Thermodynamics of Borax Dissolution Experiment 21

Experiment #21 Thermodynamics of Borax Dissolution Sample Calculations Trial 1: Na2CO3 + 2HCl  2NaCl + CO2 + H2O 0.207 g =0.00195 mol Mol N a2 C O 3= Mol HCl=0.00391 mol g 106 mol HCl M =0.00391 mol /0.0372 L=0.105 M ii. Trial 2: 2HCl + B4O5(OH)42- + 3H2O  4B(OH)3 + 2ClMol HCl=0.104 M × 0.0119 L=0.00124 molMol Borate =0.000619 mol Borate M =0.000619mol /0.005 L=0.1238 M i. iii. iv. v. vi. K sp =¿ ln(Ksp) = (-delta(H)/R)*(1/T) + delta(S)/R y = -11853x + 36.098 slope = -11853 K = -delta(H)/R delta (H)= 0.008314 kJ/mol*K * 11853 K = +98.55 kJ/mol Delta (S)/R = 36.098 Delta (S) = 0.008314 J/mol*K * 36.098 = + 0.300 kJ/mol*K Delta (G) = 98.56 kJ/mol – 298 K * 0.259 kJ/mol*K Delta (G) = 21.38 kJ/mol Data and Results: A. Standardization of "0.1 M HCl" Table 1. Data for Standardization Trials Mass Na2CO3 (g) Volume HCl (ml) 0.2070 37.20 0.2030 37.20 Mean [HCl]: St. Deviation [HCl]: [HCl] (mol/L) 0.105 0.103 0.104 0.0014 B. Determination of Ksp for Dissolution of Borax Table 2. Titration of Saturated Borate Solutions with HCl Temperature (K) Volume HCl, Endpoint (ml) 275 293 313 6.40 11.90 36.70 C. Dependence of Solubility on Temperature and [borate] (mol/L) 0.0666 0.1238 0.3817 Thermodynamic Parameters Table 3. Equilibrium Constants and Temperatures Temperature (K) Ksp 1/T (1/K) 275 1.180E-03 0.00364 293 7.590E-03 0.00341 313 2.224E-01 0.00319 ln Ksp -6.742 -4.881 -1.503 Plot 1. ln Ksp versus 1/T Discussion The purpose of his experiment was to quantify borate ion concentration resulting from the dissolution of borax, determine how the concentration of borate changes as a function of temperature and to compute the change in Gibbs free energy, enthalpy change, and entropy change from the concentration as a function of temperature data. The purpose of the standardization stage was to attain a precise value for the concentration of the hydrochloric acid so accurate measurements of the borate ion concentration can be made (using stoichiometry and titration techniques). We carried out two trials of standardization of HCl, which yielded very close values (0.103 and 0.105) making them very precise. Although the values were close, the most outstanding error has to do with the same volume of HCl neutralizing different masses of sodium carbonate (refer to Table 1). The masses, however, only differed with regards to the thousandth place making the differences almost negligible and therefore, the error was unlikely to have been very relevant to the experiment. The dissolution of borax can be represented by the following reaction: Na2B4O5(OH)4·8H2O(s) ↔ 2Na1+ (aq) + B4O5(OH)4 2- (aq) + 8H2O(l) or Borax(s) ↔ 2Na+(aq) + Borate2-(aq) Therefore, the Ksp expression can be modeled as follows:K sp =¿ To find the Ksp value, we carried out a titration of borax solution using a known concentration of HCl, which was found through its’ standardization. Methyl orange was used as an indicator to signify the equivalence point of the borax solution and HCl. The reaction that occurred as the titration was being carried out can be modeled in the following equation: 2HCl (aq) + B4O5(OH)42- (aq) + 3H2O (l)  4B(OH)3 (aq) + 2Cl- (aq) This titration reaction gave us the necessary values to calculate the concentration of the borate ions in the dissolution of borax solution from before. Part ii of the sample calculations illustrates how the calculations were carried out to find the concentration of borate ions. That concentration was put into the Ksp expression to find the value as shown in part iii of the sample calculations. Plot 1 shows a very strong correlation between temperature and K sp values (as the R-squared value is approximately 0.97). Higher temperature equates to a higher Ksp value, which is in accordance with the theory behind the experiment. The measure sign of ΔHº was positive which indicates the dissolution of borax is an endothermic reaction (absorbs surrounding energy). Moreover, the measured sign of ΔSº was found to also be positive which indicates the disorder of the system increases. There were few errors attributed to this part of the experiment. Typical errors may have influenced the results, however, including contaminated experimental tools, devices, etc. Moreover, we were only able to carry out two trials when standardizing the molarity of hydrochloric acid, which may have impacted our titration results. Percent error ΔHº = |(98.56-110)/110| * 100 = 10.4 % Percent error ΔSº = |(259-380)/380| * 100 = 31.8 % The percent error in the standard enthalpy change was relatively low at 10.4% indicating few errors. On the other hand, the percent error of the standard entropy change of reaction was three times as high at 31.8% indicating relatively significant errors influencing results. One primary source of error for that part of the experiment may have been related to the temperature of the third beaker (the hottest one). Between removing the beaker from the hot plate and getting it to the titration step, a burette broke, delaying the step and possibly allowing for the solution in that beaker to cool down significantly. This would have decreased the solubility of the borax in the water resulting in a lower Ksp value. This would have therefore skewed our data. The Ksp value would be much smaller if it were to be calculated from incomplete dissolution because the concentration of the borate ions would be calculated to be much lower resulting in a smaller Ksp value as is clear when you observe the values expression. If the volume of HCl recorded was consistently 15% higher than it should have been, that would result in a higher calculated borate ion concentration. This would result in a higher calculated Ksp value at each temperature which would cause a plot similar to Plot 1 to be much steeper meaning a higher absolute value of the slope and a higher standard enthalpy change of reaction value (because to find delta H, the slopes absolute value is multiplied by the gas constant as shown in part iv of the sample calculations). The entropy change is likely to increase as the y-intercept of the plot drawn increases (refer to part v of the sample calculations section). This is because to find the entropy change, the y-intercept of the plot is multiplied by the gas constant to find the standard enthalpy change of reaction. Conclusion The most relevant result of this experiment was finding that higher temperatures with higher solute concentrations result in higher Ksp values. Therefore, there is a strong negative linear correlation between the natural log of the Ksp value and the inverse of the temperature. It is possible to calculate the enthalpy change of the dissolution by multiplying the slope of the plot constructed by the ideal gas constant. Moreover, the entropy change can be found by multiplying the y-intercept of the graph by the ideal gas constant. This shows that as the temperature is increased, the reaction becomes more strongly product favored (because Ksp is larger). The calculations carried out also prove it is an endothermic reaction, which resulted in an increase of entropy and is non-spontaneous because the change in Gibbs free energy was found to be a positive value. The goal of this experiment was to find the molarity of borate ions in the dissolution reaction of borax at different temperatures in order to calculate the standard enthalpy change, entropy change, and change in Gibbs free energy. To do this, titrations had to be carried out which thus required a standardization procedure to ensure accurate results. There were few relevant errors related to this experiment, perhaps the only one affecting results related to the percent error of the entropy change of the reaction calculated which is likely to have occurred due to a drop in temperature and thus solubility as described in the discussion section. The relative consistency and accuracy of the rest of the results suggest a minor if any impact of errors on the rest of the results.