Reaktionsfortschritt

Reaktionsfortschritt, literally “reaction progress,” is a concept used in chemistry to describe how far a chemical reaction has proceeded. It is most commonly described by the extent of reaction, denoted ξ, a scalar quantity that links the changes in the amounts of all species to the balanced stoichiometry of the reaction.

The extent of reaction ξ is defined by dn_i = ν_i dξ for each species i, where n_i is the amount (in moles) of species i and ν_i is its stoichiometric coefficient in the balanced equation (negative for reactants, positive for products). ξ increases as reactants are consumed and products are formed. Since dn_i has units of moles, ξ also has units of moles. The reaction can proceed only until the limiting reactant is exhausted, at which point ξ reaches a maximum value ξ_max.

Conversion is another common way to describe reaction progress, focusing on a particular reactant A. The conversion X_A = (n_A0 − n_A)/n_A0 can be related to ξ via X_A = −(ν_A/n_A0) ξ. This provides a convenient link between measured amounts and the extent variable.

In practice, the reaction rate r is often expressed in terms of the extent: r = dξ/dt, and for each species i, dn_i/dt = ν_i dξ/dt. This framework is widely used in kinetics and reactor design to formulate integrated rate laws, material balances, and plots of reaction progress. Example: for A → B with ν_A = −1 and ν_B = +1, n_A = n_A0 − ξ and n_B = n_B0 + ξ.