitate form? (ans: IP = 2.04 x 10⁻⁴ > Ksp, a solid will form) IP = (0.029)(0.071) = 0.0021 Yes, IP > Ksp 5. Exactly 200 ml of 0.004 M BaCl₂ are added to exactly 600 ml of 0.008 M K₂SO₄. Will a precipitate form? The Ksp of BaSO₄ is 1.1 x 10⁻¹⁰. Start by writing an equilibrium reaction. a) What is [Ba²⁺]? (0.004 M)(0.2 L) = 0.0008 mol / 0.8 L = 0.001 M b) What is [SO₄²⁻]? (0.008 M)(0.6 L) = 0.0048 mol / 0.8 L = 0.006 M c) Will a precipitate form? (answer: IP = 6.0 x 10⁻⁶ > Ksp, a ppt forms) IP = (0.001 M)(0.006 M) = 6.0 x 10⁻⁶ Yes, IP > Ksp 6. If 2.00 mL of 0.20 M NaOH are added to 1.00 L of 0.10 M CaCl₂, will precipitation occur? The Ksp of Ca(OH)₂ is 8.0 x 10⁻⁶. a) What is [OH⁻]? (0.2 M)(0.002 L) = 0.0004 mol / 1.002 L ≈ 0.0004 M b) What is [Ca²⁺]? (0.1 M)(1 L) = 0.1 mol / 1.002 L ≈ 0.0998 M c) Will a precipitate form? (answer: IP = 1.59 x 10⁻⁸ < Ksp, no ppt) IP = [Ca²⁺][OH⁻]² = (0.0998)(0.0004)² = 1.6 x 10⁻⁸ No, IP < Ksp