# Study of Solubility Equilibrium

**Topics:**Solubility equilibrium, Solubility, Common-ion effect

**Pages:**5 (1769 words)

**Published:**February 22, 2012

Data Treatment and Analysis

Section 1: Solubility Product Constant

Temperature (˚C)| Volume of NaOH used (mL)| | |

| Titration 1| Titration 2| Average|

28| 12.7| 12.8| 12.75|

9| 10.5| 10.5| 10.5|

19| 11.3| 11.2| 11.25|

40| 16.2| 16.2| 16.2|

50| 22.8| 22.9| 22.85|

Table 1: The volume of NaOH used in the titration at various temperatures. No. of moles of KHC4H4O6 = 1.45 g ÷ 188.177g/mol = 7.71 x 10-3mol Molarity of KHC4H4O6 before filtration = 7.71 x 10-3mol ÷ 0.1L = 7.7 x 10-2M No. of moles of NaOH: (0.07415M x 12.75) /1000L = 9.454 x 10-4 mol ∴ No. of moles of HC4H4O6- = No. of moles K+ = 9.454 x 10-4 mol [HC4H4O6-] = [K+] = (9.454 x 10-4 mol) / 0.025L = 0.03785 mol/L Ksp = [K+][HC4H4O6-] = (0.03785 ÷ 1mol/L) x (0.03785 ÷ 1 mol/L) = 1.433 x 10-3 1/T = 1/(28+273.15) = 3.6 x 10-3

ln Ksp = ln (1.433 x 10-3 )= -6.548

1/Temperature(1/K) (10-3 )| ln Ksp|

3.3 | -6.548|

3.5 | -6.92|

3.4 | -6.801|

3.2 | -6.07|

3.1| -5.384|

Table 2: The inverse of different temperatures and the ln for their respective Ksp.

Graph 1: Graph of ln Ksp against 1/T

Graph 1 is a graph of ln Ksp against 1/T. It is a linear graph with a R2- value of 0.916 which is close to 1 and a standard error of regression of 0.2103 which is relatively close to zero, indicating that the model of the graph chosen is suitable and the fit of the trendline is good.. The negative gradient shows that the ln Ksp is inversely proportional to 1/T. The gradient and intercept from the graph is used to calculate the enthalpy and entropy change of the reaction. As demonstrated in the calculations below the change in enthalpy is -31.62 kJ (negative) and the change in entropy is 51.5kJ (positive). Therefore the reaction is spontaneous and the Gibb’s free energy is less than zero, pushing the reaction to the right until equilibrium is achieved (Appendix) RT ln Ksp = = Δ H - T Δ S

y = -3.803+6.2053

∴ Δ H = -3.803 x 8.314J/mol.K = -31.62x 103 J= -31.62kJ

Uncertainty of enthalpy = 0.6649×8.314J/mol.K = 0.5528J x 103= ± 0.5528 kJ Δ S = 6.2053 x 8.314J/mol.K = 51.59J x 103 =51.59kJ

Uncertainty of entrophy = 2.1962 ×8.314J/mol.K = 18.26 x 103 J= ±18.26 kJ Gradient: -3.803 ± 0.65kJ

Intercept: 6.205 ± 2.20 kJ (One estimated standard deviation error limit. Number of measurements: 5)

Section 2: Common ion effect

KNO3 K+ + NO3- KHC4H4O6 K+ + HC4H4O6- No. of moles of NaOH: (0.04474mol/L x 18.75L)/1000 = 8.388 x 10-4 mol ∴ No. of moles of K+ and HC4H4O6- = 8.388 x 10-4 mol

Molarity of HC4H4O6- = 8.388 x 10-4 mol ÷0.025 L = 0.0335 mol/L

Molarity of Ktotal: (8.388 x 10-4 mol ÷ 0.025L) + 0.01mol/L = 0.0436mol/L

Ksp = [K+][HC4H4O6-] = (0.0335mol/L ÷ 1mol/L) x (0.00335mol/L ÷ 1mol/L) = 1.13 x 10-3 Solubility of KHC4H4O6: 8.388 x 10-4 mol ÷ 0.1L = 8.344 x 10-3 mol

Graph 2: Graph of solubility of potassium hydrogen tartrate against the total concentration of potassium ions. Graph 2 which is a graph of the solubility of potassium hydrogen tartrate against the total concentration of potassium ions. It is a linear graph with a R2- value of 0.917 which is close to 1 and a standard error of regression of 0.353727 which is close to zero, indicating that the model of the graph chosen is suitable and the fit of the trendline is good.. The gradient which is -1.0652 shows that the solubility of potassium hydrogen tartrate is inversely proportional to the total concentration of potassium ions. This is in accordance to the explanation above about the common ion effect where the increase in potassium ions shifts the equilibrium to the left, decreasing the solubility of potassium hydrogen tartrate accordingly. Results and Discussion

Section 1: Solubility Product Constant

Temperature(˚C)| Concentration of HC4 H4 O 6 - ( mol/L) (10-2M)| Concentration of K+ ( mol/L) 10-2M)| Ksp of KHC4H4O6 | 28| 3.785|...

References: Chemical dymanics (n.d). Retrieved 3rd February,2012 from

http://www.shodor.org/unchem/advanced/thermo/#enthalphy

Laird, Brian. B (2009), University Chemistry. Acid-Base Equilibria and Solubility, pp. 611-663. New York. McGraw-Hill.

Ranken, M.D., Kill, R.C. and Baker, C.J.C. (1997), Food Industries Manual (Rev. ed.). Alcoholic Beverages, pp. 236-272. Great Britain. Chapman & Hall.

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