Solubility Equilibrium of Potassium Hydrogen Tartrate

1. Aim
1. To determine the solubility of potassium hydrogen tartrate (KHT) at various temperatures from 10°C to 50 °C, and determine the corresponding Ksp at these temperatures. 2. To obtain the changes in enthalpy and entropy of the dissolution of KHT from the dependence of Ksp on temperature. 2. Results and discussion

2.1 Collection of data
A portion of KHT (1 to 1.5 g) was added into about 100 mL of deionised water to prepare a saturated KHT solution. Several such solutions were prepared at various temperatures between 10°C and 50 °C, and filtrated into dry 250-mL conical flasks. For solutions made above or below the room temperature, their temperatures dropped or increased during filtrations. For each solution, two portion of 25.00±0.03 mL were pipetted into two 250-mL conical flasks and titrated with 0.07274 M of NaOH solution respectively with phenolphthalein as indicator. The temperatures of the KHT solutions and the corresponding volumes of NaOH solution used for titration are shown in Table 1. For each row, the temperature is the average of the temperatures immediately before and after the filtration, and the volume is the average of the two titrations.

It is noted that though the general trend is that the volume of NaOH increases with increasing temperature, there are some inconsistencies in this table. For example, the two volumes of NaOH at 23°C (obtained respectively by my partner and me) are different, and the volume at 42.5°C is lower than that at 37.5°C, contrary to the general trend. These will be discussed in the later subsection of error analysis, and we shall first proceed with calculations. 2.2 Determination of Ksp, ΔsolHm, and ΔsolSm

Taking the first row in Table 1 as example, the number of moles of NaOH used for titration is nNaOH=VNaOH×cNaOH=8.82×10-3L×0.07274 M=6.416×10-4mol. If it is assumed that the value for c(NaOH) is exact, then the uncertainty of n(NaOH), ∆n(NaOH), equals to the uncertainty of V(NaOH) times the value of c(NaOH). That is, ∆nNaOH=0.05×10-3 L×0.07274 M=0.036×10-4mol. As NaOH reacts with KHT in a 1:1 ratio, n(NaOH) is also the amount of KHT in the 25.00 mL of saturated KHT solution: nKHT=(6.416±0.036)×10-4mol, and the concentration of KHT is cKHT=n(KHT)V(KHT)=6.416×10-4mol25.00×10-3L=2.566×10-2M=cK+=c(HT-). Since aqueous KHT actually exists in the form of K+ and HT-, cK+=cHT-=2.566×10-2M

To determine the change in enthalpy and entropy of dissolution of KHT, a plot of ln(Ksp) versus 1T needs to be drawn, where T is measured in kelvins. The uncertainties are calculated by the equations lnKsp±ΔKsp=lnKsp±ΔKspKsp and 1T±ΔT=1T±ΔTT×1T. The values of 1T and lnKsp are shown in the last two columns of Table 2. However, the data in the 4th and the 7th rows should be omitted, as they show values of Ksp contrary to the general trend. For the remaining 6 rows, the average relative uncertainties of 1/T and ln(Ksp) are Δ1T1T×16=0.17%

ΔlnKsplnKsp×16=0.13%
These values were meant to display the error bars on the graph. However, they turned out to be too negligible to be shown clearly. The final plot is given in Figure 1. The LINEST function shows that the slope of the trendline is -4017 K, and the y-intercept is 6.690. The standard deviation of the slope is 240 K, and the standard deviation of the y-intercept is 0.80. They are taken to be the uncertainties of the slope and the y-intercept, respectively. The standard error of regression is 0.082, which is mostly contributed by the second point from the right, suggesting that the data of this point may also have human errors involved. The rest of the points agree well in a linear relationship. From the Van’t Holf equation lnK=-∆HRT+∆SR (assuming ∆H and ∆S do not vary greatly with temperature), the changes in enthalpy and entropy of dissolution are given by ∆solnHm=-slope×R=–4017±240 K×8.314 J K-1mol-1=33.4±2.0 kJ mol-1 ∆solnSm=y-intercept×R=6.690±0.80×8.314 J K-1mol-1=55.6±6.7 J K-1mol-1 ,

Figure 1 The plot of ln(Ksp) versus 1T. Detailed information is given in the paragraph above. 2.3 Discussion of errors
An online resource1 that records a similar experiment determines ∆solnHm to be 31.62 kJ mol-1 and ∆solnSm to be 51.5 J K-1 mol-1. Our peers G. Yeo and M. Yap got 37.1±2.1 kJ mol-1 and 67.3±6.7 J K-1mol-1. Therefore, our results are reasonably accurate and reliable. However, we had some data that obviously deviated from the general trend, so errors cannot be ignored. The primary factor is probably the difficulty in stablising the temperature within a range of 2 °C for long enough, such that KHT had time to fully precipitate or dissolve. In the collection of the data, we did not wait until the temperature stablise, but proceeded to filtration as soon as the temperature of the solution reached the desired value.

Therefore, the solutions may not be saturated with KHT, and causes a lower V(NaOH), which explains the 7th row of Table 2. Also, the temperature dropped significantly during filtrations (by about 5 °C) for solutions prepared at higher temperatures. It would be better if the filtration funnel were warmed. Another considerable factor is that the value of the concentration of the standard NaOH may not be constant throughout the experiment. NaOH reacts with CO2 in the air to form Na2CO3 and NaHCO3. The latter does not react with KHT, causing a higher value of V(NaOH).2 However, the above discussions do not explain the error in the 4th row of Table 2, where temperature needs not to be controlled but V(NaOH) is smaller. It could be due to inadequate stirring (causing an unsaturated solution). 3. Conclusion

We have determined the Ksp of KHT at various temperatures from 10°C to 50 °C (Table 2), from which ∆solnHm at near room temperature was found to be 33.4±2.0 kJ mol-1 and ∆solnSm to be 55.6±6.7 J K-1 mol-1 with reasonable accuracy. Errors are believed to be primarily caused by poor control over temperature, reactions of NaOH with CO2 in the air, and inadequate stirring.

References
1. Study of solubility equilibrium. http://www.bignerds.com/papers/77914/Study-Of-Solubility-Equilibrium/ (accessed October 14, 2014). 2. Solubility And K dependence on temperature. http://www.ukessays.com/essays/biology/solubility-and-k-dependence-on-temperature-biology-essay.php (accessed October 14, 2014).