Details

Snapshot 1: zero-order kinetics

Snapshot 2: first-order kinetics

Snapshot 3: second-order kinetics

Snapshot 4: fractional-order kinetics ()

Isothermal degradation of chemical reactions and biological decay processes frequently follow fixed-order kinetics with the exponent in the differential rate equation . In this equation, is the concentration at time and is the (temperature-dependent) rate constant in the corresponding units of concentration and time. For zero-order kinetics (), , where is the initial concentration. For first-order kinetics (), , and for any other order, . Note that for this equation reduces to .

In an actual degradation process such as molecule disintegration, enzyme denaturation, or cell or organism mortality, neither the concentration nor density can have negative or complex values. Thus, the general equation for -order kinetics is only applicable for , , , and combinations for which this does not happen. For , this means that the model is valid only for time , beyond which , and for , this time is .

This Demonstration lets you generate degradation curves for any kinetic order in the range of 0 to 2.5 and various combinations of and by identifying the case and using the relevant formula. You can vary all three parameters , , and , as well as the actual time and process duration. The graphic display shows the concentration decay curve (top) and corresponding degradation rate versus time curve (bottom). Also shown are the numerical values of the momentary decay ratio, , and the decay rate, , which correspond to the moving dots on the concentration and rate versus time plots.

The purpose of this Demonstration is to illustrate the concept of a reaction’s kinetic order. Therefore, not all possible decay rate curves represent an actual physical disintegration or degradation process.