Determination of an Equilibrium Constant

Determination of an Equilibrium Constant Abstract: In this experiment, two reactions were run to determine the molar absorptivity and the equilibrium constant of FeSCN2+. The main principles used in this lab are equilibrium, LeChatlier’s Principle, Beer’s Law and Spectrocopy. The first reaction was run to completion using LeChatier’s Principle and the second reaction was run to equilibrium. A spectrophotometer was used to measure absorbances. Using a graph of absorbance versus concentration of FeSCN2+ was used to determine that the molar absorptivity constant was 3670.

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Beer’s Law was used to determine that the average equilibrium constant was 33. 1793. Introduction: The purpose of this experiment is to determine the value of the equilibrium constant for the reaction: Fe3+(aq) + HSCN(aq) H+(aq) + FeSCN2+(aq) In this reaction, iron(III) nitrate, Fe(NO3)3, is mixed with thiocyanic acid, HSCN, to produce the H+ ion and the complex ion thiocyanate iron(III) [FeSCN]2+. This reaction is done twice. The first time it is run to completion and the second time it is run to equilibrium. The equation for the equilibrium constant, Keq, is given by: Keq =

The initial concentrations of Fe3+ and HSCN and the equilibrium concentrations of FeSCN2+ will by measured. With all of these concentrations determined, the equilibrium concentrations of all species can be calculated. With the equilibrium concentrations of all the species found, the equilibrium constant can be determined. The major lab techniques used in this lab are equilibrium, LeChatlier’s Principle, spectroscopy, and Beer’s Law. When species react, the concentrations of the products and reactants continuously change until equilibrium is reached. No change of concentration occurs once equilibrium is reached.

Equilibrium happens when a reaction is reversible. For the reaction studied in this lab, the double arrows mean that Fe3+ and HSCN can react to form H+ and FeSCN2+ and H+ and FeSCN2+ can react to form Fe3+ and HSCN. Eventually, all the forward and reverse rates become equal and the concentrations stop changing even though the forward and reverse reactions are still proceeding. Every equilibrium reaction for a certain species has the same equilibrium constant. Once a constant is determined, it stays the same no matter what concentrations of the species are used. The equilibrium constant does however depend on temperature.

LeChatlier’s principle states that a change in concentration, temperature, volume, or partial pressure, shifts the equilibrium to counteract the change and a new equilibrium is established2. This is used in the standard solutions. A large amount of Fe(NO3)3 is used to drive the reaction towards the products and to completion. A Spec 20 spectrophotometer is used to measure the absorbance of each solution. This is done because a spectrophotometer works by introducing light of a specific wavelength to a sample. As the light passes through the sample, some of it is absorbed by the sample and some is transmitted through the sample.

The spectrophotometer intercepts this transmitted light. By comparing this light to the incident beam, the spectrophotometer finds the percent of light transmitted. The percent transmittance is then converted by the spectrophotometer to absorbance with the equation: -log(%T/100) = Abs Beer’s Law is also used in this experiment to determine the molar absorptivity constant. Beer’s law states that the absorbance is directly proportional to the concentration of a solution. If you plot absorbance versus concentration, the resulting graph yields a straight line.

The equation for the straight line can be used to determine molar absorptivity constant. In Beer’s Law, Abs = ? l[X] where ? is the molar absorptivity constant, l is the path length and [X] is the concentration of the species. A plot of absorbance vs. concentration of FeSCN2+ in the standard solutions allow for the determination of ?. With the molar absorptivity found, Beer’s law can be used again to determine the concentration of FeSCN2+ at equilibrium. Materials and Methods: This lab was carried out using the procedure outlined in the An Introduction to Chemical System in the Laboratory1 with the following exceptions. LabQuest was not used during this experiment. Results: Table 1. Standard Solutions Solutions12345 mL Fe(NO3)325. 0025. 0025. 0025. 0025. 00 mL HSCN5. 0010. 0015. 0020. 0025. 00 mL HNO370. 0065. 0060. 0055. 0050. 00 Total mL100. 00100. 00100. 00100. 00100. 00 Intial [HSCN]3. 0*10-56. 0*10-59. 0*10-51. 2*10-41. 5*10-4 Table 2. Equilibrium Solutions Solutions12345 mL Fe(NO3)35. 005. 005. 005. 005. 00 mL HSCN1. 002. 003. 004. 005. 00 mL HNO34. 003. 002. 001. 000. 00 Total mL10. 0010. 0010. 0010. 0010. 00 Initial [Fe3+]1. 0*10-31. 0*10-31. 0*10-31. 0*10-31. 0*10-3 Intial [HSCN]2. 0*10-44. 0*10-46. 0*10-48. 0*10-41. 0*10-4 Table 3.

Absorbance of Standard and Equilibrium Solutions Solutions12345 Standard Solutions Abs0. 1350. 2230. 3450. 4560. 509 Equilibrium Solutions Abs 0. 0460. 0890. 1360. 1660. 217 Table 4. Equilibrium Concentration of FeSCN2+ Solutions12345 [FeSCN2+]1. 2534*10-52. 425*10-53. 7057*10-54. 5230*10-55. 9130*10-5 Table 5. Equilibrium Constants SolutionEquilibrium Constant 133. 855 233. 072 334. 1827 431. 385 533. 4018 Average33. 1793 Graph 1. Absorbance vs. Concentration Table 6. Molar Absorptivity of FeSCN2+ Molar Absorptivity3670 Equilibrium concentration of FeSCN2+ (Solution 1) Abs = ? l[X] 0. 046 = 3670 ? 1 ? [FeSCN2+] [FeSCN2+] = 1. 2534*10-5

Equilibrium Concentrations of all Species (Solution 1) Fe3+HSCNHNO3FeSCN2+ I1. 0*10-32. 0*10-40. 500 C-1. 2534*10-5-1. 2534*10-5+1. 2534*10-5+1. 2534*10-5 E9. 87*10-41. 87*10-40. 501. 2534*10-5 Equilibrium Concentrations of all Species (Solution 2) Fe3+HSCNHNO3FeSCN2+ I1. 0*10-34. 0*10-40. 500 C-2. 425*10-5-2. 425*10-5+2. 425*10-5+2. 425*10-5 E9. 75*10-43. 76*10-40. 502. 425*10-5 Equilibrium Concentrations of all Species (Solution 3) Fe3+HSCNHNO3FeSCN2+ I1. 0*10-3 M6. 0*10-4 M0. 50 M0 C- 3. 71*10-5- 3. 71*10-5+ 3. 71*10-5+ 3. 71*10-5 E9. 629*10-4 5. 629*10-4 0. 50 3. 71*10-5 Equilibrium Concentrations of all Species (Solution 4)

Fe3+HSCNHNO3FeSCN2+ I1. 00*10-38*10-40. 500 C-4. 523*10-5-4. 523*10-5+4. 523*10-5+4. 523*10-5 E9. 55*10-47. 955*10-30. 504. 523 x 10-5 Equilibrium Concentrations of all Species (Solution 5) Fe3+HSCNHNO3FeSCN2+ I1. 00*10-31. 0*10-30. 500 C-5. 913*10-5-5. 913*10-5+5. 913*10-5+5. 913*10-5 E9. 41*10-47. 941*10-30. 505. 913 x 10-5 Equilibrium Constant, Keq (Solution 1) Keq = Keq = Keq = 33. 855 Table 7. Observations Step in ProcedureObservation Addition of Fe(NO3) to HNO3 solutionClear colorless solution Addition of HSCN to Fe(NO3) and HNO3 solutionClear orange solution Error Analysis: Table 8. Mean and Standard Deviation

Mean33. 1793 Standard Deviation±1. 089 Average Keq = = 33. 1793 Standard Deviation = = ±1. 089 Discussion: In this experiment, the molar absorptivity constant, ? , and the equilibrium constant, Keq were determined. The molar absorptivity constant was determined by graphing absorbance versus concentration of HSCN. The equilibrium constant was determined by using the found molar absorptivity, Beer’s Law, and the equilibrium concentrations of all the species in the reaction: Fe3+(aq) + HSCN(aq) H+(aq) + FeSCN2+(aq) In the first part of the experiment, large amounts of Fe3+ were added to relatively small amounts of HSCN.

This was done to drive the reaction to completion by LeChatlier’s Principle. Since large amounts of reactants were added, it drove the reaction to the right and shifted the equilibrium to counteract the change. After measuring the absorbance of all the standard solutions, a plot of absorbance vs. concentration of HSCN was made and a best-fit line was determined. The slope of the line was equal to the molar absorptivity constant because of Beer’s Law, Abs = ? l[X], and was found to be 3670. In the second half of the experiment, smaller amounts of Fe3+ were added to HSCN to drive the reaction to equilibrium.

Once a reaction reaches equilibrium, the rate of formation of the reactants equals the rate of formation of the products. Once this occurs, the concentrations of all the species stays constant and are called equilibrium concentrations. Equilibrium concentrations of all the species present in the reaction are needed to determine the equilibrium constant. To determine the equilibrium concentrations of all the species, the concentration of FeSCN2+ at equilibrium was found first. This was done by measuring the absorbance of the equilibrium solutions and using Beer’s Law to calculate the concentration of FeSCN2+.

The calculation was possible by using a path length of one and the molar absorptivity previously determined. Once the concentration of the FeSCN2+ was found, an ICE table was used to determine the equilibrium concentrations of the rest of the products and reactants. With all the equilibriums concentrations found, the equilibrium constant was calculated using the equation: Keq = The average Keq was determined to be 33. 1793 with a standard deviation of ±1. 089. Even though the standard deviation is relatively small, there were several sources of error that could have occurred throughout the experiment.

Since the Spec 20 spectrophotometer is not very accurate, it could have resulted in less accurate absorbance values, which would have skewed the final results. Another possible source of error could have been an inaccurate absorbance due to not measuring the absorbance immediately after HSCN was added to Fe3+. This would cause an incorrect absorbance because the reading was not stable. References: 1. Chemistry 203/205: An Introduction to Chemical Systems in the Laboratory. Hayden-McNeil; Plymouth, 2011. 2. Atkins, P. ; Jones, L. ; Chemical Principles. 5th ed. , Freeman: New York, 2008.

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