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Solubility EquilibriaDissolution MmXx (s) m Mn+ (aq) + x Xy- (aq)

Precipitation m Mn+ (aq) + x Xy- (aq) MmXx (s)

For a dissolution process, we give the equilibrium constant expression the name solubility product (constant) Ksp. For

MmXx (s) m Mn+ (aq) + x Xy- (aq)

Ksp = [Mn+]m [Xy-]x

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Problem

Write the expressions for the solubility product constant Ksp of:a) AgCl

b) PbI2

c) Ca3(PO4)2

d) Cr(OH)3

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Measuring Ksp and Calculating Molar Solubility from Ksp

For the dissolution of solid CaF2 in water, we might find that the concentrations of the ions Ca2+ and F- at equilibrium are

[Ca2+] = 3.3 x 10-4 mol/L [F-] = 6.7 x 10-4 mol/L

Ksp = [Ca2+] [F-]2 = (3.3 x 10-4 mol/L) (6.7 x 10-4 mol/L)2

= 1.5 x 10-10

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Measuring Ksp and Calculating Molar Solubility from Ksp

We could also find the Ksp of a solid by mixing solutions of known concentrations of the ions, leading to the precipitation of the solid.

When the system reaches equilibrium we can measure the ion concentrations to calculate Ksp.

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The advantage of using the dissolution of the solid method is that a clear

relationship between the concentrations of the ions

exists, based upon their relative stoichiometry in the solid.

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If we mix two separate solutions that are sources of calcium ions and fluoride ions, no such relationship exists, and we can have infinitely many mixtures that still obey the solubility product expression.

Since Ksp values are equilibrium constants, they will change with

temperature!

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Molar solubility and saturation

If we know the Ksp value for a solid, we can calculate its molar solubility, which is the number of moles of the solid that can dissolve in the solvent before the solution becomes saturated (no more solid will dissolve).

Saturated means equilibrium!

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Problem

A saturated solution of Ca3(PO4)2 has

[Ca2+] = 2.01 x 10-8 mol/L and

[PO43-] = 1.6 x 10-5 mol/L.

Calculate Ksp for Ca3(PO4)2

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Problem

If a saturated solution of BaSO4 is prepared by dissolving solid BaSO4 in water, and [Ba2+] = 1.05 x 10-5 mol/L, what is the Ksp for BaSO4?

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Problem

Which has the greater molar solubility?

AgCl with Ksp = 1.8 x 10-10

or

Ag2CrO4 with Ksp = 1.1 x 10-12

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Factors that Affect Solubility

The Common-Ion Effect

If a solution already has a significant concentration of a common-ion the solution will dissolve LESS of the solid

than the same volume of pure water can.

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The Common-Ion Effect

MmXx (s) m Mn+ (aq) + x Xy- (aq)

Ksp = [Mn+]m [Xy-]x

Imagine that instead of dissolving a solid in a solution of common-ion that we add a common ion to a solution created by dissolving

the solid in pure water.

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The Common-Ion Effect

MmXx (s) m Mn+ (aq) + x Xy- (aq)

Ksp = [Mn+]m [Xy-]x

From Le Chatalier’s Principle, we know if we add one of the product ions (the common ion we added), the stress on the equilibrium is this

added product. To relieve the stress the equilibrium will shift towards the reactants

meaning more solid is created.

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Problem

Calculate the molar solubility of MgF2

(Ksp = 7.4 x 10-11) in pure water and

in 0.10 mol/L MgCl2.

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Precipitation of Ionic Compounds

Can we predict if a solid will precipitate if we mix two solutions of different ions?

YES!Consider the mixing of a solution of Ca2+ ions and a solution of F- ions. A precipitation of solid is the dissolution reaction in reverse, so we can express the reaction as

CaF2 (s) Ca2+ (aq) + 2 F- (aq) Ksp = [Ca2+ ][F-]2

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Precipitation of Ionic Compounds

When we mix the solutions, the system is most likely not at equilibrium.

For solid dissolution / precipitation reactions, we use a procedure similar to the reaction quotient Qc to define the ion product (IP) or Qsp.

Qsp = [Ca2+ ][F-]2

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If Qsp = Ksp, the solution is saturated, and the system is at equilibrium.

If Qsp > Ksp, the solution is supersaturated, so the system is not at equilibrium. The concentration

of the ions is greater than it would be at equilibrium, and so the reaction proceeds from

ions towards the solid.

We expect precipitation to occur!

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If Qsp < Ksp, the solution is unsaturated, so the system is not at

equilibrium. The concentration of the ions is less than it would be at

equilibrium, and so

we expect more solid to be able to dissolve in this solution!

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Will a precipitate form when 0.150 L of 0.10 molL-1 Pb(NO3)2 and 0.100 L of 0.20 molL-1 NaCl are mixed?

Ksp of PbCl2 is 1.2 x 10-5

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Problem

Will a precipitate form on mixing equal volumes of the following solutions?

a) 3.0 x 10-3 mol/L BaCl2 and 2.0 x 10-3 mol/L Na2CO3

b) 1.0 x 10-5 mol/L Ba(NO3)2 and

4.0 x 10-5 mol/L Na2CO3

(Ksp of BaCO3 is 2.6 x 10-9)