1. Ksp and Solubility Equilibria

2. 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.

3. 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.

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

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

6. 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.

7. 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

8. 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

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

10. 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-]

11. 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

12. 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]

13. 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 x 10-2M.

14. 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

15. 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

16. 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

17. 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

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

19. 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!

20. Copper(II) iodate has a Ksp of 1. 4 X 10-7 @ 20oC
Copper(II) iodate has a Ksp of 1.4 X 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

21. 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 = 4s3
s = 1.3 X 10-4 M

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

23. 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.

24. 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 CN-
Since both make 3 ions (4s3) – the larger Ksp is the more soluble salt - Ni(CN)2!

25. 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

26. 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

27. Comparing Solubilities
Rank the following in order of increasing solubility:
BaF2 Ksp = 1.7 X s =
BaCO3 Ksp = 8.1 X s =
Ag2CO3 Ksp = 8.1 X s=
BaCO3 Ag2CO3 BaF2

28. 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

29. 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

30. 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

31. 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) OH-(aq)

32. 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.

33. 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

34. 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

35. 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 M NaF solution.
Solution = 6.4 X 10-8 mol/L

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

37. 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.

38. 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)

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

40. 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 on P. 766

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

42. A solution is prepared by mixing
150.0 mL of 1.00 X 10-2 M Mg(NO3)2
and 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).

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

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

45. 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.

46. 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

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

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

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

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

53. 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.

54. 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.

55. 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?

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

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