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.
2


MX2 (s)  M (aq)  2X (aq)
This process can be represented
by the solubility product
constant or Ksp expression.
2


MX2 (s)  M (aq)  2X (aq)
2

2
Ksp  [M ] [X ]
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!
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-]
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 + 2ClCalculate the Ksp if the lead ion
concentration has been found to be 1.62
x 10-2M.
PbCl2  Pb+2 + 2ClConsider 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
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. What is the molar
solubility of the salt?
Cu(IO3)2(s)
-s

Cu2+
+ 2 IO3-
+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)
-s

2 Ag+
+ CO3-2
+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
Ni(CN)2


2 Ag+ + S-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
BaCO3
Ksp = 8.1 X
10-12
Ag2CO3
BaF2
s=
3
Ksp
4
Ksp
3
Ksp
4
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 + CrO42add 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
(a) Water
(b) 0.015 M AgNO3
(c) 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
(a) Water
(b) 0.010 M KI
(c) 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 Inecessary to begin precipitation of
each salt.
Solution
CuI will precipitate first.
Concentration in excess of
5.3 X 10-8 M required.