# The Study Of Solubility Equilibrium

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The first part of this experiment aims to determine the solubility product constant of potassium hydrogen tartrate in water, and thereby determine how the enthalpy and entropy change of the dissolution reaction, according to the equilibrium KHC4H4O6 (s) ƒ› K+ (aq) + HC4H4O6- (aq) --- (1), changes with temperature. The second part of this experiment aims to examine the common ion effect through determination of the Ksp of KHC4H4O6 in potassium nitrate (KNO3) solution for varying K+ concentrations.

Results

## I.

Titrating 25.0cm3 of KHC4H4O6 solution with 0.07415M NaOH solution with phenolphthalein indicator gave the following results -

To determine Ksp at 302.15K:

Amount of NaOH used = Average volume of NaOH used - 0.07415M

= 13.35 - 10-3 - 0.07415

= 9.899 - 10-4 mol

= Amount of HC4H4O6- reacted

Total volume of the solution = Average volume of NaOH used + 25.0 cm3 of HC4H4O6- solution

= 13.35 + 25.0 = 38.35 cm3

Since [K+] = [HC4H4O6-], Ksp = [K+][HC4H4O6-] = [HC4H4O6-]2 = 0.25812 = 6.662-10-4

## Table 1: Solubility product constant of potassium hydrogen tartrate at various temperatures

Temperature / K

Average VNaOH used / cm3

Amount of NaOH used / mol

Amount of HC4H4O6- reacted / mol

[HC4H4O6-] / mol dm-3

Solubility of HC4H4O6-/ mol dm-3

Ksp

ln Ksp

1/T / K-1

282.5

6.65

0.0004931

0.004931

0.01558

0.01558

0.0002427

-8.324

0.003540

292

9.25

0.0006869

0.006869

0.02003

0.02003

0.0004010

-7.821

0.003425

302

13.35

0.0009899

0.009899

0.02581

0.02581

0.0006663

-7.314

0.003311

311.5

18.35

0.001361

0.01361

0.03139

0.03139

0.0009852

-6.923

0.003210

322.5

26.65

0.001976

0.01976

0.03826

0.03826

0.001464

-6.527

0.003101

Given that ΔG°reaction = ΔH°reaction - TΔS°reaction ---------- (2) and ΔG°reaction = - RT ln K ---------- (3), combining the two equations and rearranging gives us the linear function:

## ---------- (4)

Using the data obtained in this experiment to plot this linear function gives Graph 1 shown below:

## Graph 1: Linear curve of ln Ksp against 1/T

Equation of line

## -ln Ksp = - 4113(1/T) + 6.264

=- 4113

ΔH°reaction

=- (- 4113 - 8.314)

=+34 195 J mol-1 (4s.f.) =+34.195 kJ mol-1

Uncertainty (standard deviation)

= ± 105.3 - 8.314 = ± 875.5

## ΔH°reaction

## = + 34 195 ± 875.5 J mol-1

=6.264

ΔS°reaction

=6.264 - 8.314

=+52.08 J K-1 mol-1 (4s.f.)

Uncertainty (standard deviation)

=± 0.3497 - 8.314 = ± 2.907

## ΔS°reaction

## = + 52.08 ± 2.907 J K-1 mol-1

## ΔG°reaction = [+ 34 195 - T (+ 52.08)] J mol-1

Solubility of HC4H4O6- and Ksp increases with increasing temperature, and a positive ΔH°r value shows that the dissolution of KHC4H4O6 is an endothermic process. Since the magnitude of ΔS°r is smaller than that of ΔH°r, ΔG°r is always positive in the temperature range of 282.5K to 322.5K, as carried out in this experiment. This indicates that the dissolution of KHC4H4O6 is always non-spontaneous for this temperature range, and hence KHC4H4O6 is a sparingly soluble salt.

## II.

Titration of KHC4H4O6 in KNO3 solutions of different concentrations with 0.07413M NaOH solution with phenolphthalein indicator at room temperature to observe the common ion effect gave the following results -

To determine the Ksp and solubility of HC4H4O6- at room temperature when [KNO3] = 0.01M:

Amount of K+ from KNO3 = 0.01 - 70 - 10-3 = 7.00-10-4 mol

Amount of NaOH used = 11.45 - 10-3 - 0.07413 = 8.508 - 10-4 mol

= Amount of HC4H4O6- reacted

Total amount of K+ = (7.00-10-4) + (8.508 - 10-4) = 1.55 - 10-3 mol

Total volume = 25.0 + 11.45 = 36.45 cm3

[K+]total =

Ksp =

## Table 2: Solubility product constant of potassium hydrogen tartrate at various potassium nitrate concentrations

T / K

[KNO3] / M

Average volume of NaOH used / cm3

Amount of NaOH / mol

Amount of HC4H4O6- reacted / mol

Total amount of K+ / mol

[K+]total / mol dm-3

Solubility of HC4H4O6- / mol dm-3

Ksp

301

0.01

11.45

0.0008509

0.0008509

0.001551

0.04255

0.02334

0.0009932

301

0.02

10.35

0.0007691

0.0007691

0.002169

0.06136

0.02176

0.001335

302

0.03

9.50

0.0007059

0.0007059

0.002806

0.08133

0.02046

0.001664

302

0.04

8.60

0.0006391

0.0006391

0.003439

0.1024

0.01902

0.001947

## Graph 2: Graph of solubility of KHC4H4O6 (M) against [K+]total (M)

The data obtained in this part of the experiment shows that solubility of HC4H4O6- decreases with increasing total K+ concentration for a given temperature (302K). This is due to the common ion effect - the presence of the common ion K+ suppresses the dissociation of KHC4H4O6 according to (1), since K+ concentration is greater than the equilibrium KHC4H4O6 concentration. The greater the K+ concentration, the lesser the extent of dissociation of KHC4H4O6, and hence the less soluble HC4H4O6- is in water.

Discussion

The solubility of a substance is the amount of the substance dissolved in 1 L of its saturated solution for a given temperature. Ksp on the other hand, is the product of the ion concentrations raised to their respective powers on the dissolution equilibrium equation, and is constant for a given temperature.

Since the dissolution of KHC4H4O6 is an endothermic process, when temperature increases, the forward reaction is favoured to absorb the excess heat. This causes Ksp values to increase with increasing temperature, as observed, since concentration of products, i.e. [K+] and [HC4H4O6-], increases. The heat absorbed is used to overcome solute-solute and solvent-solvent interactions, such that solute-solvent interactions can form during the dissolution process. Also, as a solid dissolves, entropy of the system is increased, since the greater number of liquid particles increases disorderliness. Hence as temperature increases, ΔG°r will be increasingly negative, indicating that the dissolution of KHC4H4O6 gets increasingly spontaneous as temperature increases.

In this experiment, ΔH°r and ΔS°r are assumed to be insignificantly dependent on temperature.

ΔrH(T2) = ΔrH(T1) + (T2-T1) ΔrCp ---------- (5) (Atkins, 2006)

From Kirchhoff's law (5), ΔrH is dependent on temperature, assuming that constant-pressure heat capacities (Cp) is independent of temperature. For the above assumption to hold true, ΔrCp should be insignificant, i.e. (Cp) of the products and reactants should have approximately equal values. Since Cp is affected by how much of a substance there is in the solution - the greater the number of particles, the greater the amount of heat energy needed to raise the overall temperature of the solution by 1K - and the KHC4H4O6 solution used in titration is saturated, the amount of substance in the solution can be approximated to be the same. Thus, Cp of the products and reactants can be approximated to be the same, and hence ΔrCp is minimum. Similarly, since ΔS°r is dependent on Cp as well, we can assume it to be insignificantly dependent on temperature as well.

For the above argument to hold true, the KHC4H4O6 solution used in titration must be saturated, and steps to ensure this should be taken - one, continual swirling of the solution before filtration to ensure all solid has been dissolved; two, maintaining supposed temperature of the solution immediately before filtering, since the saturated solution is filtered in small portions; three, apparatus used to contain the filtrate must be dry such that the saturated solution is not diluted by the presence of any water. General titration techniques were also employed, such as rinsing apparatus with the solutions that they are to contain to ensure no contamination and accurate concentrations, as well as keeping the amount of phenolphthalein indicator, a weak acid, to a minimum, to prevent the lowering of the pH of the solution, which results in more than the required amount of NaOH needed to react with the saturated KHC4H4O6 solution.

For Section 1 of this experiment, comparing experimental and literature Ksp values gives the following -

At approximately 302K:

Literature value of solubility of KHC4H4O6 in water = 7.3693 - 103 kgsalt/kgwater (Lopes, 2001)

Literature Ksp value = [(7.3693 - 103 gsalt/mlwater) ÷ (188.1772 g mol-1)]2

= (39.161 - 10-3 mol L-1)2

= 1.534 - 10-3

Experimental Ksp value (Section 1) = 6.663 - 10-4

Mean Ksp value (Section 2) = 1.485 - 10-3

The literature Ksp value in Section 1 of this experiment was 2.302 times higher than that of the experimental Ksp value at 302K. Besides, since Ksp is only dependent on temperature, Ksp values at the same temperature should be constant and independent of concentrations. The mean Ksp value obtained in the Section 2 of this experiment, however, was 2.229 times greater than that obtained in Section 1 of this experiment, though it only had a 3.300% difference from the literature Ksp value.

The abnormally low Ksp value obtained in Section 1 of this experiment indicates less than expected K+ and HC4H4O6- concentrations in the solution, and can stem from either the effect of a deviation from temperature, or from the solution being unsaturated. However, the data obtained in this experiment showed an accurate trend expected of Ksp values for increasing temperature, hence eliminating temperature deviation as a possible source of error. Furthermore, this trend also reflects expected solubility trends, and is sufficient in demonstrating the aims of this experiment.

Conclusion

The aims of this experiment have been met, as shown by the increasing trend of Ksp values for increasing temperature, as well as the decreasing solubility of HC4H4O6- in water for increasing K+ concentration, due to the common ion effect. These combined prove that Ksp is only dependent on temperature, given that care has been taken to ensure a saturated solution when carrying out the experiment.

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