Catalysis of Organic..

138Aminoalcohols to Aminocarboxylic Acid Salts[IDA] = [DEA] 0 [1 + {k 1 exp(-k 2 t) – k 2 exp(-k 1 t)}/(k 2 – k 1 )] [13]The value of k 1 can be calculated from a plot of ln[DEA] versus time. Thecalculation needs to be confined to low conversion since examination of equation [8]shows that Y DEA depends on the difference between A a and A c and this becomesimprecise at high conversion. The second rate constant, k 2 , cannot be calculateddirectly but its ratio relative to k 1 can be estimated from the maximum mole fractionattained by HEG in the following way. The time at which this occurs, obtained bydifferentiation of equation [12], is given by (13)t(max) = ln(k 1 /k 2 ) / (k 1 – k 2 )Substitution of this in place of t in [12] and simplification leads toY HEG (max) = R R/(1 - R) [14]where R is the ratio, k 2 /k 1 .Figure 6 shows a plot of this relationship as a function of k 2 /k 1 together withhorizontal lines corresponding to the maximum values attained by Y HEG duringreaction over the unpromoted catalyst (~0.53) and for the promoted catalyst (~0.43).These values correspond to R = 0.41 and 0.71 respectively. Table 4 lists the valuesfor k 1 and k 2 obtained for the two catalysts on this basis. The CH 2 OH groups in DEAappear to be about twice as active as those in HEG (but see below).1.0Y HEG(maximum)0.80.60.40.2equation [11]unpromoted Cupromoted Cu0.00.0 0.5 1.0 1.5 2.0 2.5 3.0k 2/k 1ratioFigure 6. Theoretical dependence of Y HEG on k 2 /k 1 in comparison with valuesobserved for the reaction of DEA over unpromoted and chromia-promoted coppercatalystsThe dashed lines in Figure 5 show mole fractions for the three componentscalculated on the basis that the ratio of k 2 to k 1 is 0.5. The fit is reasonably good untilwell past the maximum in Y HEG . However the growth in Y IDA and fall-off in Y HEG athigh conversions is clearly underestimated. A ratio of 0.41 as estimated above gave