Catalysis of Organic..

Liu, Cant and Smith 137noting that the proportionality constant is identical for these equations when usingthe same spectrum. Substituting Equations [5-7] into the usual equations for relativemole fractions (Y), for example Y IDA = n IDA / (n DEA + n HEG + n IDA ), gives:Y DEA = (A a - A c ) / (A a + A b + A c ) [8]Y HEG = 2A c / (A a + A b + A c ) [9]Y IDA = A b / (A a + A b + A c ) [10]Given that the number of a and d protons are the same, an identical set ofequations with Ad in place of Aa can also be used. Here we have used an average ofAa and Ad with the areas assessed after Lorentzian deconvolution in order to providebetter separation of the 2.99 and 3.02 ppm lines. Mole fractions derived using thisNMR method for reaction over the unpromoted copper catalyst are shown as afunction of time in Figure 5. Clearly IDA is formed largely via HEG as intermediatesince the concentration of the latter passes through a well-defined maximum.1.00.8DEAHEGIDANMR datamodelMole fraction0.60.40.20.00 2 4 6 8Time, hoursFigure 5. Mole fractions versus time for the reaction of diethanolamine overunpromoted copper.The reaction was modeled in an attempt to obtain rate constants for the reactionsof DEA and HEG separately. This was done on the assumption that the system wasentirely sequential, with both reacting according to first order kinetics, i.e.k 1 k 2DEA → HEG → IDAIn this case the equations for the concentrations of the three components as afunction of time are as follows when DEA alone is present initially (13)[DEA] = [DEA] 0 exp (-k 1 t) or ln[DEA] = ln[DEA] 0 – k 1 t [11][HEG] = {k 1 /(k 2 - k 1 )} [DEA] 0 {exp(-k 1 t) – exp(-k 2 t)} [12]