Thermodynamic Analysis of Borax Solubility in Water

Abstract

In this experiment, the Gibbs free energy change (ΔGo), the enthalpy change (ΔHo), and the entropy change (ΔSo) values of the solvation of borax in water at 45.0 °C and 55.0 °C were studied by using the thermodynamics equations and the Ksp values of saturated borax solutions at 45.0 °C and 55.0 °C. The concentrations of saturated borax solutions determined by titrating with hydrochloric acid at 45.0 °C and 55.0 °C were 0.444 M and 0.796 M, respectively. The Ksp values based on the saturated borax solutions were calculated to be 0,3501 at 45.

0 °C and 2.017 at 55.0 °C.

The larger Ksp value at higher temperature indicated that increasing temperature resulted in the increase in solubility of borax in water. The values of ΔGo found using thermodynamics equation were 2.775 kJ/mol for 45.0 °C and -1.913 kJ/mol for 55.0 °C, which indicated that the solvation of borax was spontaneous at 55.0 °C while it was nonspontaneous at 45.0 °C. The value of ΔHo for both temperatures was calculated to be 1.519x102 kJ/mol, which was fairly close to the literature value of 110 kJ/mol with percent (%) error of 38,1 %.

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The value of ΔSo for both temperatures was calculated to be 469 J/molK, which was also fairly close to the literature value of 380 J/molK with percent (%) error of 23.4 %.

Introduction

The extent to which a solid or salt can dissolve in an aqueous solution at a particular temperature is different for each solute. When the maximum amount of solute is dissolved in the solvent, the resulting solution is said to be saturated and any extra solute that gets added into this solution precipitates.

In a saturated solution, a chemical equilibrium exists so that the concentrations of reactants and products of a reaction stay constant due to the rate of product formation being same as the rate of reactant formation.

From this equilibrium reaction, a solubility product constant (Ksp), which indicates how well a solute can dissolve in an aqueous solution, can be determined using the formula. A high Ksp value indicates that the salt is highly soluble, and a low Ksp value indicates that the salt is only slightly soluble. Ksp value can further be used to calculate the thermodynamic quantities such as the Gibbs free energy change of the reaction (ΔGo), the enthalpy change of the reaction (ΔHo), and the entropy change of the reaction (ΔSo). Positive ΔGo indicates that the reaction is spontaneous, while negative ΔGo indicates that it is nonspontaneous. Positive ΔHo means that the reaction is endothermic, requiring heat as a reactant, while negative ΔHo means that it is exothermic and therefore releases heat as a product. Positive ΔSo suggests that the randomness or disorder increases when products form, while negative ΔSo suggests that the randomness decreases when products form.

This experiment aimed to determine the values of ΔGo, ΔHo, and ΔSo after dissolving borax in distilled water at 45.0 °C and 55.0 °C. Saturated solution of borax at 55.0 °C was prepared by dissolving solid borax in water at 55.0 °C until extra salt precipitated. The solution was then decanted to remove the precipitates and titrated with 0.200 M HCl to find the molar concentration of the borax dissolved solution. The same procedure was performed to prepare and determine the concentration of the borax solution at 45.0 °C. Methyl red indicator was used during the titration at both degrees to allow for visual inspection of the equilibrium points.

The Ksp values of the borax solution at each temperature was calculated using the equation depicted in figure 4 based on the dissociation reaction. ΔGo at each temperature was then calculated by using the Ksp value and the thermodynamics equation. The Ksp values and temperature in Kelvin values for both temperatures and another thermodynamics equation shown in figure 6 were then used for the calculation of ΔHo, which is not affected by temperature. The last thermodynamics quantity, ΔSo, was determined by using the equation in figure 7 and ΔGo and ΔHo values calculated. Finally, the experimental ΔHo and ΔSo were compared with the literature values.

aA(s) ⇌bB(aq) + cC(aq)

Ksp = [B]b[C]c

Na2B4O7·10H2O(s) ⇌ 2 Na+(aq) + B4O5(OH)42-(aq) + 8 H2O(l)

Ksp = [Na+]2[B4O5(OH)42-]

Ksp = (2x)2 (x) = 4x3 where x = [Na2B4O7·10H2O]

Ksp = [Na2B4O7·10H2O]3

ΔGo = - RTlnK where R = 8.314 J/molK

ln⁡(K1/K2)= (-ΔH)/R [1/T1-1/T2]

ΔGo = - ΔHo - TΔSo

Experimental Methods

Part A. Preparation of Saturated Solution. Approximately 25 g of borax was mixed with about 1 mL of distilled water. The mixture was heated until its temperature reached 57 or 58°C while being constantly stirred. About 100 mL of distilled water was also heated alongside the beaker containing the borax solution. The temperature of the mixture was constantly monitored in order to prevent it from exceeding 60°C and decomposing the borax.

Part B. Collection of Saturated Solution Samples at Different Temperatures and Titration with HCl. At 57 or 58°C, the mixture was removed from heat and stirred until it reached 55°C. The solution was then left to settle while maintaining the temperature near 55°C. The exact temperature of the solution at this point was recorded. 5.0 mL of the supernatant was immediately decanted into a 10 mL graduated cylinder that was pre-warmed with the heated distilled water from Part A in order to prevent the borax from precipitating due to the cold temperature of the glass. The supernatant was transferred to another beaker and saved for titration.

The 10 mL graduated cylinder was rinsed with the heated distilled water from Part A and added to the same beaker containing the supernatant. The remaining borax mixture was then cooled to 45°C while being stirred. Following the same sample collection process as 55°C, the borax sample for titration was prepared by allowing the borax mixture to settle and decanting 5.0 mL of it into the pre-warmed graduated cylinder then into a new beaker. Distilled water was added to each saturated solution sample to make the total volume 100 mL. 5 to 6 drops of methyl red indictor were then added to both samples and the samples were heated to re-dissolve any precipitated borax. The samples were titrated with 0.2 M hydrochloric acid (HCl) until the solution color changed from yellow to salmon pink at the titration endpoints.

Data Tables

Table 1: Preparation of Saturated Borax Solution

Table 2: Titration Results

Table 3: Ksp Values

Table 4: Thermodynamic Quantities

Standard Entropy Change (ΔSo) for Temperatures 45.0 °C (318K) and 55.0 °C (328K)

The solubility product constant (Ksp) values of borax at 45.0 °C and 55.0 °C were calculated to be 0.3501 and 2.017, respectively. Larger Ksp value at 55.0 °C suggested that borax dissolved better in higher temperature. The experimental value of the Gibbs standard free energy (ΔGo) for the solvation reaction of borax in water at 45.0 °C was determined to be 2.775 kJ/mol. The positive value of ΔGo indicated that this reaction was non-spontaneous. On the other hand, the experimental value of the Gibbs standard free energy (ΔGo) for the dissociation of borax in water at 55.0 °C was -1.913 kJ/mol, suggesting that this reaction was spontaneous.

The experimental value of the standard enthalpy change (ΔHo) for borax dissociation at both temperatures was calculated to be 1.519 x 102 kJ/mol. Based on the positive value of ΔHo, dissociation of borax was an endothermic reaction. The experimental value of the standard entropy change (ΔSo) at both temperatures was calculated to be 469 J/Kmol. The experimental values of ΔHo and ΔSo were fairly close to the reported literature values of 110 kJ/mol and 380 J/molK10 with percent errors of 38.1% and 23.4%, respectively.

Results and Conclusion

The solvation of borax in water demonstrates temperature-dependent solubility, with higher solubility at increased temperatures. The spontaneous nature of the solvation at 55.0 °C contrasts with the non-spontaneity at 45.0 °C. The calculated ΔHo and ΔSo values suggest the reaction is endothermic with an increase in system entropy. Although the experimental values of ΔHo and ΔSo slightly deviate from literature values, they underline the significance of temperature in solute solubility and reaction spontaneity.