Reaction extent or advancement of the reaction: A new general definition

Following the classical works by De Donder, Aris, and Croce we extend the general investigation of the concept of reaction extent to the case of an arbitrary number of species and (reversible or irreversible) reaction steps, not restricted to mass-action type kinetics. In typical cases, the reaction extent tends to infinity. However, we have defined quantities tending to 1, as it is assumed many times. We have calculated the reaction extent also for exotic (oscillatory and chaotic) reactions in order to see their meaning. Our approach tries to adhere to the customs of the chemists and to be mathematically correct and avoids some generally followed bad practice -- mainly in the educational literature.