Ksp and Solubility Equilibria

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Ksp and Solubility Equilibria
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• 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.

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• 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.

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This process can be represented by the solubility
product constant or Ksp expression.
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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?
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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.
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What youll need to be able to do

• Write Ksp expresssions
• Calculate Ksp given solubility
• Calculate solubility given Ksp
• Compare solubilities of different salts

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What youll 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

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Write Ksp expresssions

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

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• 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-

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• For a saturated solution of
• Bi2S3, the equation would be
• Bi2S3 (s) ? 2 Bi3 (aq) 3S-2 (aq)

• The solubility product expression
• would be
• Ksp Bi32 S-23

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Write Ksp expresssions

• NiCO3
• NiCO3 (s) ? Ni2 (aq) CO3-2 (aq)
• Ksp Ni2 CO3-2
• Ag2SO4
• Ag2SO4 (s) ? 2 Ag (aq) SO4-2 (aq)
• Ksp Ag2 SO4-2

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Calculate Ksp given solubility
Example Lead (II) chloride dissolves to a
slight extent in water according to the
equation PbCl2 ? Pb2
2Cl- Calculate the Ksp if the lead ion
concentration has been found to be 1.62 x
10-2M.
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PbCl2 ? Pb2 2Cl-

• Consider the equation, if leads concentration is
  x , then chlorides concentration is 2x.
• So. . . . Ksp Pb2 Cl-2
• Ksp (1.62 x 10-2)(3.24 x 10-2)2
• 1.70 x 10-5

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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
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Ag2S ? 2 Ag S-2 Sulfide ion
concentration is only ½ of silvers So. . . .
Ksp Ag2 S-2 Ksp (5.8 x 10-17)2 (2.9 x
10-17) 9.8 X 10-50
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• Copper(I) bromide has a measured
• solubility of 2.0 X 10-4 mol/L at
• 25C. Calculate its Ksp value.
• Ksp 4.0 X 10-8

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

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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!

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Copper(II) iodate has a Ksp of 1.4 X 10-7 _at_
20oC. What is the molar solubility of the salt?
Cu(IO3)2(s) ? Cu2 2 IO3-
-s s 2s
Ksp Cu2 IO3-2 (s) (2s)2 4s3Ksp 1.4
X 10-7 4s3 s 3.3 X 10-3 M
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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 Ag2 CO3-2 (2s)2 (s) 4s3Ksp
8.1 X 10-12 4s3 s 1.3 X 10-4 M
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Calculate solubility given Ksp

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

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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
• IONION ratio.

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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-2Ni(CN)2 ? Ni2 2 CN- Since both make 3
ions (4s3) the larger Ksp is the more soluble
salt - Ni(CN)2!
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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
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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
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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
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Calculate the effect of a common ion on pH or
solubility
Introduction of a common ion causes salts to
become less soluble think Le Chateliers
Principle
PbCrO4 ? Pb2 CrO42-add K2CrO4 - shift left
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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 salts ions
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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
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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)

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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.
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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

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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

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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

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Determine if a precipitate will form

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

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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.

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Determine if a precipitate will form

• 1. Q Ksp, the system is at equil. (saturated)
• 2. Q lt Ksp, the system is not at equil.
  (unsaturated shift right)
• 3. Q gt Ksp, the system is not at equil.
  (supersaturated shift left)

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Determine if a precipitate will form

• Precipitates
• form when the
• solution is supersaturated!

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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

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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!

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• 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).

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Solution

• Mg2 2.1 X 10-6 M
• F- 5.50 X 10-2 M

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Why Would I Ever Care About Ksp ???

• Keep reading to find out !
• Actually, very useful stuff!

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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.

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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

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

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

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

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• Cadmium and nickel are more
• subtle.
• Use their Ksps with sulfide ion.
• Who ppts first???

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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.

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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.

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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?

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

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Solution

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