The score of this experiment is to determine the value of an equilibrium continuous at various temperatures and also use this data to calculation the enthalpy and entropy the reaction. The value of one equilibrium constant for a reaction varies, depending upon the temperature. In endothermic reactions, the worth of K increases as the temperature increases since heat deserve to be thought of as a reactant. In exothermic reactions, and also the value of K decreases as temperature increases since heat deserve to be assumed of as a product. Equation (1) defines the relationship in between standard free-energy change, temperature, enthalpy and entropy of reaction, and also the equilibrium constant, whereby the right gas continuous R= 8.314 J/mol·K.
You are watching: Ln ksp vs 1/t graph
∆G° = -RT lnK = ∆H° – T∆S° Equation (1)
If us assume that ∆H° is temperature-independent over various temperatures, it complies with that ∆S° will also be temperature-independent. With this assumption, Equation (1) have the right to be rearranged to give Equation (2), i m sorry is in the kind of a right line. If we were to plot ln K vs 1/T(K) and determine a line of finest fit, the slope of the line would certainly be -∆H°/R and the y-intercept would certainly be ∆S°/R.
ln K = -∆H°/R(1/T) + (∆S°/R) Equation (2)
In this experiment, we studied the solubility equilibrium of salt tetraborate dodecahydrate (commonly recognized as borax). The equilibrium reaction is displayed below.
The equilibrium constant for Equation (3) is the same as the solubility constant, Ksp, because that borax in water. In this reaction, we figured out the value of Ksp in ~ five various temperatures. Then, after ~ calculating ln(Ksp), do a scatter plot of ln(Ksp) vs. 1/T(K), and then determining a heat of finest fit in the kind of Equation (2), we deserve to determine the values of the enthalpy and entropy the reaction. To identify the value of Ksp, we first have to determine the concentration that the tetraborate ion in the equilibrated mixture. Because this ion is a base, its concentration can be established by titrating v a standardized systems of HCl, as shown in Equation (4).
B4O5(OH)42- (aq) + 3 H2O (l) + 2 H+ (aq) > 4 H3BO3 (aq) Equation (4)
From the titration data, we deserve to determine the concentration that the tetraborate ion in the equilibrated aliquot. The concentration that the salt ion will be twice this value. From this information, we can calculate the value of Ksp, using Equation (5).
A 600-mL beaker was filled with 300 mL the distilled water. The manufacturer was inserted on a warm plate and also a thermometer was clamped come a ring stand and also placed in the beaker. The water heated come 95º C. (The maker was kept at this temperature throughout the entire experiment.) to a 250-mL beaker to be sequentially added exactly 40.0288 g of borax and also 100 mL the distilled water. This beaker was then placed on a warm plate and another thermometer was clamped come a ring stand and also placed in the beaker. The solution was heated come 65º C. Together the equipment was gift heated, a 50-mL buret was conditioned and then filled through 50 mL the 0.5065 M HCl. The beaker was then gotten rid of from the hot plate. Then, specifically 5.007 g that borax was added to the beaker since there to be no corpuscle at the bottom the the beaker after ~ the solution got to 65º C. The solution was climate left come cool down. Once the temperature reached 47º C, a 10-mL pipet to be filled with warm water indigenous the 600-mL beaker and then drained into the sink. Then, when the temperature that the solution got to 46º C, come a 250-mL Erlenmeyer flask to be sequentially included a 10 mL aliquot of equipment without pipetting any undissolved solid in ~ the bottom that the beaker, 10 mL of hot water native the 600-mL beaker using the exact same pipet to do sure every one of the systems escaped the pipet, and also 30 mL of distilled water making use of a graduated cylinder. Then, 10 drops of bromocresol green was added to the flask and the flask to be stirred. The equipment was then titrated with the 0.5065 M HCl until the systems turned from blue come yellow. The final buret analysis was recorded and then the buret was re-filled with the 0.5065 M HCl. This procedure of heater the pipet with warm water, draining that in the sink, acquisition 10 mL aliquots that borax solution, chasing v 10 mL of warm water, adding 30 mL that distilled water, including 10 fall of bromocresol green, and titrating v 0.5065 M HCl till the solution turned from blue come yellow, recording the final buret reading and also re-filling the buret v 0.5065 M HCl was repeated as the systems cooled under to 41º, 36º, 31º, and 26º C. Then, utilizing the molality that the HCl and also the stoichiometry associated with Equation (4), the concentrations of the tetraborate ion and the salt ion were calculated and then the Ksp values were calculate at each temperature. Then, making use of Microsoft Excel, a plot of ln(Ksp) vs. 1/T(K) to be made and a line of best fit was determined. Next, making use of the LINEST function, the worths of -∆H°/R and ∆S°/R were determined. Finally, ∆H° and ∆S° of equipment were calculated.
Table 1: The volume of HCl added, the concentration of
Figure 1: The graph that ln(Ksp) vs. 1/T(K), the line of ideal fit linked with the data, the equation because that the heat of finest fit, and the worth of the coefficient of regression, r2.
Table 2: The identified values native the heat of best fit that the slope (-ΔHº/R), the intercept (ΔSº/R), the unpredictabilities of those values, and also the calculated values of ΔHº and also ΔSº.
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The data reflects a clear trend that as the temperature decreases, the concentration of the tetraborate ion decreases, which follows that the worth of Ksp decreases as temperature decreases (Table 1), which thus follows that the value of ln(Ksp) decreases together temperature reduce (Table 1 and Figure 1). The worth of the coefficient that regression, r2 (Figure 1), is likewise shown. This value means that the changes in 1/T(K) explains 99.15% of the variations in ln(Ksp). This is great because it reflects that there are not any kind of influential points that deserve to drastically readjust the heat of best fit, i beg your pardon could likewise drastically change the worths of the slope and the intercept. The identified line of best fit because that the graph of ln(Ksp) vs. 1/T(K) is in the kind of y=mx+b (Figure 1). This deserve to be analyzed to Equation (2), whereby y=ln(Ksp), m=-ΔHº/R, x=1/T(K), and also b=ΔSº/R. From this, the values of ΔHº and also ΔSº to be calculated (Table 2).
The results show the tendency that as temperature decreases, the worth of the equilibrium constant also decreases. This satisfies the first goal of this experiment in studying the temperature-dependence of the equilibrium constant. The 2nd goal that this experiment was to recognize the worths of the enthalpy and also entropy that dissolution, which room 170 kJ/mol and also 560 J/mol·K, respectively. The literature values of the enthalpy and entropy of dissolution of borax in water room 110 kJ/mol and 380 J/mol·K, respectively1. The percent errors in this values room 55% and 47%, respectively. These errors potentially resulted indigenous the addition of extra borax ~ the solution was heated to 65º C. However, although there is a far-reaching experimental error in the values of enthalpy and also entropy that dissolution, the data is consistent. As displayed through number 1, the coefficient of regression is significantly close come a worth of 1, which method that there room not any influential data points or outliers that would significantly readjust the slope and also intercept the the line of best fit if any type of of the clues were gotten rid of from the plot. The indicators of the enthalpy and entropy of dissolution are both positive. It renders sense the the ΔHº of solution is positive, an interpretation that the reaction is endothermic, since the mixture was heated and also therefore the molecules necessary to absorb the heat in order to turn into a solution. This additionally helps to know why the sign of ΔSº is positive. When the signs of both ΔHº and ΔSº space positive, the reaction will be spontaneous in ~ high temperatures (i.e. ΔGº References
1 college of California Irvine room of Chemistry. Enthalpy and Entropy the a Borax Solution. http://faculty.sites.uci.edu/chem1l/files/2011/03/E06MANborax.pdf (Accessed in march 2, 2014)