17.4: Solubility of Salts
- Page ID
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In general chemistry 1 students memorized a series of solubility rules (section 3.4.3) to predict if an ionic compound was soluble or not. Using these rules we would predict that insoluble salts formed precipitates and soluble salts dissolved. In this section we will apply chemical equilibria to the concept of solubility and introduce a type of equilibrium constant, the solubility constant, to allow us to calculate how soluble a salt really is.
Solubility Equilibrium defines the dynamic equilibria between a precipitate and its dissolved ions when the rate of dissolution equals the rate of crystallization and the resulting solution is a saturated solution, that contains the maximum concentration of dissolved ions that coexist with the undissolved solute (precipitate).
What do we mean by solubility of a salt? If I say one mole of sodium sulfate dissolves in water I am really meaning for every mole of sodium sulfate that dissolves, two moles of sodium are formed and one mole of sulfate. We will use the concept of solubility to describe the moles the salt that dissolves to form a saturated solution, and the actual ion concentration depends on the formula.
Solubility Product
This is the equilibrium constant for the process of dissolution. Consider the generic salt
\[M_xA_y(s) \leftrightharpoons xM^{+m}(aq) + yA^{-n}(aq)\]
Noting from charge neutrality that x(+m)+y(-n)=0, then the equilibrium constant expression is:
\[K_{sp}=[M^{+m}]^x[A^{-n}]^y\]
The solid reactant is not part of the equilibrium, and it is called the solubility product because it is the product of the concentration of all the ions a salt breaks into. It is important to realize this is a heterogeneous equilibrium that defines a saturated solution and the solid is part of the process, although it does not influence the equilibrium concentration. That is, if all the solid is dissolved, you may have an unsaturated solution, and the solubility product defines the concentration of a saturated solution. At the end of this chapter is a solubility product table for ionic compounds at 25oC.
Lets look at the solubility product for Calcium phosphate
\[Ca_3(PO_4)_2(s) \leftrightharpoons 3Ca^{+2} + 2PO_4^{-3}\]
\[K_{sp}(Ca_3(PO_4)_2)=[Ca^{+2}]^3[PO_4^{-3}]^2\]
Solubility Calculations
As in most equilibrium calculations, there are two types of problems. Knowing K, what are the equilibrium concentrations, and knowing the equilibrium concentration of one thing, what is K
Solubility of a Salt
The solubility of a salt is "x" (from the ICE table), but we will not be using ICE tables in solubility product calculations, and are just using it now to explain what is going on. From the following ICE table you can see that for every x moles of the calcium phosphate that dissolves per liter (its solubility), the solution gains 3 times that many moles of calcium and twice that many of phosphate, and there is no calcium phosphate floating around, just calcium and phosphate.
| ICE Table | \(Ca_{3}(PO_4)_{2}(s)\) | \( \leftrightharpoons \) | \(Ca^{+2}\) | \(PO_4^{-3}\) |
| Initial | [solid] | 0 | 0 | |
| Change | still solid | +3x | +2x | |
| Equilibrium | still solid | 3x | 2x |
That is, x the extent of reaction is a ICE diagram is the solubility of a salt. So you do not use a rice diagram, you say that for every x moles of solid that dissolves, the ions are that times the number of the ions in the formula So for Calcium phosphate
\[[Ca^{+2}]= 3x \; and \; [PO_4^{-3}] =2x]\]
\[K_{sp}(Ca_{3}(PO_4)_{2})=[3x]^3[2x]^2 = 108x^5\]
Solving for the solubility (x) and noting that Ksp(calcium phosphate) = 2.07 × 10−33
\[x=\sqrt[5]{\frac{K_{sp}}{108}}=\left ( \frac{2.07x10^{-33}}{108} \right )^{\frac{1}{5}}=1.14x10^{-7} = 114nM\]
So there are three questions that can be answered here
- The solubility of calcium phosphate is 114nM in water (x)
- The solubility of calcium is 341 nM in water (3x)
- The solubility of phosphate is 228 nM in water (2x)
Exercise \(\PageIndex{1}\)
Which is more soluble, silver thiocyanide (Ksp = 1.1 x 10-12) or silver sulfite (Ksp = 1.50 x 10-14)
- Answer
-
Silver sulfite, you can only compare Ksp values if the number of ions are the same, see video below.
For silver thiocyanide,
\[ K_{sp}=[Ag^+][SCN^-]=x^2 \\ x=\sqrt{k_{sp}} =\sqrt{1.1x10^{-12}} = 1.0x10^{-6} \nonumber\]
For silver sulfite,
\[ K_{sp}=[Ag^+][SO_3^{-2}]^2=x(2x)^2 = 4x^3 \\ x= \sqrt[3]{\frac{K_{sp}}{4}} = \sqrt[3]{\frac{1.50 x 10^{-14}}{4}} \\ = 1.56x10^{-5}\]
Video \(\PageIndex{1}\): Solution to exercise \(\PageIndex{1}\).
Determining Ksp
If a saturated solution of La(IO3)3 has an iodate concentration of 0.006M, what is Ksp?
\[La(IO_3)_3 \leftrightharpoons La^{+3}+3IO_3^-\]
The lanthanum ion concentration = x and the iodate ion concentration = 3x=0.0060. So x=0.0020
\[K_{sp}=[La^{+3}][IO_3^{-3}]^3=[0.0020]0.0060]^3=4.2x10^{-10}\]
Solubility and Common ion Effect
In section 17.1.3 solubility was introduced as an example of the common ion effect, and this problem was explained using ICE table and Le Chatelier's Principle.
What is the solubility of Calcium phosphate in a 0.100M sodium phosphate solution?
This is the same problem as above except that there is a common ion as the soluble sodium phosphate introduces phosphate that shifts the calcium phosphate to the left, reducing its solubility.
\[Ca_3PO_4(s) \leftrightharpoons 3Ca^{+2} + 2PO_4^{-3}\]
\[K_{sp}(Ca_3PO_4)=[Ca^{+2}]^3[PO_4^{-3}]^2\]
noting that \([PO_4^{-3}] = 0.100M+3x\) and ignoring the x (see section 17.1.3)
\[K_{sp}(Ca_3PO_4)=[3x]^3[.1]^2 = 0.27x^3\]
\[x=\left ( \frac{K_{sp}}{0.27} \right )^{\frac{1}{3}}=\left ( \frac{2.07x10^{-33}}{0.27} \right )^{\frac{1}{3}}=1.97x10^{-11}\]
Exercise \(\PageIndex{2}\)
What is the lead concentration for a saturated solution of lead(II)bromide, and then mathematically demonstrate Le Chatlier's principle by determining the lead concentration when in the presence of a common ion by making the solution 1M in sodium bromide.
- Answer
-
As the following video shows, the lead is 0.0118 in the absence of sodium bromide and is reduced to 6.6x10-6 in the presence of 1 M NaBr. This demonstrates Le Chatlier's principle as adding the bromide with the soluble sodium bromide salt pushed the equilbria of the insoluble lead(II)bromide salt to the left (consuming the bromide added), and thus removing the lead.
Video \(\PageIndex{2}\): Solution to exercise \(\PageIndex{2}\).
Solubility Product Table
This values relate to 25oC.
| Compound Name | Compound Formula | Ksp |
|---|---|---|
| Aluminum phosphate | AlPO4 | 9.84 × 10−21 |
| Barium bromate | Ba(BrO3)2 | 2.43 × 10−4 |
| Barium carbonate | BaCO3 | 2.58 × 10−9 |
| Barium chromate | BaCrO4 | 1.17 × 10−10 |
| Barium fluoride | BaF2 | 1.84 × 10−7 |
| Barium iodate | Ba(IO3)2 | 4.01 × 10−9 |
| Barium nitrate | Ba(NO3)2 | 4.64 × 10−3 |
| Barium sulfate | BaSO4 | 1.08 × 10−10 |
| Barium sulfite | BaSO3 | 5.0 × 10−10 |
| Beryllium hydroxide | Be(OH)2 | 6.92 × 10−22 |
| Bismuth arsenate | BiAsO4 | 4.43 × 10−10 |
| Bismuth iodide | BiI3 | 7.71 × 10−19 |
| Cadmium carbonate | CdCO3 | 1.0 × 10−12 |
| Cadmium fluoride | CdF2 | 6.44 × 10−3 |
| Cadmium hydroxide | Cd(OH)2 | 7.2 × 10−15 |
| Cadmium iodate | Cd(IO3)2 | 2.5 × 10−8 |
| Cadmium phosphate | Cd3(PO4)2 | 2.53 × 10−33 |
| Cadmium sulfide | CdS | 8.0 × 10−27 |
| Calcium carbonate | CaCO3 | 3.36 × 10−9 |
| Calcium fluoride | CaF2 | 3.45 × 10−11 |
| Calcium hydroxide | Ca(OH)2 | 5.02 × 10−6 |
| Calcium iodate | Ca(IO3)2 | 6.47 × 10−6 |
| Calcium phosphate | Ca3(PO4)2 | 2.07 × 10−33 |
| Calcium sulfate | CaSO4 | 4.93 × 10−5 |
| Cesium perchlorate | CsClO4 | 3.95 × 10−3 |
| Cesium periodate | CsIO4 | 5.16 × 10−6 |
| Cobalt(II) arsenate | Co3(AsO4)2 | 6.80 × 10−29 |
| Cobalt(II) hydroxide | Co(OH)2 | 5.92 × 10−15 |
| Cobalt(II) phosphate | Co3(PO4)2 | 2.05 × 10−35 |
| Copper(I) bromide | CuBr | 6.27 × 10−9 |
| Copper(I) chloride | CuCl | 1.72 × 10−7 |
| Copper(I) cyanide | CuCN | 3.47 × 10−20 |
| Copper(I) iodide | CuI | 1.27 × 10−12 |
| Copper(I) thiocyanate | CuSCN | 1.77 × 10−13 |
| Copper(II) arsenate | Cu3(AsO4)2 | 7.95 × 10−36 |
| Copper(II) oxalate | CuC2O4 | 4.43 × 10−10 |
| Copper(II) phosphate | Cu3(PO4)2 | 1.40 × 10−37 |
| Copper(II) sulfide | CuS | 6.3 × 10−36 |
| Europium(III) hydroxide | Eu(OH)3 | 9.38 × 10−27 |
| Gallium(III) hydroxide | Ga(OH)3 | 7.28 × 10−36 |
| Iron(II) carbonate | FeCO3 | 3.13 × 10−11 |
| Iron(II) fluoride | FeF2 | 2.36 × 10−6 |
| Iron(II) hydroxide | Fe(OH)2 | 4.87 × 10−17 |
| Iron(III) hydroxide | Fe(OH)3 | 2.79 × 10−39 |
| Iron(III) sulfide | FeS | 6.3 × 10−18 |
| Lanthanum iodate | La(IO3)3 | 7.50 × 10−12 |
| Lead(II) bromide | PbBr2 | 6.60 × 10−6 |
| Lead(II) carbonate | PbCO3 | 7.40 × 10−14 |
| Lead(II) chloride | PbCl2 | 1.70 × 10−5 |
| Lead(II) fluoride | PbF2 | 3.3 × 10−8 |
| Lead(II) hydroxide | Pb(OH)2 | 1.43 × 10−20 |
| Lead(II) iodate | Pb(IO3)2 | 3.69 × 10−13 |
| Lead(II) iodide | PbI2 | 9.8 × 10−9 |
| Lead(II)selenite | PbSeO4 | 1.37 × 10−7 |
| Lead(II) sulfate | PbSO4 | 2.53 × 10−8 |
| Lead(II) sulfide | PbS | 8.0 × 10−28 |
| Lithium carbonate | Li2CO3 | 8.15 × 10−4 |
| Lithium fluoride | LiF | 1.84 × 10−3 |
| Lithium phosphate | Li3PO4 | 2.37 × 10−11 |
| Magnesium carbonate | MgCO3 | 6.82 × 10−6 |
| Magnesium fluoride | MgF2 | 5.16 × 10−11 |
| Magnesium hydroxide | Mg(OH)2 | 5.61 × 10−12 |
| Magnesium phosphate | Mg3(PO4)2 | 1.04 × 10−24 |
| Manganese(II) carbonate | MnCO3 | 2.24 × 10−11 |
| Manganese(II) iodate | Mn(IO3)2 | 4.37 × 10−7 |
| Mercury(I) bromide | Hg2Br2 | 6.40 × 10−23 |
| Mercury(I) carbonate | Hg2CO3 | 3.6 × 10−17 |
| Mercury(I) chloride | Hg2Cl2 | 1.43 × 10−18 |
| Mercury(I) fluoride | Hg2F2 | 3.10 × 10−6 |
| Mercury(I) iodide | Hg2I2 | 5.2 × 10−29 |
| Mercury(I) oxalate | Hg2C2O4 | 1.75 × 10−13 |
| Mercury(I) sulfate | Hg2SO4 | 6.5 × 10−7 |
| Mercury(I) thiocyanate | Hg2(SCN)2 | 3.2 × 10−20 |
| Mercury(II) bromide | HgBr2 | 6.2 × 10−20 |
| Mercury (II) iodide | HgI2 | 2.9 × 10−29 |
| Mercury(II) sulfide (red) | HgS | 4 × 10−53 |
| Mercury(II) sulfide (black) | HgS | 1.6 × 10−52 |
| Neodymium carbonate | Nd2(CO3)3 | 1.08 × 10−33 |
| Nickel(II) carbonate | NiCO3 | 1.42 × 10−7 |
| Nickel(II) hydroxide | Ni(OH)2 | 5.48 × 10−16 |
| Nickel(II) iodate | Ni(IO3)2 | 4.71 × 10−5 |
| Nickel(II) phosphate | Ni3(PO4)2 | 4.74 × 10−32 |
| Palladium(II) thiocyanate | Pd(SCN)2 | 4.39 × 10−23 |
| Potassium hexachloroplatinate | K2PtCl6 | 7.48 × 10−6 |
| Potassium perchlorate | KClO4 | 1.05 × 10−2 |
| Potassium periodate | KIO4 | 3.71 × 10−4 |
| Praseodymium hydroxide | Pr(OH)3 | 3.39 × 10−24 |
| Rubidium perchlorate | RbClO4 | 3.00 × 10−3 |
| Scandium fluoride | ScF3 | 5.81 × 10−24 |
| Scandium hydroxide | Sc(OH)3 | 2.22 × 10−31 |
| Silver(I) acetate | AgCH3CO2 | 1.94 × 10−3 |
| Silver(I) arsenate | Ag3AsO4 | 1.03 × 10−22 |
| Silver(I) bromate | AgBrO3 | 5.38 × 10−5 |
| Silver(I) bromide | AgBr | 5.35 × 10−13 |
| Silver(I) carbonate | Ag2CO3 | 8.46 × 10−12 |
| Silver(I) chloride | AgCl | 1.77 × 10−10 |
| Silver(I) chromate | Ag2CrO4 | 1.12 × 10−12 |
| Silver(I) cyanide | AgCN | 5.97 × 10−17 |
| Silver(I) iodate | AgIO3 | 3.17 × 10−8 |
| Silver(I) iodide | AgI | 8.52 × 10−17 |
| Silver(I) oxalate | Ag2C2O4 | 5.40 × 10−12 |
| Silver(I) phosphate | Ag3PO4 | 8.89 × 10−17 |
| Silver(I) sulfate | Ag2SO4 | 1.20 × 10−5 |
| Silver(I) sulfide | Ag2S | 6.3 × 10−50 |
| Silver(I) sulfite | Ag2SO3 | 1.50 × 10−14 |
| Silver(I) thiocyanate | AgSCN | 1.03 × 10−12 |
| Strontium arsenate | Sr3(AsO4)2 | 4.29 × 10−19 |
| Strontium carbonate | SrCO3 | 5.60 × 10−10 |
| Strontium fluoride | SrF2 | 4.33 × 10−9 |
| Strontium iodate | Sr(IO3)2 | 1.14 × 10−7 |
| Strontium sulfate | SrSO4 | 3.44 × 10−7 |
| Thallium(I) bromate | TlBrO3 | 1.10 × 10−4 |
| Thallium(I) bromide | TlBr | 3.71 × 10−6 |
| Thallium(I) chloride | TlCl | 1.86 × 10−4 |
| Thallium(I) chromate | Tl2CrO4 | 8.67 × 10−13 |
| Thallium(I) iodate | TlIO3 | 3.12 × 10−6 |
| Thallium(I) iodide | TlI | 5.54 × 10−8 |
| Thallium(I) thiocyanate | TlSCN | 1.57 × 10−4 |
| Thallium(III) hydroxide | Tl(OH)3 | 1.68 × 10−44 |
| Tin(II) hydroxide | Sn(OH)2 | 5.45 × 10−27 |
| Tin(II) sulfide | SnS | 1.0 × 10−25 |
| Yttrium carbonate | Y2(CO3)3 | 1.03 × 10−31 |
| Yttrium fluoride | YF3 | 8.62 × 10−21 |
| Yttrium hydroxide | Y(OH)3 | 1.00 × 10−22 |
| Yttrium iodate | Y(IO3)3 | 1.12 × 10−10 |
| Zinc arsenate | Zn3(AsO4)2 | 2.8 × 10−28 |
| Zinc carbonate | ZnCO3 | 1.46 × 10−10 |
| Zinc fluoride | ZnF2 | 3.04 × 10−2 |
| Zinc hydroxide | Zn(OH)2 | 3 × 10−17 |
| Zinc selenide | ZnSe | 3.6 × 10−26 |
| Zinc sulfide (wurtzite) | ZnS | 1.6 × 10−24 |
| Zinc sulfide (sphalerite) | ZnS | 2.5 × 10−22 |
Source of data: CRC Handbook of Chemistry and Physics, 84th Edition (2004); sulfide data from Lange’s Handbook of Chemistry, 15th Edition (1999).
Test Yourself
Homework: Section 17.4
Contributors and Attributions
Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, rebelford@ualr.edu. You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to: