Solubility Product Constant, Ksp

Solubility is the maximum amount of solute in a solvent at a given temperature saturated solution, [ ]max equilibrium between: solid crystals  dissolved ions eg. AgNO3(s)  Ag1+(aq) + NO31-(aq)

1st 1st - H2O needs to separate - H-bonding needs to be overcome - dissolving - NRG input

3rd 2nd 3rd 2nd - H2O removes ions from the lattice - dissociation - NRG input 2nd 3rd - hydration of ions - Ion – dipole force 3rd - NRG output -  with  H2O

• solubility is a contest between: • ionic bond strengths vs ion-dipole forces • lattice energies vs hydration energies • usually exothermic with increased disorder • if undissolved solid is present, then it is a mixture with a saturated sol’n phase

Solubility Product Constant, Ksp: equilibrium expression for slightly soluble salts If: AxBy(s)  xAm+(aq) + yBn-(aq) Then:

Saturation can be tested by Q: If: Q = Ksp then it is a saturated solution Q > Ksp there is noticeable precipitate Q < Ksp unsaturated Terminology: refers to the amount of solid that can dissolve not how much is in solution solubility units are g/100g or g/100 mL or g/L

To find molar solubility from solubility: (concentration) [ ]max = solubility ÷ Msolute x V adjustment or 1/ Msolute eg. Solubility of Mg(OH)2 is 3.45 g/100 mL.

To find solubility from molar solubility: (concentration) Solubility = molar solubility x Msolute x V adjustment eg. Molar solubility of Mg(OH)2 is 0.591 mol/L. Do not divide by 100 mL

1st - calculate the [ ] from solubility: 1) Ksp from solubility eg. Calculate the Ksp of Ag2CO3 given its solubility of 0.0014 g/100g. 1st - calculate the [ ] from solubility: 2nd - create ICE table. - Since dealing with a solid, the equilibrium is simplified

Ag2CO3 ↔ 2 Ag+ + CO32- ; Q – not necessary 100 Rule – not necessary

2) Solubility from Ksp types: solubility, molar solubility, [ion]eq, amount of solid that will dissolve - all from calculating “x” eg. How much PbI2 at SATP will dissolve in 1.00 L of water? Give the solute ion concentration, [Pb2+]eq, solubility (g/100mL) and molar solubility. - when not given the Ksp and not asked to calculate it, find it in the reference table or the textbook Ksp of PbI2 from textbook is 8.5 x 10-9

PbI2 ↔ Pb2+ + 2 I1- ; ICE +x +2x = the molar solubility - as the solid is not included and the [ion]i = 0, we can write ICE horizontally instead of vertically PbI2 ↔ Pb2+ + 2 I1- ; ICE +x +2x = the molar solubility

Predicting Precipitation: Don’t  by 100 - it is a unit 100 mL Predicting Precipitation: • Used to determine precipitation when mixing 2 sol’ns just like in double displacement rxns

eg. Will precipitation occur when 5. 0 ml of 0 eg. Will precipitation occur when 5.0 ml of 0.030 M AgNO3 is mixed with 1.0 ml of 0.0050 M Na2CrO4? (Ksp = 1.1 x 10-12 for Ag2CrO4)? 1st – write down each reaction and calculate the V and C values

3rd – calculate Q and compare with Ksp 2nd – write down the equilibrium equation, calculate the new [ ] in the combined sol’n Ag2CrO4 ↔ 2 Ag+ + CrO42- ; 3rd – calculate Q and compare with Ksp

eg. Will 0. 10 mg of Ba(OH)2 added to 75 mL of 2 eg. Will 0.10 mg of Ba(OH)2 added to 75 mL of 2.0 x 10-3 M AgNO3 solution form a precipitate? (Ksp (AgOH) = 1.5 x 10-17)? Ba(OH)2  Ba2+ + 2 OH-   = 1.17 x 10-6 mol C = 2.0 x 10-3 M V = 0.075 L

AgOH ↔ Ag+ + 2 OH- ; C = 2.0 x 10-3 M = 1.56 x 10-5 M Ksp = [Ag+][OH-] = 1.5 x 10-17 C = 2.0 x 10-3 M     = 1.56 x 10-5 M Q = (2.0 x 10-3)(1.56 x 10-5) = 3.1 x 10-8 M Q (3.1 x 10-8) > Ksp (1.5 x 10-17)