Chemical Engineering - Industrial Organic Chemistry

Reaction order estimate

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Reaction Order Estimate To observe the order of a reactionR!( P= R) P, is to plot the conversion registered after a time, as a function of the initial concentrationC 0. This estimate is of importance when probing the initial concentration eect to the conversion, as shown in the maleic anhydride synthesis.The rate law reads as follows: dCd t= kCn which can be integrated to obtainC(t): (C1 n =C1 n 0 (1n)kt n6 = 1 C=C 0e kt n= 1 Using the conversion denitionC=C 0(1 ), then the function(t)is obtained forn6 = 1, and it has general validity: = 1 1(1n)ktCn 1 0 1=(1n) Lettingk=k 0kn 1 1such that k 0= 1 =, the observation timeis then independent from the reaction order. The objective term is thusk=kn 1 1 and the conversion relations become: 8 > < > : = 1 11 n( k 1C 0)1 n 1=(1n) n6 = 1 = 1e 1 n= 1 wherek 1C 0acts as a dimensionless variable, which is the independent vari- able with range(0:5;4), chosen arbitrarily and for qualitative analysis. In practical situations, only the kinetic constantkand the observation timeare known, and it is possible to recoverk 1= ( k)1 =(n1) , and from the Damköhler numberDa =k Cn 1 0= ( k 1C 0)n 1 is readily obtained: (= 1(1(1n)Da)1 =(1n) n6 = 1 = 1e 1 n= 1 However, sincenis unknown, we setk 1= 1 and the objectivek 1C 0range becomes theC 0range and Da =Cn 1 0. The (C 0) plots do not change their monotonic trends nor their derivative's sign, which are the only properties of interest. We remark that this proceduredoes notextract the exact reaction ordern, but it only gives a robust estimation procedure ifnlies above or below1. We can derive a lower limit fork 1C 0, setting = 1forn6 = 1: (k 1C 0) l= (1 n)1 =(1n) whenk=kn 1 1 1 Figure 1: Dimensionless observation plot for a generic n-th order unimolec- ular reaction. The distinction betweenn >1andn (1n)1 =(1n) or, in terms of initial concentration:C0> [k(1n)]1 =(1n) therefore we see thatn= 0leads a minimum valuek 1C 0= 1 . This lower limit is due to thechoice, because once it is xed, there is a limit initial concentration such that at that specic time all the reactant has been con- verted. Thus, ifC 0< (C 0) lthen we would reach full conversion before the observation time. We evaluate the derivative of, or@ =@(k 1C 0) atk 1C 0= 1 : 8 > > > < > > > :@ @ (k 1C 0) 1= ( n1)nn= (1n) n6 = 1 @ @ (k 1C 0) 1= 0 n= 1 2 this means that if the value of conversion decreaseswhen we increasek 1C 0 then the reaction order isn