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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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