11. Interfacial Mechanism and Kinetics of Phase-Transfer Catalysis

dy 1ady o¼ QYy ody 2ody o¼ QXy ody 2a¼ dy 2o y 1o y oym 1a QY 1 1 y 3a y 4a yþ 1ay 1o K d1 y 1o y 1o y 1o y oy 2o ym 2ay QX P1o y 11oy 2a 2 y 3a y 5ak d2 y 1o y o QXy oy 2oy 1om QXy 2ay 1ody 3ady o¼ 2y 3a y 5aK d2 y 1o y oþ 1y 3a y 4aK d1 y 1o y o 1y 1ay 1o y o 2y 2ay 1o y oð17Þð18Þð19Þð20ÞThe mass balances for Q i ,Y , and Xare given below:1 ¼ y 1o þ y 1a þ y 2o þ y 2a þ y 3a ð21Þy 4a ¼ P 2 y 1a y 1o þðy o 1ÞP 1 ð22Þy 5a ¼ P 3 þ 1 y 2a y 2o þð1 y o ÞP 1 ð23Þin which the dimensionless variables and parameters are defined asy o ¼ ½RXŠ o; y½RXŠ 1o ¼ V o½QYŠ oiy 3a ¼ V a½Q þ Š aQ iQ i; y 4a ¼ V a½Y Š aQ i QY ¼ K QYA=V o; Pk o Q i =V 1 ¼ V 0½RXŠ ioQ i; y 1a ¼ V a½QYŠ aQ i; y 2o ¼ V o½QXŠ o; yQ 2a ¼ V a½QXŠ a;iQ i; y 5a ¼ V a½X Š a; Q QX ¼ K QXA=V a;ik o Q i =V o; P 2 ¼ V a½MYŠ i; PQ 3 ¼ V a½MXŠ i;iQ i 1 ¼ k d1k o; 2 ¼ k d2k o; ¼ V oV a; ¼ tk oQ iV oð24Þand ½MXŠ i , ½MYŠ i , and ½RXŠ i represent the initial concentrations of reactants MX, MY,and RX, respectively. By introducing the values of the parameters into Eqs (15)–(23), thedynamic phenomena of a liquid–liquid PT-catalytic reaction was obtained.Wang and Yang [57] reported that the ion-exchange reaction-rate constant wascalculated with three differential equations as below for the dynamics of QY in boththe aqueous and organic phases in a two-phase reaction without adding the organicreactant by the numerical shooting method and correlating it with the experimental data.d C QYdtdC QYdt¼ K QY AC QY¼ K da C QY C QXC QY =m QYK QY A VV C QYC QY =m QYð25Þð26ÞdC MYdt¼ K da C QY C QX ð27ÞThe intrinsic reaction-rate constant in the organic phase is obtained by reacting QYwith RX in a homogeneous solvent and using Eq. (12). According to the literature, Wangand Yang [57] and Wu and Meng [69] have found the intrinsic reaction-rate constant fromtheir systems. The equilibrium constant and mass transfer constant of the catalyst betweentwo phases obtained are discussed in the next section.Copyright © 2003 by Taylor & Francis Group, LLC