Initial rate estimation from reaction progress

Figure C3.1.2 Comparison of lipase activities using an olive oil substrate emulsion prepared with different emulsifying agents. The lipase used in the reaction mixture was from C. rugosa (at 0.06 mg/ml) in the presence of 5% (w/v) each of gum arabic (triangles) or Triton X-100 (diamonds). Reaction progress analysis was obtained using titrimetry. Broken lines represent estimation of initial reaction rates.

In order to estimate the initial rate, the entire course of this reversible reaction was integrated according to Eq. (18.73), and redrawn in a linear form in Fig. 8B. Since the reaction was started with a saturating concentration of one of the substrates and, in this case, iCp /Ca and [Bo] [Ao], it is admissible to treat reaction (18.74) as an irreversible monosubstrate reaction and fit the entire reaction progress curve to Eq. (18.73). From the linear plot, one can calculate the maximal velocity V (equd to a reciprocal intercept on ordinate) and V/K (equal to a reciprocal slope). 

Two types of cteviation from the first-orda kinetics are noted for photo-aialthamal isomerization reactions in polymer films. The first is the normal type, in which the reaction rate is the same as or smaller than that in solutions at the initial stage and then progressively becomes smaller. Typical examples are thermal decoloration of the photocolored merocyanine form of spirobenzopyran molecularly dispersed in or chemically bound to a polymer matrix > and photoisomerization of the transazobenzene residue incorporated in polymer main chains The first interpretation for the decoloration of the merocyanine form assumed the existence of different isomers, each of which fades independently following first-order kinetics On the other hand, Kryszewski et al. proposed the kinetic matrix effect, which means that the distribution of free volume may lead to the deviation from first-order kinetics. His idea was based on the finding that deviations from first-order kinetics can be observol even in simple molecules such as azobenzene which has only one trans or cis isomeric form. The effect of free volume distribution on reactivity was further demonstrated by studies of annealed polymer films The distribution function of free volume as well as the critical free volume v were estimated for the merocyanine form of spiropyran in poly(methyl methacrylate) derivatives of azobenzene in polystyrene and azobenzene in polycarbonate The deviation from first-order kinetics was also observed in cyclizing imidization of model poly(amic acid) in a polyamide matrix... 

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