Ksp and Solubility Equilibria

Saturated solutions of salts are another type of chemical equilibrium. Slightly soluble salts establish a dynamic equilibrium with the hydrated cations and anions in solution.

When the solid is first added to water, no ions are initially present. As dissociation continues, the concentration of aqueous ions increases until equilibrium is reached.

This process can be represented by the solubility product constant or Ksp expression.

Why would a change in temperature alter the value of Ksp? Even “insoluble” salts dissociate a little – their Ksp values range from 10-10 to 10-50. A Ksp value is unique to a given salt at a given temperature. Why would a change in temperature alter the value of Ksp?

Solubility mol/L g/L mg/L Solubility indicates the amount of salt that dissociates to form a saturated solution – think solubility curve! In essence, it indicates the equilibrium position for a given set of conditions. You can have different solubilities with the same Ksp.

What you’ll need to be able to do Write Ksp expresssions Calculate Ksp given solubility Calculate solubility given Ksp Compare solubilities of different salts

What you’ll need to be able to do Calculate the effect of a common ion or pH on solubility Determine if a precipitate will form given concentrations of ions and Ksp Determine the order of precipitation in a mixture of ions

Write Ksp expresssions Write the dissocation equation first! Write the Ksp expression – leaving out the solid Note: some of these have quite large exponents!

AgCl (s)  Ag+ (aq) + Cl- (aq) For a saturated solution of AgCl, the equation would be: AgCl (s)  Ag+ (aq) + Cl- (aq) The solubility product expression would be: Ksp = [Ag+] [Cl-]

Bi2S3 (s)  2 Bi+3 (aq) + 3S-2 (aq) For a saturated solution of Bi2S3, the equation would be: Bi2S3 (s)  2 Bi+3 (aq) + 3S-2 (aq) The solubility product expression would be: Ksp = [Bi+3]2 [S-2]3

Write Ksp expresssions NiCO3 NiCO3 (s)  Ni+2 (aq) + CO3-2 (aq) Ksp = [Ni+2] [CO3-2] Ag2SO4 Ag2SO4 (s)  2 Ag+ (aq) + SO4-2 (aq) Ksp = [Ag+]2 [SO4-2]

Calculate Ksp given solubility Example: Lead (II) chloride dissolves to a slight extent in water according to the equation: PbCl2  Pb+2 + 2Cl- Calculate the Ksp if the lead ion concentration has been found to be 1.62 x 10-2M.

PbCl2  Pb+2 + 2Cl- Consider the equation, if lead’s concentration is “x” , then chloride’s concentration is “2x”. So. . . . Ksp = [Pb+2] [Cl-]2 Ksp = (1.62 x 10-2)(3.24 x 10-2)2 = 1.70 x 10-5

Example: When silver sulfide dissolves at 25oC, the equilibrium concentration of silver ion is 5.8 x 10-17M. What is the Ksp of silver sulfide? Ag2S  2 Ag+ + S-2

So. . . . Ksp = [Ag+]2 [S-2] Ag2S  2 Ag+ + S-2 Sulfide ion concentration is only ½ of silver’s So. . . . Ksp = [Ag+]2 [S-2] Ksp = (5.8 x 10-17)2 (2.9 x 10-17) = 9.8 X 10-50

Copper(I) bromide has a measured solubility of 2.0 X 10-4 mol/L at 25°C. Calculate its Ksp value. Ksp = 4.0 X 10-8

Calculate the Ksp value for bismuth sulfide (Bi2S3), which has a solubility of 1.0 X 10-15 mol/L at 25°C. Ksp = 1.1 X 10-73

Calculate solubility given Ksp Write the dissociation equation Use the equation to consider the amount of ions given that s of the solid dissociates Write the Ksp expression and substitute your s values and solve Pay attention to freaky powers and roots!

Copper(II) iodate has a Ksp of 1. 4 X 10-7 @ 20oC Copper(II) iodate has a Ksp of 1.4 X 10-7 @ 20oC. What is the molar solubility of the salt? Cu(IO3)2(s)  Cu2+ + 2 IO3- -s +s +2s Ksp = [Cu+2] [IO3-]2 = (s) (2s)2 = 4s3 Ksp = 1.4 X 10-7 = 4s3 s = 3.3 X 10-3 M

In a saturated solution of silver carbonate, what is the molar solubility of the salt? Ksp = 8.1 X 10-12 Ag2CO3(s)  2 Ag+ + CO3-2 -s +2s +s Ksp = [Ag+]2 [CO3-2] = (2s)2 (s) = 4s3 Ksp = 8.1 X 10-12 = 4s3 s = 1.3 X 10-4 M

Calculate solubility given Ksp The Ksp for CaCO3 is 3.8 x 10-9 @ 25°C. Calculate the solubility of calcium carbonate in pure water in a) moles per liter b) grams per liter

Comparing Solubilities The relative solubilities can be deduced by comparing values of Ksp. BUT, BE CAREFUL! These comparisons can only be made for salts having the same ION:ION ratio.

Comparing Solubilities Which salt is more soluble? Ag2S Ksp = 1.0 X 10-49 Ni(CN)2 Ksp = 3.0 X 10-23 Ag2S  2 Ag+ + S-2 Ni(CN)2  Ni+2 + 2 CN- Since both make 3 ions (4s3) – the larger Ksp is the more soluble salt - Ni(CN)2!

Comparing Solubilities Which salt is more soluble? PbCl2 Ksp = 1.6 X 10-5 PbBr2 Ksp = 4.6 X 10-6 PbI2 Ksp = 1.4 X 10-8

Comparing Solubilities Rank the following in order of increasing solubility: BaF2 Ksp = 1.7 X 10-6 BaCO3 Ksp = 8.1 X 10-9 Ag2CO3 Ksp = 8.1 X 10-12

Comparing Solubilities Rank the following in order of increasing solubility: BaF2 Ksp = 1.7 X 10-6 s = BaCO3 Ksp = 8.1 X 10-9 s = Ag2CO3 Ksp = 8.1 X 10-12 s= BaCO3 Ag2CO3 BaF2

Calculate the effect of a common ion on pH or solubility Introduction of a common ion causes salts to become less soluble – think Le Chatelier’s Principle PbCrO4  Pb+2 + CrO42- add K2CrO4 - shift left

Calculate the effect of a common ion on pH or solubility The pH of a solution can also affect solubility if H+ or OH- can interact with the salt’s ions

Calculate the effect of a common ion on pH or solubility How will the solubility of calcium carbonate be affected if it is dissolved in a solution of calcium chloride? presence of Ca2+ ions will shift equilibrium position to left – CaCO3 will be less soluble How will the solubility of silver phosphate be affected by an decrease in pH? H+ react with PO43- thus causing a shift right and increasing solubility

Calculate the effect of a common ion on pH or solubility Would magnesium hydroxide (milk of magnesia) be more soluble in an acid or a base? Why? Mg(OH)2(s)  Mg2+(aq) + 2 OH-(aq)

Calculate the effect of a common ion on pH or solubility How will the solubility of magnesium hydroxide be affected by an increase in pH? more OH- will cause shift left – decrease sol. How will the solubility of magnesium hydroxide be affected by an decrease in pH? H+ will react with OH- cause shift right – increase sol.

Calculate the effect of a common ion on pH or solubility Calculate the molar solubility of silver chromate (Ksp = 9.0 X 10-12) in Water 0.015 M AgNO3 0.015 M K2CrO4

Calculate the effect of a common ion on pH or solubility Calculate the molar solubility of lead(II) iodide (Ksp = 1.0 X 10-8) in Water 0.010 M KI 0.020 M Pb(NO3)2

Calculate the effect of a common ion on pH or solubility Calculate the solubility of solid CaF2 (Ksp = 4.0 X 10-11) in a 0.025 M NaF solution. Solution = 6.4 X 10-8 mol/L

Determine if a precipitate will form With some knowledge of the reaction quotient (Q), we can decide 1) whether a ppt will form, AND

Determine if a precipitate will form With some knowledge of the reaction quotient (Q), we can decide 1) whether a ppt will form, AND 2) what concentrations of ions are required to begin the ppt. of an insoluble salt.

Determine if a precipitate will form 1. Q = Ksp, the system is at equil. (saturated) 2. Q < Ksp, the system is not at equil. (unsaturated – shift right) 3. Q > Ksp, the system is not at equil. (supersaturated – shift left)

Determine if a precipitate will form Precipitates form when the solution is supersaturated!

Determine if a precipitate will form Substitute molarities into Q Compare Q to Ksp If precipitation occurs, consider the stoichiometry and limiting reactant Readjust to equilibrium Look at sample 15.16 on P. 766

Determining Precipitation Conditions A solution is prepared by adding 750.0 mL of 4.00 X 10-3 M Ce(NO3)3 to 300.0 mL of 2.00 X 10-2 M KIO3. Will Ce(IO3)3 (Ksp = 1.9 X 10-10) precipitate from this solution? Yes!

A solution is prepared by mixing 150.0 mL of 1.00 X 10-2 M Mg(NO3)2 and 250.0 mL of 1.00 X 10-1 M NaF. Calculate the concentrations of Mg2+ and F- at equilibrium with solid MgF2 (Ksp = 6.4 X 10-9).

Solution [Mg2+] = 2.1 X 10-6 M [F-] = 5.50 X 10-2 M

Why Would I Ever Care About Ksp ??? Keep reading to find out ! Actually, very useful stuff!

Solubility, Ion Separations, and Qualitative Analysis …introduce you to some basic chemistry of various ions. …illustrate how the principles of chemical equilibria can be applied.

Selective Precipitation A solution of 0.10 M potassium carbonate was added to a mixture of barium and silver ions. Which precipitate will form first? BaCO3 Ksp = 8.1 X 10-9 Ag2CO3 Ksp = 8.1 X 10-12

Separate the following metal ions: silver, lead, cadmium and nickel

From solubility rules, lead and silver chloride will ppt, so add dilute HCl. Nickel and cadmium will stay in solution.

Separate by filtration: Lead chloride will dissolve in HOT water… filter while HOT and those two will be separate.

Cadmium and nickel are more subtle. Use their Ksp’s with sulfide ion. Who ppt’s first???

Precipitation of Insoluble Salts Metal-bearing ores often contain the metal in the form of an insoluble salt, and, to complicate matters, the ores often contain several such metal salts.

Precipitation of Insoluble Salts Dissolve the metal salts to obtain the metal ion, concentrate in some manner, and ppt. selectively only one type of metal ion as an insoluble salt.

Selective Precipitation A solution contains 1.0 X 10-4 M Cu+ and 2.0 X 10-3 M Pb2+. If a source of I- is added gradually to this solution, will PbI2 (Ksp = 1.4 X 10-8) or CuI (Ksp = 5.3 X 10-12) precipitate first?

Specify the concentration of I- necessary to begin precipitation of each salt.

Solution CuI will precipitate first. Concentration in excess of 5.3 X 10-8 M required.