Zero-order reactions are those in which the rate of transformation of a substrate is unaffected by changes in the substrate concentration (the exponent on S on the right-hand side of the equation is zero, S0 = 1, thus zero order). Zero-order kinetics can be described using the following equation
In this case, the reaction rate is determined by factors other than the substrate concentration, such as the amount of catalyst. At high substrate concentrations, at which substrate levels are not limiting, enzymatic reactions are usually zero order, e.g., nitrification at high NH4 levels and denitrification at high NO- levels. Figure 16.1 shows plots of zero-order reactions compared to plots of other kinetic equations. After integration, the equation can be solved for the substrate concentration as a function of time and becomes
where St (concentration) is the amount of substrate remaining at any time, S0 (concentration) the initial amount of substrate in the system, k (concentration time-1) the rate constant, and t (time) the time since the initiation of the reaction. A useful term to describe the reaction kinetics is the half-life, which is the time required to transform one-half of the initial substrate, e.g.,
The mean residence time (or turnover time) is the time required to transform a quantity of material equal to the starting amount S0 (i.e., St = S0) then at steady state tmrt = S0 /k (4)
FIGURE 16.1 Graphical representation of kinetic equations depicting the shapes of substrate decomposition curves: (a) zero order, (b) first order, (c) with exponential growth, and (d) with logistic growth.
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