Evaluating the Solubility Product Constant of an Ionic Salt from Titrations

Calculating Ksp of an Ionic Salt from Titrations

Introduction

Different substances dissolve to different degrees in water. Some ionic salts may completely dissociate into their ions, while some salts may only partially dissociate. The degree to which a substance is soluble in water is called Ksp, or the solubility product constant, which is unitless. For substances that dissolve very well in water, their Ksp will be larger, and substances that don't dissolve very well in water will have a smaller Ksp. Ksp can be calculated by multiplying the concentrations of the products and dividing by the product of the concentration of the reactants. Each product and reactant concentration is raised to the power of its stoichiometric coefficient before multiplying them together.1 Solids are not included in Ksp expressions, which means for ionic salts, their Ksp will just be the product of the concentrations of the ions they form.

Experimental

A mass of potassium hydrogen tartrate, or KHT, was weighed out to get between 1.9 and 2.0 grams. The KHT was moved into a 400-mL beaker, and about 150 mL of distilled water was added. The solution was stirred continuously with a stirring rod, to dissolve as much KHT as possible. A piece of dry filter paper was placed in a dry funnel, and the KHT solution was poured into the funnel with a 250-mL beaker at the receiving end. This filtered out any solid pieces of KHT to create a saturated solution. A sodium hydroxide solution was obtained and the concentration was recorded. Two 50-mL burets were rinsed with distilled water. One buret was then rinsed with the KHT solution, and the other buret was rinsed with the NaOH solution. The buret rinsed was KHT was then filled to about the 0.00 mL line, and the exact volume was recorded. The buret rinsed was NaOH solution was also filled to about the 0.00 mL line, and the exact volume was recorded. The KHT solution was drained from the buret into a 250-mL Erlenmeyer flask, and the exact volume was recorded. A few drops phenolphthalein indicator were added to the flask. Sodium hydroxide was added to the flask from the buret until the solution changed to a permanent pink color, and the exact volume of NaOH was recorded. Two more titrations were done in this same process, to get a total of three trials.

Results

Table 1: Concentration and Volumes of Titrated Solutions

Trial 1 Trial 2 Trial 3

Volume of NaOH initial (mL) 0.20 6.03 11.78

Volume of NaOH final (mL) 6.03 11.78 17.70

Concentration of NaOH (M) 0.198 0.198 0.198

Volume of KHT initial (mL) 0.00 0.00 11.14

Volume of KHT final (mL) 35.00 35.00 46.20

Concentration of KHT (M) 0.0330 0.0325 0.0334

Average solubility of KHT (M) 0.0330

Ksp of KHT 0.00109 0.00106 0.00112

Average Ksp of KHT 0.00109

Calculations

1. Concentrations of KHT

MAVA = MBVB

VB = 6.03 mL - 0.20 mL = 5.83 mL * (1 L / 1000 mL) = 0.00583 L

VA = 35.00 mL - 0.00 mL = 35.00 mL * (1 L / 1000 mL) = 0.03500 L

MA = (0.198 M * 0.00583 L) / (0.03500 L) = 0.0330 M

2. Concentrations of K+ and HT-

0.0330 M KHT * (1 mol K+ / 1 mol KHT) = 0.0330 M K+

0.0330 M KHT * (1 mol HT- / 1 mol KHT) = 0.0330 M HT-

3. Average solubility of KHT

(0.0330 M + 0.0325 M + 0.0334 M) / 3 = 0.0330 M

4. Ksp of KHT

Ksp = [K+][HT-]

Ksp = (0.0330 M)2 = 0.00109

5. Average Ksp of KHT

(0.00109 + 0.00106 + 0.00112) /3 = 0.00109

6. Percent error

(|0.00109 - 0.000917| / 0.000917) * 100% = 18.8%

Discussion

The volumes for each of the three trials were supposed to be the same, but there were small variations between each one. The concentration of sodium hydroxide was known, and the volumes of NaOH and KHT could be calculated by subtracting the initial volume from the final volume. Using these three known values and the dilution law, the concentration of KHT could be calculated. Because KHT dissolves into F in one to one ratios, the concentration of KHT was equal to the concentration of K+ and HT-. Ksp was determined by multiplying the concentration of K+ and HT-, and it was compared to the actual value. The percent error was moderately high, perhaps due to an overshoot during the titration, because the phenolphthalein indicator turned a dark purple in every trial. Another source of error may have been from excess water in the buret and beakers that may have diluted the solutions.

Conclusion

The percent error for this experiment was 18.8%, which is beyond the acceptable 5% margin. The experimental procedure ensured a saturated solution of KHT to be titrated with a solution of NaOH at a known concentration, but excess water may have altered these concentrations. Both the actual (0.000917) and experimental (0.00109) Ksp for KHT were very small numbers, which means KHT does not dissociate much into its ions in water; the equilibrium between KHT and K+ and HT- is reactant favored. Further experimentation could be done by titrating other solutions and determining their Ksp, to judge how good other solutions dissolve compared to KHT.