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20Ionic Equilibria III:

The SolubilityProduct Principle



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Chapter Goals

1. Solubility Product Constants

2. Determination of Solubility ProductConstants

3. Uses of Solubility Product Constants

4. Fractional Precipitation



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Solubility Product Constants

• Silver chloride, AgCl,is rather insoluble in water.

• Careful experiments show that if solid AgCl is

placed in pure water and vigorously stirred, a

small amount of the AgCl dissolves in the water.

aqaq ClAgClAg



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• The equilibrium constant expression for this

dissolution is called a solubility product constant.

– Ksp = solubility product constant

-10-

sp 101.8]][Cl[AgK



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• The solubility product constant, Ksp, for a

compound is the product of the concentrations of

the constituent ions, each raised to the power

that corresponds to the number of ions in oneformula unit of the compound.

• Consider the dissolution of silver sulfide in water.

Ag S 2 Ag + S2+ 2- H O + 2-2

100%



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• The solubility product expression for Ag2S is:

K Ag Ssp2 2

10 10 49.



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• The dissolution of solid calcium phosphate in

water is represented as:

22+ 3 2 3

3 4 ( ) 4 ( )2 s100Ca PO 3 Ca 2 POo

H O

aq aqC

The solubility product constant expression is:

You do it!

K Ca POsp2 3

43 2

1 0 10 25

.



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• In general, the dissolution of a slightly solublecompound and its solubility product expressionare represented as:

2s r

r s s100

r ss r

sp

M Y r M s Y

K M Y

o

H O

C



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• The same rules apply for compounds that have

more than two kinds of ions.

• One example of a compound that has more than

two kinds of ions is calcium ammoniumphosphate.

3

44

2

sp

3

aq4

1

aq4

2

aqs44

PO NHCaK

PO NHCaPOCaNH



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Determination of Solubility

Product Constants• The equation for the dissociation of silver

chloride, the appropriate molar concentrations,

and the solubility product expression are:

AgCl Ag Cl

1.34 10 1.34 10K Ag Cl

s

-5 -5

sp

M M



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Product Constants• Substitution of the molar concentrations into the

solubility product expression gives:

K Ag Clsp

134 10 134 10

18 10

5 5

10

. .

.



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Product ConstantsExample 20-2: One liter of saturated calcium

fluoride solution contains 0.0167 gram of CaF2 at

25oC. Calculate the molar solubility of, and Ksp for,

CaF2.



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Uses of Solubility

Product Constants• The solubility product constant can be used to

calculate the solubility of a compound at 25oC.



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Uses of Solubility

Product ConstantsExample 20-3: Calculate the molar solubility of

barium sulfate, BaSO4, in pure water and the

concentration of barium and sulfate ions in

saturated barium sulfate at 25o

C. For bariumsulfate, Ksp= 1.1 x 10-10.



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Uses of Solubility

Product ConstantsExample 20-4: The solubility product constant for

magnesium hydroxide, Mg(OH)2, is 1.5 x 10-11.

Calculate the molar solubility of magnesium

hydroxide and the pH of a saturated magnesiumhydroxide solution at 25oC.

You do i t !



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The Common Ion Effect in

Solubility CalculationsExample 20-5: Calculate the molar solubility of

barium sulfate, BaSO4, in 0.010 M sodium sulfate,

Na2SO4, solution at 25oC. Compare this to the

solubility of BaSO4 in pure water. (Example 20-3).(What is the common ion?)



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The Common Ion Effect in

Solubility Calculations

• The molar solubility of BaSO4 in 0.010 M Na2SO4

solution is 1.1 x 10-8 M .

• The molar solubility of BaSO4 in pure water is 1.0 x

10-5 M .

– BaSO4 is 900 times more soluble in pure water than in

0.010 M sodium sulfate!

– Adding sodium sulfate to a solution is a fantastic

method to remove Ba2+ ions from solution!



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The Reaction Quotient in

Precipitation Reactions• The reaction quotient, Q, and the Ksp of a

compound are used to calculate the

concentration of ions in a solution and

whether or not a precipitate will form.




Precipitation Reactions

Qsp = Ksp saturated solution

Qsp < Ksp unsaturated sol’n; precipitation cannot occur

Qsp > Ksp supersaturated sol’n; precipitation should occur

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Precipitation ReactionsExample 20-6: We mix 100 mL of 0.010 M

potassium sulfate, K2SO4, and 100 mL of 0.10 M

lead (II) nitrate, Pb(NO3)2 solutions. Will a

precipitate form?



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Precipitation ReactionsExample 20-7: Suppose we wish to remove

mercury from an aqueous solution that contains a

soluble mercury compound such as Hg(NO3)2. We

can do this by precipitating mercury (II) ions as theinsoluble compound HgS. What concentration of

sulfide ions, from a soluble compound such as

Na2S, is required to reduce the Hg2+ concentration

to 1.0 x 10-8 M ? For HgS, Ksp=3.0 x 10-53.You do i t !



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Precipitation ReactionsExample 20-7: What concentration of sulfide ions,

from a soluble compound such as Na2S, is required

to reduce the Hg2+ concentration to 1.0 x 10-8 M ?

For HgS, Ksp=3.0 x 10-53

.



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Precipitation ReactionsExample 20-8: Refer to example 20-7. What volume

of the solution (1.0 x 10-8 M Hg2+ ) contains 1.0 g of

mercury?



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Fractional Precipitation

• The method of precipitating some ions from a

solution while leaving others in solution is called

fractional precipitation.

– If a solution contains Cu+

, Ag+

, and Au+

, each ion canbe precipitated as chlorides.

13

sp

10sp

7

sp

100.2ClAuK ClAuAuCl

108.1ClAgK ClAgAgCl

109.1ClCuK ClCuCuCl



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Example 20-9: If solid sodium chloride is slowly

added to a solution that is 0.010 M each in Cu+, Ag+,

and Au+ ions, which compound precipitates first?

Calculate the concentration of Cl-

required to initiateprecipitation of each of these metal chlorides.



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• These three calculations give the [Cl-] required

to precipitate AuCl ([Cl-] >2.0 x 10-11 M ), to

precipitate AgCl ([Cl-] >1.8 x 10-8 M ), and to

precipitate CuCl ([Cl-] >1.9 x 10-5 M ).• It is also possible to calculate the amount of

Au+ precipitated before the Ag+ begins to

precipitate, as well as the amounts of Au+ and

Ag+ precipitated before the Cu+ begins to

precipitate.



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Example 20-10: Calculate the percentage of Au+

ions that precipitate before AgCl begins to

precipitate.

– Use the [Cl-

] from Example 20-9 to determine the [Au+

]remaining in solution just before AgCl begins to

precipitate.



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• The percent of Au+ ions unprecipitated just

before AgCl precipitates is:



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• A similar calculation for the concentration

of Ag+ ions unprecipitated before CuCl

begins to precipitate is:



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• The percent of Ag+ ions unprecipitated justbefore AgCl precipitates is:



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Ionic Equilibria III:

The SolubilityProduct Principle

Download - Chapter20 Solubility Product Constant

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