Introduction

The purpose of the lab was to determine how the solubility of Borax (Na2B4(OH)4) and other thermodynamic quantities such as enthalpy, entropy, and Gibbs free energy depend on temperature. When Sodium borate octahydrate (Borax) dissociates in water it forms two sodium ions, one borate ion and eight water molecules. The chemical reaction is shown as:

(reaction 1)

A simple acid-base titration can be used to determine the concentration of the borate ion base. By dissolving Borax into distilled (DI) water at two different temperatures, the amount of borate that went into the solution at each temperature can be measured. The balanced equation:

(reaction 2)

represents the titration of the borax where the endpoint of the reaction is signaled by the change of bromocresol purple indicator, from purple to yellow. To understand how temperature affects thermodynamic quantities equation 1 – equation 4 shown in Appendix A were used to calculate the solubility product constant, enthalpy, entropy, and Gibbs free energy respectively. Using these equations, the aforementioned thermodynamic quantity’s dependence on temperature is more understood by the lab’s completion.

Experimental Methods

To start the experiment two separate titrations were set up, one at room temperature and the other in an ice bath. For the room temperature Borax titration, a saturated solution was created by adding 1.5 grams of solid Borax to 50mL of DI water and a stir bar to a beaker that was stirred for at least ten minutes. To assure that equilibrium was sustained throughout the stirring, it was stopped periodically to assure that there was solid Borax present in the beaker keeping a saturated solution. Next, a burette was filled with approximately 50mL of the .103M Hydrochloric Acid solution (HCl).

For the room temperature Borax titrations the temperature of the saturated solution was measured first. Then, DI water and bromocresol purple indicator were added to two separate flasks of the saturated solution. Each HCl solution was then titrated to its yellow endpoint and the HCl volume was recorded. For the ice bath temperature Borax, the titration was completed with the same procedure as the room temperature Borax.

Results and Discussion

For both room temperature titrations at the start of the lab, the initial temperature was found to be 18˚C, while the two titrations set in an ice bath were found to be 8˚C. After each titration was complete, the volumes of the .103M HCl solution needed to titrate the saturated solution were recorded in Table 1.

After the Borax dissociated in the water it was important to calculate the concentrations of both the Na+ and the , because these are needed to calculate the solubility product constant (Ksp) of the solution. By using the titration endpoint, the equivalence point was approximated and the latter was calculated.

The equation:

was used to find the appropriate values of and are shown in Appendix B. To find the concentration of Na+, the concentration of the borate ion was multiplied by two because the ratio presented in reaction 1 shows that for every mole of borate produced there are two moles of Na+ produced. The values were then averaged for both room temperature titrations as well as the two ice bath titrations. The values found were shown in Table 2.

Table 2. Concentration of Ions

After these values were calculated, the average concentrations of both the borate ion and N+ ion were used in equation 1 to find the solubility product constant at room temperature and ice bath temperature. The Ksp values were found to be 1.794*10-3 for room temperature and 1.271*10-3 for the ice bath. The steps used to find this value are shown in Appendix C.

The solubility of a salt is dependent on the temperature of the solution. When equilibrium is established in a saturated solution such as the one created in the lab, the rate of the formation of ions in solution is equal to the rate of precipitation of solid. The values found for the solubility product constant show that as temperature decreases in a saturated solution in equilibrium, the formation of ions slows down significantly.

The next thermodynamic quantity that was calculated was enthalpy using equation 2. The enthalpy change for both room temperature and the ice bath were found to be equal to each other at a value of 23.25 kJ/mol. The solution process for ΔH˚ is shown in Appendix D.

Enthalpy describes the amount of energy that is gained or lost in a system such as the titration solutions that were used in this particular experiment. Equation 2 shows that as the difference in temperatures of the two titration solutions decreases the energy gained by the system increases. The equation presents the importance of temperature in regard to the energy gained or lossed by a system by showing the relationship between temperature and the solubility constant.

After the enthalpy change was found, equation 3 was used to find the change in entropy (ΔS˚). Similar to that of enthalpy, the values for entropy were equal to each other at a value of 27 J/mol*K. The solution for the change in entropy is shown in Appendix E.

Entropy measures the amount of disorder the solution possesses. Equation 3 displays that as the temperature of the solution increases the less disorder or entropy the solution has. This is significant in analyzing the importance temperature has in calculating the entropy of a solution.

Finally, the Gibbs free energy (ΔG˚) could be calculated using equation 4. The room temperature value of Gibbs free energy was equal to 15.58 kJ/mol while the ice bath value was equal to 15.30 kJ/mol. The solution set that was used to calculate these values is shown in Appendix F.

After the values of solubility product constant, enthalpy, entropy and Gibbs free energy were calculated; the results were placed in Table 3.

Table 3. Thermodynamic Quantity Values

Next, the percent error values for enthalpy and entropy were calculated using the accepted literature values of ΔH˚ = 110 kJ/mol and ΔS˚ = 380 J/mol*K. To calculate the percent error the equation:

was used where the errors were equal to 78.8% for enthalpy and 92.9% for entropy.

For this lab, the percent error was extremely high when calculating entropy and enthalpy of the titrated solutions. Some possible sources of error when the experiment was conducted was reading the thermometer and recording the corresponding temperature. Also, when recording the volume of HCl. Finally, the percent error could be extremely high because of the fact that the given values are given at standard temperature and pressure while the values that were calculated in this specific experiment were not at standard temperature. Therefore, the final values for the solubility product constant, enthalpy, entropy, and Gibbs free energy do not correlate to the accepted literature values given in the lab.

Conclusions

The purpose of conducting this experiment was to understand how the solubility of Borax and other thermodynamic quantities such as solubility product constant, enthalpy, entropy and Gibbs free energy depend on temperature. By dissociating Borax in DI water into Borate and Sodium ions, an acid-base titration allowed the group to calculate the aforementioned quantities. The major findings of the lab was that the Enthalpy of the titrated solutions was equal to 23.25 kJ/mol, while the entropy of the solutions was 27 J/mol*K. Using these values the importance of temperature in regards to thermodynamic quantities was evident and allowed the group to realize the relationships between the aforesaid quantities and temperature.

References

1. Applications of Chemistry II, Spring 2013: Experiment 5, Thermodynamics of Borax, Department of Chemistry, United States Air Force Academy, February 2013.

Documentation: C3C James Stofel and C3C Charlie Meyen proofread my paper and corrected small grammar errors and assisted me with transitions and general flow of the lab report.