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Nickel Ethylenediamine Complexes Ethylenediamine, H2NCH2CH2NH2, which will usually be abbreviated as en, is a bidentate ligand that can form two coordinate covalent bonds with a metal atom through the lone pair electrons on both nitrogens. In aqueous solution the structure of the 1:1 complex of Ni2+ and ethylenediamine is: Ni2+ forms three complexes with ethylenediamine: K1 Ni2+ (aq) + en (aq) –––––> Ni(en)2+ (aq) (1) K2 Ni(en)2+ (aq) + en (aq) –––––> Ni(en)22+ (aq) (2) K3 Ni(en)22+ (aq) + en (aq) –––––> Ni(en)32+ (aq) (3) While uncomplexed Ni2+ forms light green aqueous solutions, binding to the ethylendiamine ligands alters the energies of the nickel d-orbitals and the ethylenediamine complexes range in color from blue green to purple. At a particular wavelength, e.g., 1, all the Ni2+ species contribute to the total measured absorbance, AT,l1: AT,1 = ANi2+,1 + ANi(en)2+,1+ ANi(en)22+,1 + ANi(en)32+,1 1 Assuming that each Ni2+ species follows Beer's law, the total absorbance can be expressed in terms of the concentrations of the Ni2+ species: AT,1 = Ni2+, 1 [Ni2+] L + Ni(en)2+, 1 [Ni(en)2+] L + Ni(en)22+, 1 [Ni(en)22+] L + Ni(en)32+, 1 [Ni(en)32+] L Here Ni2+, 1 is the molar absorptivity of Ni2+ at the wavelength 1, [Ni2+] is the molar concentration of Ni2+, and L is the radiation path length in the absorbance cell. A single measurement of the absorbance of a solution of Ni2+ and ethylenediamine thus yields a single equation containing the four unknown concentrations and therefore provides insufficient information to solve for these concentrations. Measurements at three other wavelengths, however, provide a total of four equations in the four unknown concentrations Ni2+ species: AT,2 = Ni2+, 2 [Ni2+] L + Ni(en)2+, 2 [Ni(en)2+] L + ••• AT, 3 = Ni2+, 3 [Ni2+] L + Ni(en)2+, 3 [Ni(en)2+] L + ••• AT, 4 = Ni2+, 4 [Ni2+] L + Ni(en)2+, 4 [Ni(en)2+] L + ••• which can in principle be simultaneously solved for these concentrations. Matrix algebra provides a convenient method for solving these four simultaneous linear equations. In matrix form the equations are: Ni2+, Ni(en)2+, Ni(en) 2+, Ni(en) 2+, [Ni2+] 1 1 2 1 3 1 AT, 1 Ni2+, Ni(en)2+, Ni(en) 2+, Ni(en) 2+, [Ni(en)2+] 2 2 2 2 3 2 AT, 2 L = Ni2+, Ni(en)2+, Ni(en) 2+, Ni(en) 2+, [Ni(en)22+] 3 3 2 3 3 3 AT, 3 2 Ni2+, Ni(en)2+, Ni(en) 2+, Ni(en) 2+, [Ni(en)32+] 4 4 2 4 3 4 AT, 4 The matrix equation can be written in the shorthand form: ECL= A Here E represents the 4x4 square matrix of the molar absorptivities, C represents the 1x4 column matrix of the concentrations of the Ni2+ species, A represents the 1x4 column matrix of the total measured absorbances at the four wavelengths, and L is the cell path length. This matrix equation can be solved for the column matrix C whose elements are four the unknown concentrations by multiplying both sides from the left by the inverse of the absorptivity matrix, E –1, and from the right of the reciprocal of the cell path length: C = E –1E C L (1/L) = E –1A (1/L) The matrix inversion and multiplication necessary to solve this equation are readily accomplished in most spreadsheets. The approach described above requires that the molar absorptivities of all the four Ni 2+ species be known at each wavelength in order to evaluate the absorptivity matrix. These molar absorptivities at a particular wavelength, e.g., 1, can be determined in a previous experiment in which the total absorbances at one of the wavelengths is measured for four Ni2+ and ethylenediamine solutions containing different total Ni2+ and ethylenediamine concentrations. Since the concentrations of the individual absorbing species will vary as the total Ni2+ and ethylenediamine concentrations are varied, this procedure will yield four independent simultaneous equations that can be solved for the four unknown molar absorptivities at that wavelength: AT1,1 = Ni2+, 1 [Ni2+]1 L + Ni(en)2+, 1 [Ni(en)2+]1 L + ••• AT2, 1 = Ni2+,1 [Ni2+]2 L + Ni(en)2+, 1 [Ni(en)2+]2 L + ••• • • • Here AT1, 1 is now the total measured absorbance for the 1st set of concentrations, [Ni(en)x2+]1, at 1. Once again these equations are conveniently put in matrix form: 3 [Ni2+] 1 [Ni(en)2+] 1 [Ni(en)22+] 1 [Ni(en)32+] 1 [ Ni2+, ] AT , 1 1 1 [Ni2+] 2 [Ni(en)2+] 2 [Ni(en)22+] 2 [Ni(en)32+] 2 [ Ni(en)2+, ] AT , 1 2 1 L = [Ni2+] 3 [Ni(en)2+] 3 [Ni(en)22+] 3 [Ni(en)32+] 3 [ Ni(en) 2+, ] AT , 2 1 3 1 [Ni2+] 4 [Ni(en)2+] 4 [Ni(en)22+] 4 [Ni(en)32+] 4 [ Ni(en) 2+, ] AT , 3 1 4 1 and solved using matrix algebra: C' E1 L = A1 Here C' represents the 4x4 square matrix of the concentrations of the absorbing Ni2+ species at each of the total nickel and ethylenediamine concentrations, E1 represents the 1x4 column matrix of the molar absorptivities of these Ni2+ species at 1, A1 represents the 1x4 column matrix of the total measured absorbances at each of the total nickel and ethylenediamine concentrations, and L is the cell path length. E1, contains the unknown molar absorptivities of each Ni2+ species at 1 as elements and is calculated from: E1 = (C')–1 A1 (1/L) The calculation of the molar absorptivities as described above requires that the concentrations of Ni2+ and its ethylenediamine complexes be known. These concentrations can be determined from the equilibrium constant expressions for the Ni2+ ethylenediamine complex equilibria (see reactions 1-3): K1 = [Ni(en)2+] / ([Ni2+] [en]) K2 = [Ni(en)22+] / ([Ni(en)2+] [en]) K3 = [Ni(en)32+] / ([Ni(en)22+] [en]) and mass balance expressions on nickel and ethylenediamine: [Ni]total = [Ni2+] + [Ni(en)2+] + [Ni(en)22+] + [Ni(en)32+] 4 [en]total = [en] + [Ni(en)2+] + 2 [Ni(en)22+] + 3 [Ni(en)32+] The stepwise formation constants for the nickel ethylenediamine complexes can be found in the literature1-2. These five equations can be solved simultaneously by successive elimination for the five unknown concentrations; [Ni2+], [en], [Ni(en)2+], [Ni(en)22+], and [Ni(en)32+], but are more easily solved using mathematical software such as MathCad, Maple, or Mathematica. 5 Procedure and Data Each group should find in the laboratory: Reagent grade NiSO4•6H2O (s). Reagent grade ethylenediamine. A Ni2+ ethylenediamine unknown. A water ethylenediamine blank. Two one liter volumetric flasks. One 25 mL volumetric flask. A visible spectrometer A sheaf of labels and tape. One 5 mL and 10 mL volumetric pipette. Eight plastic bottles with caps 1. Prepare one liter stock solutions of 0.0500 M NiSO4•6H2O and 0.0500 M ethylenediamine from the reagent grade chemicals. 2. Using a 5 mL and 10 mL volumetric pipettes, and 25 mL volumetric flasks prepare the following nickel ethylenediamine calibration solutions: calibration 0.0500 M 0.0500 M solution NiSO4•6H2O ethylenediamine 1 5.0 mL 20.0 mL 2 10.0 mL 15.0 mL 3 15.0 mL 10.0 mL 4 20.0 mL 5.0 mL Store these solutions in labeled tightly stoppered 25 mL volumetric flasks. 3. Using a 5 mL and 10 mL volumetric pipettes, and 25 mL volumetric flasks prepare the following ethylenediamine water blank solutions: calibration distilled 0.0500 M solution water ethylenediamine 1 5.0 mL 20.0 mL 2 10.0 mL 15.0 mL 3 15.0 mL 10.0 mL 4 20.0 mL 5.0 mL Store these solutions in labeled tightly stoppered 25 mL volumetric flasks. These blank solutions will correct for the slight absorbance of the light yellow uncomplexed ethylenediamine. 4. Measure the absorbance of your unknown nickel ethylenediamine solution from 325 nm to 650 nm. Use of the visible spectrometer will be demonstrated by the instructor. An appropriate ethylenediamine blank will be provided for the 6 unknown. Obtain a properly labeled printout of the unknown spectrum. Based on this plot choose four wavelengths at which to study the nickel ethylenediamine complexes. This spectrum with the four wavelengths clearly marked on it and with the axes clearly labeled should be handed in with your final report for this laboratory. 5. Now measure the absorbance of the four nickel ethylenediamine calibration solutions at each of the four wavelengths you chose: calibration 1 2 3 4 solution (nm) (nm) (nm) (nm) 1 2 3 4 6. Now measure the absorbances of the unknown nickel ethylenediamine solution at your four chosen wavelengths 1-4. 1 2 3 4 (nm) (nm) (nm) (nm) unknown solution 7 Calculations Note these calculations are best carried out in a spreadsheet. 1. Obtain the stepwise equilibrium constants; K1, K2, and K3, for the formation of the Ni2+ ethylenediamine complexes from the literature1-2. 2. Calculate the total nickel and ethylenediamine concentrations in each of the four calibration solutions. 3. Use these equilibrium constants and the total nickel and ethylenediamine concentrations in the four calibration solutions to simultaneously solve the three Ni2+ ethylenediamine equilibrium constant expressions and the two mass balance expressions on nickel and ethylenediamine for the five unknown concentrations; [Ni2+], [en], [Ni(en)2+], [Ni(en)22+], and [Ni(en)32+] in each of these calibration solutions. While these five equations can be solved by successive elimination to yield a single polynomial equation in one of the concentrations, which is then iteratively solved for this concentration using Newton's method, they are most easily solved using mathematical software such as MathCad, Maple, or Mathematica. 4. These Ni2+ and complex concentrations form the elements of the concentration matrix, C', and are then used with the four measured total absorbances for the four calibration solutions to solve the matrix equation: E1 = (C')–1 A1 (1/L) for the molar absorptivities at each of the wavelengths. 5. These sixteen molar absorptivities form the elements of the molar absorptivity matrix, E, which is then used with the measured absorbances of the unknown solution at the four wavelengths to solve the matrix equation: C = E –1A (1/L) for the concentrations of Ni2+ and its ethylenediamine complexes in the unknown solution. References 1. Stability Constants of Metal-Ion Complexes, Section II: Organic Ligands, Bjerrum, H., Schwarzenbach, G., and Sillerr, L. G., The Chemical Society (London), pp. 372-373, (1957). 8 2. IUPAC Stability Constants Database, compiled by L. D. Pettit and H. K. Powell (1997), Chemical Society (London) and IUPAC Commission on Equilibrium Data. This database is available in digital form in the Montana Tech Library (see the Referernce Librarian for help). 9

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