Experiments to Calculate the Value of the Formation Constant of Tetraamminecopper

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Experiments #7A & 7B

7A. Electrochemical Cells
7B. Formation of a Complex Ion

Chem 102
Section 3095
Grace H. Kim
Dec. 15, 2011
Abstract
Two experiments were conducted to figure out the value of the formation constant of tetraamminecopper(II), Kf, with different methods and which experimental method produces more accurate result. One was electrochemistry using a Daniel cell and the other one was spectrometry by estimating concentration of complex solution using a calibration curve. The formation constant of cupric ammine complex Cu(NH3)42+, Kf, came out with 1.93x10^15 using electrochemical cell method and 9.79x10^12 using spectrophotometer method. Considering the literature value of Kf is around 4.8x10^12 ~ 1.7x10^13, spectrophotometer gives more accurate result than electrochemical cell method. Formation constant of complex ion can be derived easily by Nernst equation in electrochemical cell method, but mass action expression with K4, Ksp, and Kb in spectrophotometer method generates more accurate and closer to literature value with less percentage error.

Introduction
The purpose of these experiments is to figure out the value of the formation constant of tetraamminecopper(II), Kf, through two different methods and which experimental method produces more accurate result. Two methods are electrochemistry using a Daniel cell and spectrometry by estimating concentration of complex solution. The color of anhydrous copper sulfate (CuSO4) is white because it reflects lights in visible region of spectrum. Once water is added, it changes to blue as the structure of the copper transitional compound becomes Cu(H2O)4 SO4 - H2O where four water molecules are bound to the copper ion and the fifth is a water of crystallization. This compound absorbs light of wavelengths from 600 to 800nm (yellow-to-red region) light and blue light is transmitted. When ammonia is added to a solution of copper(II) cation, tetraamminecopper(II) complex ion, Cu(NH3)42+, is formed and color changes to deep blue.

Cu(H2O)42+ + 4NH3 Cu(NH3)42+ + 4H2O (1)
Kf, is the formation constant of the tetraamminecopper(II) ion at equilibrium can be written as below:
Kf = [Cu(NH3)42+]
[Cu2+] [NH3]4 (2)

This reaction can be written for a Daniel cell as below:
Cu NH3, Cu(NH3)42+ KCl Cu2+ Cu
More specifically, oxidation reaction of Cu + 4NH3 ⇌ Cu(NH3)42+ + 2e- occurs at anode and reduction reaction of Cu2+ + 2e- ⇌ Cu occurs at cathode. With the value of n = 2, the emf of the cell can be expressed as follows with Nernst equation:

E = Eo - 2.3RT log [Cu(NH3)42+]
2F [Cu2+] [NH3]4 (3)
The emf (E) developed by such a cell at equilibrium must be zero. Therefore, the formation constant, Kf, is related by
log Kf = (2F Eo) / (2.3 RT) (4)
With the value of Eo, the value of Kf is calculated. (7A. Electrochemisty)
The same logic can be applied to the reaction Cu2+ + 2OH- ⇌ Cu(OH)2 (s). This cell can be written as Cu OH- Cu(OH)2 KCl Cu2+ Cu. Since the overall cell reaction is the reverse...
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