Propose a way to determine whether a saltwater solution is unsaturated saturated or supersaturated

The solubility product expression tells us that the equilibrium concentrations of the cation and the anion are inversely related. That is, as the concentration of the anion increases, the maximum concentration of the cation needed for precipitation to occur decreases—and vice versa—so that Ksp is constant. Consequently, the solubility of an ionic compound depends on the concentrations of other salts that contain the same ions. This dependency is another example of the common ion effect discussed in Chapter 16 "Aqueous Acid–Base Equilibriums", Section 16.6 "Buffers": adding a common cation or anion shifts a solubility equilibrium in the direction predicted by Le Châtelier’s principle. As a result, the solubility of any sparingly soluble salt is almost always decreased by the presence of a soluble salt that contains a common ion.

Consider, for example, the effect of adding a soluble salt, such as CaCl2, to a saturated solution of calcium phosphate [Ca3(PO4)2]. We have seen that the solubility of Ca3(PO4)2 in water at 25°C is 1.14 × 10−7 M (Ksp = 2.07 × 10−33). Thus a saturated solution of Ca3(PO4)2 in water contains 3 × (1.14 × 10−7 M) = 3.42 × 10−7 M Ca2+ and 2 × (1.14 × 10−7 M) = 2.28 × 10−7 M PO43−, according to the stoichiometry shown in Equation 17.1 (neglecting hydrolysis to form HPO42− as described in Chapter 16 "Aqueous Acid–Base Equilibriums"). If CaCl2 is added to a saturated solution of Ca3(PO4)2, the Ca2+ ion concentration will increase such that [Ca2+] > 3.42 × 10−7 M, making Q > Ksp. The only way the system can return to equilibrium is for the reaction in Equation 17.1 to proceed to the left, resulting in precipitation of Ca3(PO4)2. This will decrease the concentration of both Ca2+ and PO43− until Q = Ksp.

Calculate the solubility of calcium phosphate [Ca3(PO4)2] in 0.20 M CaCl2.

Given: concentration of CaCl2 solution

Asked for: solubility of Ca3(PO4)2 in CaCl2 solution

Strategy:

A Write the balanced equilibrium equation for the dissolution of Ca3(PO4)2. Tabulate the concentrations of all species produced in solution.

B Substitute the appropriate values into the expression for the solubility product and calculate the solubility of Ca3(PO4)2.

Solution:

A The balanced equilibrium equation is given in the following table. If we let x equal the solubility of Ca3(PO4)2 in moles per liter, then the change in [Ca2+] is once again +3x, and the change in [PO43−] is +2x. We can insert these values into the table.

B The Ksp expression is as follows:

Because Ca3(PO4)2 is a sparingly soluble salt, we can reasonably expect that x << 0.20. Thus (0.20 + 3x) M is approximately 0.20 M, which simplifies the Ksp expression as follows:

This value is the solubility of Ca3(PO4)2 in 0.20 M CaCl2 at 25°C. It is approximately nine orders of magnitude less than its solubility in pure water, as we would expect based on Le Châtelier’s principle. With one exception, this example is identical to Example 2—here the initial [Ca2+] was 0.20 M rather than 0.

Exercise

Calculate the solubility of silver carbonate in a 0.25 M solution of sodium carbonate. The solubility of silver carbonate in pure water is 8.45 × 10−12 at 25°C.

Answer: 2.9 × 10−6 M (versus 1.3 × 10−4 M in pure water)

1. Write an expression for Ksp for each salt.

2. Some species are not represented in a solubility product expression. Why?

3. Describe the differences between Q and Ksp.

4. How can an ion product be used to determine whether a solution is saturated?

5. When using Ksp to directly compare the solubilities of compounds, why is it important to compare only the Ksp values of salts that have the same stoichiometry?

6. Describe the effect of a common ion on the solubility of a salt. Is this effect similar to the common ion effect found in buffers? Explain your answer.

7. Explain why the presence of MgCl2 decreases the molar solubility of the sparingly soluble salt MgCO3.

1. 1. Ksp = [Ag+][I−]
   2. Ksp = [Ca2+][F−]2
   3. Ksp = [Pb2+][Cl−]2
   4. Ksp = [Ag+]2[CrO42−]

5. For a 1:1 salt, the molar solubility is simply Ksp; for a 2:1 salt, the molar solubility is Ksp/43. Consequently, the magnitudes of Ksp can be correlated with molar solubility only if the salts have the same stoichiometry.

7. Because of the common ion effect. Adding a soluble Mg2+ salt increases [Mg2+] in solution, and Le Châtelier’s principle predicts that this will shift the solubility equilibrium of MgCO3 to the left, decreasing its solubility.

2. Predict the molar solubility of each compound using the Ksp values given.

   1. Li3PO4: 2.37 × 10−11
   2. Ca(IO3)2: 6.47 × 10−6
   3. Y(IO3)3: 1.12 × 10−10

3. A student prepared 750 mL of a saturated solution of silver sulfate (Ag2SO4). How many grams of Ag2SO4 does the solution contain? Ksp = 1.20 × 10−5.

6. Silicon dioxide, the most common binary compound of silicon and oxygen, constitutes approximately 60% of Earth’s crust. Under certain conditions, this compound can react with water to form silicic acid, which can be written as either H4SiO4 or Si(OH)4. Write a balanced chemical equation for the dissolution of SiO2 in basic solution. Write an equilibrium constant expression for the reaction.

7. The Ksp of Mg(OH)2 is 5.61 × 10−12. If you tried to dissolve 24.0 mg of Mg(OH)2 in 250 mL of water and then filtered the solution and dried the remaining solid, what would you predict to be the mass of the undissolved solid? You discover that only 1.0 mg remains undissolved. Explain the difference between your expected value and the actual value.

8. The Ksp of lithium carbonate is 8.15 × 10−4. If 2.34 g of the salt is stirred with 500 mL of water and any undissolved solid is filtered from the solution and dried, what do you predict to be the mass of the solid? You discover that all of your sample dissolves. Explain the difference between your predicted value and the actual value.

9. You have calculated that 24.6 mg of BaSO4 will dissolve in 1.0 L of water at 25°C. After adding your calculated amount to 1.0 L of water and stirring for several hours, you notice that the solution contains undissolved solid. After carefully filtering the solution and drying the solid, you find that 22.1 mg did not dissolve. According to your measurements, what is the Ksp of barium sulfate?

10. In a saturated silver chromate solution, the molar solubility of chromate is 6.54 × 10−5. What is the Ksp?

11. A saturated lead(II) chloride solution has a chloride concentration of 3.24 × 10−2 mol/L. What is the Ksp?

12. From the solubility data given, calculate Ksp for each compound.

    1. AgI: 2.89 × 10−7 g/100 mL
    2. SrF2: 1.22 × 10−2 g/100 mL
    3. Pb(OH)2: 78 mg/500 mL
    4. BiAsO4: 14.4 mg/2.0 L

13. From the solubility data given, calculate Ksp for each compound.

    1. BaCO3: 10.0 mg/500 mL
    2. CaF2: 3.50 mg/200 mL
    3. Mn(OH)2: 6.30 × 10−4 g/300 mL
    4. Ag2S: 1.60 × 10−13 mg/100 mL

14. Given the following solubilities, calculate Ksp for each compound.

    1. BaCO3: 7.00 × 10−5 mol/L
    2. CaF2: 1.70 mg/100 mL
    3. Pb(IO3)2: 2.30 mg/100 mL
    4. SrC2O4: 1.58 × 10−7mol/L

15. Given the following solubilities, calculate Ksp for each compound.

    1. Ag2SO4: 4.2 × 10−1 g/100 mL
    2. SrSO4: 1.5 × 10−3 g/100 mL
    3. CdC2O4: 6.0 × 10−3 g/100 mL
    4. Ba(IO3)2: 3.96 × 10−2 g/100 mL

16. The Ksp of the phosphate fertilizer CaHPO4·2H2O is 2.7 × 10−7 at 25°C. What is the molar concentration of a saturated solution? What mass of this compound will dissolve in 3.0 L of water at this temperature?

17. The Ksp of zinc carbonate monohydrate is 5.5 × 10−11 at 25°C. What is the molar concentration of a saturated solution? What mass of this compound will dissolve in 2.0 L of water at this temperature?

18. Silver nitrate eye drops were formerly administered to newborn infants to guard against eye infections contracted during birth. Although silver nitrate is highly water soluble, silver sulfate has a Ksp of 1.20 × 10−5 at 25°C. If you add 25.0 mL of 0.015 M AgNO3 to 150 mL of 2.8 × 10−3 M Na2SO4, will you get a precipitate? If so, what will its mass be?

19. Use the data in Chapter 26 "Appendix B: Solubility-Product Constants (" to predict whether precipitation will occur when each pair of solutions is mixed.

    1. 150 mL of 0.142 M Ba(NO3)2 with 200 mL of 0.089 M NaF
    2. 250 mL of 0.079 M K2CrO4 with 175 mL of 0.087 M CaCl2
    3. 300 mL of 0.109 M MgCl2 with 230 mL of 0.073 M Na2(C2O4)

20. What is the maximum volume of 0.048 M Pb(NO3)2 that can be added to 250 mL of 0.10 M NaSCN before precipitation occurs? Ksp = 2.0 × 10−5 for Pb(SCN)2.

21. Given 300 mL of a solution that is 0.056 M in lithium nitrate, what mass of solid sodium carbonate can be added before precipitation occurs (assuming that the volume of solution does not change after adding the solid)? Ksp = 8.15 × 10−4 for Li2CO3.

22. Given the information in the following table, calculate the molar solubility of each sparingly soluble salt in 0.95 M MgCl2.

1. 1. 1.84 × 10−3 M
   2. 7.73 × 10−9 M
   3. 1.9 × 10−10 M

5. 1. 4.15 × 10−4 M
   2. 7.26 × 10−4 M
   3. 6.26 × 10−6 M
   4. 6.54 × 10−5 M
   5. 5.86 × 10−4 M

7. 22.4 mg; a secondary reaction occurs, where OH− from the dissociation of the salt reacts with H+ from the dissociation of water. This reaction causes further dissociation of the salt (Le Châtelier’s principle).

15. 1. 8.8 × 10−6
    2. 6.7 × 10−9
    3. 9.0 × 10−8
    4. 2.16 × 10−9

19. Precipitation will occur in all cases.