Solubility Product Constant, Ksp

Solubility:

• is the maximum amount of solute in a solvent at a

given temperature

• saturated solution, [ ]max

• equilibrium between: (see Dissolving salts OH)

solid crystals dissolved ions

eg. AgNO3(s) Ag1+(aq) + NO3

1-(aq)

• solubility is a contest between:

• ionic bond strengths vs ion-dipole forces

• lattice energies vs hydration energies

• usually exothermic with increased disorder

• if undissolved solid is present, then it is a mixture with

a saturated sol’n phase

Solubility Product Constant, Ksp: • equilibrium expression for slightly soluble salts

If: AxBy(s) xAm+(aq) + yBn-

(aq)

Then:

y]-n[B x]m[A Ksp

(solid)constant is ]yBx[A and

]yBx[A

y]-n[B x]m[A

Ksp

Saturation can be tested by Q:

If: Q = Ksp then: it is a saturation solution

Q > Ksp there is noticeable precipitate

Q < Ksp unsaturated

Terminology: • refers to the amount of solid that can dissolve not how

much is in solution • solubility in g/100g or g/100 mL or g/L

[ ]max = solubility x Msolute and volume adjustment

• molar solubility in mol/L (CONCENTRATION !)

= solubility / Msolute

Calculations: 1) Ksp from solubility

eg. Calculate the Ksp of Ag2CO3 given its solubility

of 0.0014 g/100g.

mol/L 10 x 5.1 and

+ 2 + E

+ 2 C

0 0 I

]CO[][Ag = K ; CO Ag 2 COAg

mol/L 10 x 5.1

g 275.75

mol 1 x

L 0.1

g 100 x

g 100

g 0.0014 ]CO[Ag

5-

-23

2sp

-2332

5-

32

x

xx

xx

Ksp = [Ag ]2[CO32- ]

(2(5.1 x 10 -5))2(5.1 x 10 -5 )

5.3 x 10 -13

2) Solubility from Ksp

types: solubility, molar solubility, [ion]eq, amount of

solid that will dissolve

eg. How much PbI2 at SATP will dissolve in 1.00 L of

water? Give the solute ion concentration, [Pb2+]eq,

solubility (g/100mL) and molar solubility.

(Ksp of PbI2 from textbook is 8.5 x 10-9)

xx

xx

2+ + E

2+ C

10 x 8.5 0 0 I

]I][[Pb = K ; I 2 Pb PbI

9-

2-12sp

-122

eq23-

9-3

9-2

9-2-12sp

][Pb mol/L 10 x 1.3

10 x 8.5 4

10 x 8.5 ))(2(

10 x 8.5 ]I][[Pb = K

x

x

xx

mL g/100 0.060

mL 100

L 0.10 x

mol

g 461.00 x

L

mol 10 x 1.3 PbI of solubility

mol/L 10 x 1.3 PbI of solubilitymolar

3-

2

3-2

Predicting Precipitation:

• Used to determine precipitation when mixing 2 sol’ns

as with double displacement rxns

eg. Will precipitation occur when 5.0 ml of 0.030 M

AgNO3 is mixed with 1.0 ml of 0.0050 M Na2CrO4?

(Ksp = 1.1 x 10-12 for Ag2CrO4).

form willeprecipitat a

)10 x (1.1 Ksp > 10 x 5.2 (0.00083)(0.025) Q

0.00083 0.025

0.0060

0.0050 x 0.0010

0.0060

0.030 x 0.0050

V

VC

V

VC

10 x 1.1 ]CrO[][Ag = K ; CrO Ag 2 CrOAg

M 0.0050 C L, 0.0010 V ; CrO Na 2 CrONa

M 0.030 C L, 0.0050 V ; NO Ag AgNO

12-7-2

total

22

total

11

12--24

2sp

-2442

22-2

41

42

11-1

31

3