Applications of conductivity measurements: Calculating the solubility product of a partially soluble salt (Lab report)

Theory

The solubility of poorly soluble salts is expressed as the solubility product. That is the product of the concentration of ions in the solution which are in equilibrium with the solid ion. These concentrations can be determined via conductivity measurements. In this practical PbSO₄ is used.

                                 PbSO₄ ⇌ Pb²⁺ + SO₄^2-

Assume concentration of solid is a constant.

Concentration of Pb²⁺= concentration of SO₄^2- = C

                             \  Ksp = [Pb²⁺_aq] [SO₄^2-_aq]

                                    Ksp = C²

The measurement of the specific conductivity, K of the saturated solution leads to a value of the concentration.

                      i.e.       C = K/ Λ₀

                      As,   Ksp = C²

                               Ksp = (K/ Λ₀)²

 Λ₀ for PbSO₄ = 3.02 × 10^-2 m²Smol^-

Λ₀ = Molar conductivity at infinite dilution

Procedure

About 2g of finely powdered PbSO₄ was measured using the electric balance into a clean, dry watch glass.

It was added to a clean beaker. The watch glass was washed with distilled water and that washed water was also added to the beaker.

To remove impurities it was shaken by adding distilled water. It was kept aside for a while, for the salt to be collected at the bottom of the beaker. Then the upper layer was decanted and repeated this step for several times.

An empty reagent bottle was kept in a water bath at 24⁰C in order to maintain the temperature of the reagent bottle at 25⁰C.

Then the well- washed salt was added to the reagent bottle and added 100mL of distilled water.

After awhile without disturbing the solid, the clear upper solution was decanted into a clean beaker and the conductivity was measured.

Results

K of distilled water at 25⁰C = 4.2 µS/cm

K of PbSO₄ at 25⁰C = 39.2 µS/cm

Calculations

Corrected conductivity of PbSO₄ = (39.2 – 4.2) µS/cm

                                                           = 35.0 µS/cm

                                                                  = 35.0 × 10^-2 Sm^-

C = K/ Λ₀

C = 35.0 × 10^-2 Sm^- / 3.02 × 10^-2 m²Smol^-

C = 0.11589 molm^-3

C = 0.11589 × 10^-3 moldm^-3

PbSO₄ ⇌ Pb²⁺ + SO₄^2-

Ksp = [Pb²⁺_aq] [SO₄^2-_aq]

Ksp = C²

Ksp = (0.11589 × 10^-3 moldm^-3)²

         = 1.3430 × 10^-8 mol² dm^-6

Conclusion

Exact given Ksp at 25⁰C is 1.6 × 10^-8 mol² dm^-6. Practically obtained Ksp at 25⁰C is 1.3430× 10^-8 mol² dm^-6

As the both values are closer we can use conductivity measurements in order to calculated KSP.

Discussion

The precipitate was washed in order to remove impurities that may affect the results. It should be washed several times to obtain a well- washed precipitate. During this process, precipitate can be also removed. Therefore all 2g of the sample wouldn’t be left.

When maintaining the temperature  of 25⁰C, the water bath was kept at a temperature about 24⁰C. this is because we measure the temperature of the water bath assuming the temperature inside the reagent bottle is at 25⁰C. But actually the temperature of the solution inside would be slightly higher than the temperature of the water bath as the glass of the reagent bottle separates both. Therefore the temperature of the water bath was kept at lower temperature to obtain the required temperature for the solution.

Reagent bottle should be shaken time to time when it was kept in the water bath. This is to increase the dissociation and reach the equilibrium. If not, we might have not measured the conductivity at the equilibrium and that will alter the true Ksp value.

The calculated Ksp value is slightly smaller than the exact given Ksp value due to errors occurred during the experiment. Mainly the personal errors. Such as temperature maintaining errors, measuring errors and personal carelessness.

When preparing the solutions, the distilled water was added. Distilled water also contains ions it self. Therefore additional conductivity from the distilled water would be raised in the solution. For this reason the conductivity of the solution is corrected by deducting the conductivity of water.