Thermodynamics and Equilibrium

College of Western Idaho

ABSTRACT

The purpose of this experiment was to measure how the solubility product constant (Ksp) changes with temperature and to use this information to determine ΔH, ΔS, and ΔG. The reaction studied was the temperature dependent solubility of borax (sodium tetraborate decahydrate, Na2B4O7•10H2O) in water. The conjugate base in this reaction was titrated with 0.498 M HCl dispensed from a burette. The resulting amounts were used to calculate the Ksp values at different temperatures and ΔH and ΔS were calculated from these to be 150 (± 70) kJ/mol*K and 0.5 (± 0.2) kJ/mol*K, respectively. The value of ΔGº at 25 ºC was found to be -1.6 kJ/mol*K. For this experiment, the ΔH and ΔS values were assumed to be independent of temperature.

INTRODUCTION

The reaction in which borax dissolves in water to tetraborate ions and sodium ions in solution is:

+ 2− Na2[B4O5(OH)4]·8H2O (s) → 2Na (aq) + B4O5(OH)4 (aq) (1)

The equilibrium constant for this type of reaction is a solubility product, Ksp. In this case, the solubility product is expressed by:

+ 2 2- Ksp = [Na ] [B4O5(OH)4 ] (2)

If x is used to represent the concentration of the dissolved tetraborate ion, using stoichiometry, the sodium ion is twice the concentration, and thus the equilibrium expression can be represented as:

+ 2 2- 2 3 Ksp = [Na ] [B4O5(OH)4 ] = [2x] [x] = 4x (3)

The goal of this experiment is to determine Ksp at different temperatures. To do so, the concentration of tetraborate ion is needed as a measurement. To determine the concentration of the tetraborate ion, a titration with a strong acid can be used as the tetraborate ion is a weak base that reacts with water to produce two hydroxides. This reaction is represented by:

2- - B4O5(OH)4 (aq) + 5H2O(l) ⇌ 4H3BO3(aq) + 2OH (aq) (4)

Since the equilibrium of the borate ion creates a basic solution, titration with HCl can be used to determine the amount of borate in solution at the differing temperatures and thus the concentration.

Once Ksp were calculated, they were used to determine the values for ΔH˚, ΔS˚, and ΔG˚ using the following equations:

ln K = -ΔH˚/RT + ΔS˚/R (5)

ΔG˚ = ΔH˚ - T ΔS˚ (6)

The values of ΔH˚ and ΔS˚ were assumed to be independent of temperature over the range of samples taken in this study.

Knowledge of the solubility product constant has many industrial and agricultural applications. The salt content of soil is important to understand as it has many consequences. Excess soil salinity leads to negative effects on plant growth and yield, damage to infrastructure (i.e. roads, bricks, pipes and cables), reduction of water quality for users, and ultimately soil erosion when crops are adversely affected by high salt levels. In the work of Visconti, et al (2010), the solubility of calcite and gypsum were studied in water-saturated soil samples and found their lower rates of solubility lead to a better assessment of processes involved in soil salinity, which will lead to ways to counteract the negative effects (1).

MATERIALS AND METHODS

The experiment was performed according to the procedure as described in the CHEM112 laboratory manual: McClain, B., Experiment 9: Thermodynamics and Equilibrium. Lab Guide. College of Western Idaho, 2016. (2). The actual concentration of HCl used was 0.498 M instead of listed value of 0.500 M, and the actual temperatures taken were 56.1 ºC, 52.3 ºC, 48.5 ºC, 44.8 ºC, 41.0 ºC, and 23.2 ºC.

RESULTS AND DISCUSSION

The basic nature of the dissolved tetraborate ion allows its concentration to be measured by titration with a strong acid. The two hydroxides produced in equation (4) can be used to determine the concentration of borate to calculate Ksp using equation (3). The strong acid neutralized the hydroxides as described in the following reaction:

- + OH (aq) + HCl(aq)  Cl (aq) + H2O(l) (7)

The six samples from different temperatures were titrated with 0.498 M HCl to give the following data points:

Table 1: HCl Volume for titrations. HCl Volume Final Initial T (K) ∆ (L) (mL) (mL) 296.35 2.94 0.42 0.00252 314.15 10.60 0.38 0.01022 317.95 16.30 0.33 0.01597 321.65 18.10 0.42 0.01768 325.45 15.08 0.19 0.01489

329.25 17.95 0.21 0.01774

Using the molarity and the volume, the number of moles of HCl used were calculated and used to determine Ksp.

0.498 M HCl * 0.00252 L = 0.00125496 moles HCl Moles HCl = Moles OH- in solution Moles of borate = moles OH-/2 by stoichiometry 0.00062748 moles borate/0.005 L = 0.125496 M 3 3 -3 Ksp = 4x by equation 3 = 4(0.125496) = 7.91* 10

Table 2: Concentration data Moles of Moles of Conc of borate T(K) 1/T K ln K HCl borate (M) sp sp - 1 296.35 0.003374388 0.00125496 0.00062748 0.125496 0.00790587 4.840149819 - 2 314.15 0.003183193 0.00508956 0.00254478 0.508956 0.527352133 0.639886769 3 317.95 0.003145149 0.00795306 0.00397653 0.795306 2.012161189 0.699209363 4 321.65 0.003108969 0.00880464 0.00440232 0.880464 2.730202133 1.004375648 5 325.45 0.003072669 0.00741522 0.00370761 0.741522 1.630917951 0.489143016 6 329.25 0.003037206 0.00883452 0.00441726 0.883452 2.758092746 1.014539407

Once Ksp was determined for all temperature samples, the natural logarithm of the solubility product constant was plotted against the inverse of the temperature. 3

0 0.003 0.00305 0.0031 0.00315 0.0032 0.00325 0.0033 0.00335 0.0034

-1 sp

ln K ln -2 y = -18054x + 56.557 R² = 0.909 -3

-4

-5

-6 -1 1/T (K ) Figure 1: Natural logarithm of solubility product constant vs. 1/temperature in Kelvin. The linear regression was calculated for the trendline of the plot.

-1 Table 3: Linear regression for ln Ksp vs. 1/T (K ) Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 56.55683988 9.014791427 6.27378241 0.003294847 31.52776635 81.58591341 X Variable 1 -18054.19662 2856.857732 6.319599475 0.003207481 -25986.10529 56.55683988

From equation 5, the values for ΔH˚ and ΔS˚ were calculated.

ln K = -ΔH˚/RT + ΔS˚/R ΔH˚ = -(-18000) * 8.3145 J/mol*K ΔH˚ = 149652 J/mol*K *1 kJ/1000 J ΔH˚ = +149.7 kJ/mol*K

ΔS˚ = 60 * 8.3145 J/mol*K ΔS˚ = 498.84 J/mol*K * 1 kJ/1000 J ΔS˚ = +0.499 kJ/mol*K

With ΔH˚ and ΔS˚ tabulated at 150 (± 70) kJ/mol and 0.5 (± 0.2) kJ/mol, respectively, the values for ΔG˚at the temperature samples could be calculated using equation (6).

ΔG˚ = ΔH˚ - T ΔS˚ ΔG˚ = (150 kJ/mol*K) – (296.35 K)* (0.5 kJ/mol*K) ΔG˚ = 1.82 kJ/mol*K

Table 4: ΔG˚ at each temperature ∆G (kJ/mol*K) T (K) 1.82135 296.35 -7.06085 314.15 -8.95705 317.95 -10.80335 321.65 -12.69955 325.45 -14.59575 329.25

The values of ΔG˚ were then plotted against the temperature.

335

330

325

320

315

310

Temperature Temperature (K) y = -2.004x + 300 R² = 1 305

300

295

290 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 ∆Go (kJ/mol)

Figure 2: Plot of delta G (kJ/mol) vs. temperature in Kelvin.

In the analysis, it was assumed that ΔH and ΔS did not change with temperature. Because the plot of ΔG˚vs. the temperature in K is linear, it can be concluded that that assumption is correct over the span in temperature for the measurements.

The trend observed is that ΔG˚ increases as the temperature decreases. The reaction becomes non-spontaneous at positive ΔG˚ values, therefore as the temperature rises and ΔG˚ drops, the reaction becomes spontaneous. At the molecular level, the molecules of the solution are gaining energy and their kinetics increase. The entropy in the system increases with the disorder of the molecules moving quicker, and the solid borax changes phase to liquid accordingly. The reaction is favored to the right and borax spontaneously moves into aqueous sodium and borate ions.

CONCLUSION

From the titration of hydroxides produced from the basic solution of borate ions, the ΔH was found to be 150 (± 70) kJ/mol*K and ΔS was found to be 0.5 (± 0.2) kJ/mol*K. The value of ΔGº at 25 ºC was calculated to be -1.6 kJ/mol*K, indicating a spontaneous reaction at room temperature. The plot of ΔGo against temperature indicated the assumption that ΔH and ΔS were independent of temperature in this experiment was appropriate. As the temperature rises, the Ksp also increased, indicating a favored reaction to the right and an increase in spontaneity.

REFERENCES

Visconti, F., De Paz, J. M., & Rubio, J. L. (2010). Calcite and gypsum solubility products in water-saturated salt-affected soil samples at 25°C and at least up to 14 dS m−1. European Journal Of Soil Science, 61(2), 255-270. doi:10.1111/j.1365-2389.2009.01214.x (1)

McClain, B., Lab Guide. College of Western Idaho, 2016. (2)