The chemically relevant so-called phenomenological forward and reverse rate coefficients of reversible bimolecular solution reactions, for nonlocal reactivities defined via attributed irreversible diffusion-kinetic schemes [W. Naumann and A. Molski, J. Chem. Phys. 103, 3474 (1995)], are exactly expressed by formal operator expressions. It is shown that this rate coefficient definition corresponds to the so-called integral encounter theory by Gopich, Kipriyanov, and Doktorov [J. Chem. Phys. 110, 10888 (1999)], an isolated reactive pair approximation. Assuming detailed balance, for the bimolecular isomerization A + B reversible arrowB + C the operator expressions lead to exact relations with the rate coefficients of the irreversible partial reactions A + B -->B + C and A + B <--B + C. Generalizations of the well-known Noyes formula to reversible reactions result when the corresponding Wilemski-Fixman closure approximations of the irreversible and reversible rate coefficients are inserted. (C) 2001 American Institute of Physics.