Solubility and K Dependence on Temperature

An exothermic reaction is one which has a negative ΔH value while an endothermic reaction is one which has a positive ΔH value. Based on the results, the dissolution of potassium hydrogen tartrate has a ΔH° value of 3.89 *104. Therefore as 3.89 *104 > 0, the dissolution of potassium hydrogen tartrate is endothermic, i.e. heat must be added to dissolve the salt in water. This is further supported by the negatively sloped graph above. It can be inferred from the graph that the higher the temperature, the greater the solubility of potassium hydrogen tartrate.

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The spontaneity of a reaction depends on the change in enthalpy (ΔH) and entropy (ΔS), as well as on the absolute temperature. The change in the Gibbs free energy (ΔG) can be used to determine if a reaction is spontaneous or not. Represented by the equation ΔG° = ΔH° – TΔS°, when ΔG is negative, a process proceeds spontaneously in the forward direction. When ΔG is positive, the process proceeds spontaneously in reverse. When ΔG is zero, the process is in equilibrium, with no net change taking place over time.
Therefore as the ΔG° calculated at both 10.0°C and 50.0°C are positive, it can be deduced that the dissolution of potassium hydrogen tartrate is non-spontaneous in the forward direction at the temperatures tested (10.0°C to 50.0°C). The process however proceeds spontaneously in reverse at the mentioned temperatures. In fact, based on the results, the dissolution will only be spontaneous at 513.6K (ΔH° / ΔS°) and above.
Although both entropy and enthalpy are functions of temperature, this experiment assumes that ΔH° and ΔS° do not change significantly over the range of temperatures used. This assumption is valid over relatively small ranges. In this experiment, the various measurements occur within a small range of 40K. Therefore it is safe to assume that the values of ΔH° and ΔS° are relatively invariant over the small changes in temperature.
Many reasons could cause the experimental value to disagree with the literature value. Probably the most significant source of error would be the inability to maintain the respective temperatures during the slow step of filtering the salt solution after heating/cooling. Gravity filtration was adopted in this experiment, and although the filter papers were fluted to encourage rapid filtration, the process still spanned several minutes. During this time, the temperature of the salt solution could have easily deviated from the desired temperatures towards room temperature. This could cause undesirable recrystallization/dissolution of the salt, thereby, affecting the molarity of the filtrate. This limitation could be overcome by using vacuum filtration to minimize such errors.
Besides the possible undesirable recrystallization/dissolution before filtering was over, recrystallization could also occur in the filtrate before the 25mL aliquots were obtained. This would only apply to the samples that were experimented at temperatures above room temperature. As the filtrate cools, the salt would recrystalise, causing a change in homogeneity and molarity of the filtrate. Although the protocol was to immediately aliquot 25mL after filtration, the time for the filtrate to reach at least 25mL was sufficient enough for significant cooling of the solution, with the large surface area of the solution filtering dropwise and the contact with the cool conical flask. A possible solution to this problem is to heat the filtrate again after filtration before aliquoting to ensure all the salts that may have recrystalised dissolve. However, the heating should be gentle to prevent significant lost of solvent and prevent change in molarity.
Another source of error would be the assumption that the molarity of the given NaOH solution is accurate. Alkaline solutions such as NaOH absorb carbon dioxide from the atmosphere according to the reaction: CO2 + 2OH- ↔ + CO32- + H2O. Since hydroxide ion is consumed by this reaction, the concentration of the sodium hydroxide solution will be changed. Therefore the precise concentration of the NaOH solution may not be the value that what was stated on the bottle, especially if the solution was prepared long before the experiment was conducted. Standardization of the NaOH solution should be done just before the experiment is conducted.
Although in this experiment, the molarity of the provided NaOH solution was assumed to be accurate and no further standardization was done, precautions were taken to protect the solution from the carbon dioxide that is always present in the atmosphere. As during titration, the NaOH solution in the buret will be exposed to air, the buret used was prepared for use only when it was needed, and fresh sodium hydroxide should be added if it.
The initial steps of the procedure was to obtain approximately 200ml of NaOH solution from the stock bottle. To obtain higher accuracy though, the NaOH taken from the stock bottle should not be more than what is needed for one titration. More NaOH solution should be taken from the stock bottle when needed.
Other precautions were also taken during the experiment to reduce contamination. Apparatus were scrupulously cleaned and rinsed with solutions that they were to contain before use. The experiment was also cautiously done to prevent loss of material through spillage, splashing or splattering.
Conclusion
This experiment successfully demonstrated the relationships between state functions, including entropy and enthalpy, free energy, spontaneity, and equilibrium constants. Since ΔH° and ΔS° were both positive, the dissolution of potassium hydrogen tartrate was spontaneous at high temperatures. This means that the potassium hydrogen tartrate needed energy from the surroundings to dissolve. The reverse process however, is spontaneous.
A significant percentage error was obtained by comparing of the obtained solubility product constant with the literature value. Although precautions were taken to ensure accuracy, such an error proves that solubility product constants are extremely difficult to obtain experimentally because of limitations of the experiment and the necessity to identify all chemical species and processes present in the chemical system used to obtain the values.