A modified Bhatnagar - Gross - Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher - moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13 - moment distribution functions: (2) simple, classical assumptions provide sufficient models for reaction dynamics, (3) the reaction rate is energy independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.