K sp and Solubility Equilibria. Saturated solutions of salts are another type of chemical...

KKspsp and and Solubility Solubility EquilibriaEquilibria

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.

(aq)2X(aq)2M(s)2MX

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

(aq)2X(aq)2M(s)2MX

2][X]M[K 2sp

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/LSolubility 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 doWhat 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 doWhat 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 KWrite Kspsp expresssions 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

• 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]

Write Ksp expresssionsWrite Ksp expresssions

Calculate Ksp given solubilityCalculate 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.

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

PbCl2 Pb+2 + 2Cl-

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

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!

Calculate solubility given KCalculate solubility given Kspsp

Copper(II) iodate has a Ksp of Copper(II) iodate has a Ksp of 1.4 X 101.4 X 10-7-7 @ 20 @ 20ooC. What is the C. What is the

molar solubility of the salt?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 In a saturated solution of silver carbonate, what is the molar carbonate, what is the molar

solubility of the salt? Ksp = 8.1 X 10solubility of the salt? Ksp = 8.1 X 10--

1212

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

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

Calculate solubility given KCalculate solubility given Kspsp

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 SolubilitiesComparing 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!


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


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


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= 34

Ksp

34

Ksp

Ksp

BaCO3 Ag2CO3 BaF2

Calculate the effect of a Calculate the effect of a common ion on pH or solubilitycommon ion on pH or solubility

Introduction of a common ion causes salts to become less soluble – think Le Chatelier’s Principle PbCrO4 Pb+2 + CrO4

2-

add K2CrO4 - shift left

Calculate the effect of a common Calculate the effect of a common ion on pH or solubilityion on pH or solubility

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


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

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)



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 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 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 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


With some knowledge of the reaction quotient (Q), we can decide

1) whether a ppt will form, AND

Determine if a precipitate will formDetermine 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.


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)


Precipitates form when the

solution is supersaturate

d!


• 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 Determining Precipitation ConditionsConditions

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).

SolutionSolution

[Mg2+] = 2.1 X 10-6 M

[F-] = 5.50 X 10-2 M

Why Would I Ever Care About Why Would I Ever Care About KKspsp ??? ???

Keep reading to find out !

Actually, very useful stuff!

Solubility, Ion Separations, and Solubility, Ion Separations, and Qualitative AnalysisQualitative Analysis

…introduce you to some basic

chemistry of various ions.

…illustrate how the principles of

chemical equilibria can be applied.

Selective PrecipitationSelective 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 SaltsPrecipitation 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.

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.

Precipitation of Insoluble SaltsPrecipitation of Insoluble Salts

Selective PrecipitationSelective 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.

SolutionSolution

CuI will precipitate first.

Concentration in excess of

5.3 X 10-8 M required.

K sp and Solubility Equilibria. Saturated solutions of salts are another type of chemical...

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