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CALCULATING THE MOLAR SOLUBILITY FROM Ksp

The molar solubility of any slightly soluble salt, along with the concentration of any of its ions, can be calculated from its Ksp value. The formula of the salt must be known, however, so that its dissociation and ionization can be written (See Table 2.2).

It is important to note that simply comparing the Ksp values of two salts to determine which has a higher or lower molar solubility can often be misleading. This comparison of numerical values is valid only when the two salts have the same stoichiometry, that is, the subscripts in the formulas are identical.

Table 2.2. The solubility product constants of common insoluble salts at 25°C

Salt

Solubility Equilibrium

Ksp

Fluorides

MgF2

MgF2(s) ^ Mg2+(aq) + 2F (aq)

6.6 X 10-9

CaF2

CaF2(s) ^ Ca2+(aq) + 2F-(aq)

3.9 x 10-11

SrF2

SrF2(s) ^ Sr2+(aq) + 2F-(aq)

2.9 x 10-9

BaF2

BaF2(s) ^ Ba2+(aq) + 2F-(aq)

1.7 x 10-6

LiF

LiF(s) ^ Li+(aq) + F-(aq)

1.7 x 10-3

PbF2

PbF2(s) ^ Pb2+(aq) + 2F-(aq)

3.6 x 10-8

Chlorides

CuCl

CuCl(s) ^ Cu+(aq) + Cl-(aq)

1.9 x 10-7

AgCl

AgCl(s) ^ Ag+(aq) + Cl-(aq)

1.8 x 10-10

Hg2Cl2

Hg2Cl2(s) ^ Hg22+(aq) + 2Cl-(aq)

1.2 x 10-18

TlCl

TlCl(s) ^ Tl+(aq) + Cl-(aq)

1.8 x 10-4

PbCl2

PbCl2(s) ^ Pb2+(aq) + 2Cl-(aq)

1.7 x 10-5

AuCls

AuCls(s) ^ Au3+(aq) + 3Cl-(aq)

3.2 x 10-25

Bromides

CuBr

CuBr(s) ^ Cu+(aq) + Br-(aq)

5 x 10-9

AgBr

AgBr(s) ^ Ag+(aq) + Br-(aq)

5.0 x 10-13

Hg2Br2

Hg22+(s) ^ Hg22+(aq) + 2Br-(aq)

5.6 x 10-23

HgBr2

HgBr2(s) ^ Hg2+(aq) + 2Br-(aq)

1.3 x 10-19

PbBr2

PbBr2(s) ^ Pb2+(aq) + 2Br-(aq)

2.1 x 10-6

Iodides

Cul

Cul(s) ^ Cu+(aq) + I-(aq)

1 x 10-12

Agl

Agl(s) ^ Ag+(aq) + 1-(aq)

8.3 x 10-17

Hg2l2

Hg2l2(s) ^ Hg22+(aq) + 2l-(aq)

4.7 x 10-28

Hgl2

Hgl2(s) ^ Hg2+(aq) + 2l-(aq)

1.1 x 10-28

Pbl2

Pbl2(s) ^ Pb2+(aq) + 2l-(aq)

7.9 x 10-9

Salt

Solubility Equilibrium

К,

Hydroxides

Mg(OH)2

Mg(OH)2(s) ^

Mg2+(aq) + 2OH (aq)

7.1 x 10-12

Ca(OH)2

Ca(OH)2(s) ^

Ca2+(aq) + 2OH-(aq)

6.5 x 10-6

Mn(OH)2

Mn(OH)2(s) ^

Mn2+(aq) + 2OH-(aq)

1.6 x 10-13

Fe(OH)2

Fe(OH)2(s) ^

Fe2+(aq) + 2OH-(aq)

7.9 x 10-16

Fe(OH)3

Fe(OH)3(s) ^

Fe3+(aq) + 3OH-(aq)

1.6 x 10-39

Co(OH)2

Co(OH)2(s) ^

Co2+(aq) + 2OH-(aq)

1 x 10-15

Co(OH)3

Co(OH)3(s) ^

Co3+(aq) + 3OH-(aq)

3 x 10-45

Ni(OH)2

Ni(OH)2(s) ^

Ni2+(aq) + 2OH-(aq)

6 x 10-16

Cu(OH)2

Cu(OH)2(s) ^

Cu2+(aq) + 2OH-(aq)

4.8 x 10-20

V(OH)3

V(OH)3(s) ^

V3+(aq) + 3OH-(aq)

4 x 10-35

Cr(OH)3

Cr(OH)3(s) ^

Cr3+(aq) + 3OH-(aq)

2 x 10-30

Ag2O

Ag2O(s) + H2O ^ 2Ag+(aq) + 2OH (aq)

1.9 x 10-8

Zn(OH)2

Zn(OH)2(s) ^

Zn2+(aq) + 2OH (aq)

3.0 x 10-16

Cd(OH)2

Cd(OH)2(s) ^

Cd2+(aq) + 2OH-(aq)

5.0 x 10-15

Al(OH)3 (alpha form)

Al(OH)3(s) ^

Al3+(aq) + 3OH-(aq)

3 x 10-34

Cyanides

AgCN

AgCN(s) ^

Ag+(aq) + CN-(aq)

2.2 x 10-16

Zn(CN)2

Zn(CN)2(s) ^

Zn2+(aq) + 2CN-(aq)

3 x 10-16

Sulfites

CaSO3

CaSO3(s) ^

Ca2+(aq) + SO32-(aq)

3 x 10-7

Ag2SO3

Ag2SO3(s) ^

2Ag+(aq) + SO32-(aq)

1.5 x 10-14

BaSO3

BaSO3(s) ^

Ba2+(aq) + SO32-(aq)

8 x 10-7

Sulfates

CaSO4

CaSO4(s) ^

Ca2+(aq) + SO42-(aq)

2.4 x 10-5

SrSO4

SrSO4(s) ^

Sr2+(aq) + SO42-(aq)

3.2 x 10-7

Salt

Solubility Equilibrium

Kp

BaSO4

BaSO4(s) ^ Ba2+(aq) + SO42-(aq)

1.1 X 10-1»

RaSO4

RaSO4(s) ^ Ra2+(aq) + SO42-(aq)

4.3 x 10-11

Ag2SO4

Ag2SO4(s) ^ 2Ag+(aq) + SO42-(aq)

1.5 x 10-5

Hg2SO4

Hg2SO4(s) ^ Hg22+(aq) + SO42-(aq)

7.4 x 10-7

PbSO4

PbSO4(s) ^ Pb2+(aq) + SO42-(aq)

1.6 x 10-8

Chromates

BaCrO4

BaCrO4(s) ^ Ba2+(aq) + CrO42-(aq)

2.1 x 10-10

CuCrO4

CuCrO4(s) ^ Ba2+(aq) + CrO42-(aq)

3.6 x 10-6

Ag2CrO4

Ag2CrO4(s) ^ 2Ag+(aq) + CrO42-(aq)

1.2 x 10-12

Hg2CrO4

Hg2CrO4(s) ^ Hg22+(aq) + CrO42-(aq)

2.0 x 10-9

CaCrO4

CaCrO4(s) ^ Ca2+(aq) + CrO42-(aq)

7.1 x 10-4

PbCrO4

PbCrO4(s) ^ Pb2+(aq) + CrO42-(aq)

1.8 x 10-14

Carbonates

MgCOs

MgCOs(s) ^ Mg2+(aq) + COs2-(aq)

3.5 x 10-8

CaCOs

CaCOs(s) ^ Ca2+(aq) + COs2-(aq)

4.5 x 10-9

SrCOs

SrCOs(s) ^ Sr2+(aq) + COs2-(aq)

9.3 x 10-10

BaCOs

BaCOs(s) ^ Ba2+(aq) + COs2-(aq)

5.0 x 10-9

MnCOs

MnCOs(s) ^ Mn2+(aq) + COs2-(aq)

5.0 x 10-10

FeCOs

FeCOs(s) ^ Fe2+(aq) + COs2-(aq)

2.1 x 10-11

C0CO3

CoCOs(s) ^ Co2+(aq) + COs2-(aq)

1.0 x 10-10

NiCOs

NiCOs(s) ^ Ni2+(aq) + COs2-(aq)

1.3 x 10-7

CuCO3

CuCOs(s) ^ Cu2+(aq) + COs2-(aq)

2.3 x 10-10

Ag2COs

Ag2COs(s) ^ 2Ag+(aq) + COs2-(aq)

8.1 x 10-12

Hg2COs

Hg2COs(s) ^ 2Hg+(aq) + COs2-(aq)

8.9 x 10-17

ZnCOs

ZnCOs(s) ^ Zn2+(aq) + COs2-(aq)

1.0 x 10-10

CdCOs

CdCOs(s) ^ Cd2+(aq) + COs2-(aq)

1.8 x 10-14

PbCOs

PbCOs(s) ^ Pb2+(aq) + COs2-(aq)

7.4 x 10-14

Salt

Solubility Equilibrium

K„

Phosphates

Mg3(POzi)2

Mg3(PO4)2(s) ^ 3Mg2+(aq) + 2PO43-(aq)

6.3 x 10-26

SrHPO4

SrHPO4(s) ^ Sr2+(aq) + HPO42-(aq)

1.2 x 10-7

BaHPO4

BaHPO4(s) ^ Ba2+(aq) + HPO42-(aq)

4.0 x 10-8

LaPO4

LaPO4(s) ^ La3+(aq) + PO43-(aq)

3.7 x 10-23

Fe3(PO4)2

Fe3(PO4)2(s) ^ 3Fe2+(aq) + 2PO43-(aq)

1 x 10-36

Ag3PO4

Ag3PO4(s) ^ 3Ag+(aq) + PO43-(aq)

2.8 x 10-18

FePO4

FePO4(s) ^ Fe3+(aq) + PO43-(aq)

4.0 x 10-27

Zn3(PO4)2

Zn3(PO4)2(s) ^ 3Zn2+(aq) + 2PO43-(aq)

5 x 10-36

Pb3(PO4)2

Pb3(PO4)2(s) ^ 3Pb2+(aq) + 2PO43-(aq)

3.0 x 10-44

Ba3(PO4)2

Ba3(PO4)2(s) ^ 3Ba2+(aq) + 2PO43-(aq)

5.8 x 10-38

Ferrocyanides

Zn2[Fe(CN)6]

Zn2[Fe(CN)6](s) ^ 2Zn2+(aq) + Fe(CN)64-(aq)

2.1 x 10-16

Cd2[Fe(CN)6]

Cd2[Fe(CN)6](s) ^ 2Cd2+(aq) + Fe(CN)64-(aq)

4.2 x 10-18

Pb2[Fe(CN)6]

Pb2[Fe(CN)6](s) ^ 2Pb2+(aq) + Fe(CN)64-(aq)

9.5 x 10-19

Example 2.10 Calculate

A. The molar solubility of calcium fluoride, CaF2, and

B. The concentration of the fluoride ion, in solution at 25°C. The Ksp of CaF2 is 4.0 x 10-11 at 25°C. Here, the unit of Ksp is (moles/L)3 or M3. This unit may change depending on the identity, that is, the subscripts of the ions, of the salt.

Solution

A. The equilibrium for the salt is as follows:

The Ksp expression is:

Let S = the solubility (saturation concentration) of the Ca2+ ion in moles per liter.

Then 2S = the solubility (saturation concentration) of the F- ion. Substitute S into the Ksp expression:

Thus, the molar solubility of a CaF2 is 2.15 x 10-4 M. This is also [Ca2+].

B. [F-] = 2 x 2.15 x 10-4 M = 4.30 x 10-4 M Example 2.11

The molar solubility of tin iodide, SnL, is 1.28 x 10-2 mol/L. What is Ksp for this compound?

Solution

The solubility equilibrium for SnL is:

The Ksp expression is

Note that 1.0 mol of SnL produces 1.0 mol of Sn2+, but 2.0 mol of I

Substituting these values into the Ksp expression yields:

 
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