c(1) is the concentration of di-isocyanate, c(2) and c(3) the
two intermediates when one of the two cyanate groups
reacted with an R–OH group, c(4) is the product concentration
and finally, c(5) is the R–OH concentration. The
initial concentrations are known such that a numerical
integration of the five coupled differential equations can be
performed, for example by the Runge–Kutta method. In
Fig. 2a, the change of reaction agents are shown for typical
kinetic constants of the un-catalyzed reaction. In the
model, both R–OH groups are assumed as independent
reaction centers, therefore, the concentration starts at
a relative value of 2. The NCO concentration also diminishes
according to above equations. In Fig. 2b, the same equations
are solved for the case of a catalytic reaction with kinetic
parameters about a factor of 10 faster. The equilibrium state
is, therefore, reached in a much shorter reaction time.