A quantum mechanical approach to treat diatom-triatom exchange processes of the type AB+CDE -->A+BCDE is presented. The initial nine degree-of-freedom problem is simplified to a reaction having active only five of such degrees of freedom, which emulates a rotating-stretching AB molecule colliding colinearly with a linear CDE molecule. This model is then applied to study the H-2+C2H -->H+C2H2 reaction. In the present work, the H-2 rotations are treated using the infinite-order-sudden-approximation (IOSA) method, whereas the coupled states (CS or j(z)) approximation is employed to uncouple the total angular momentum J from internal rotations. Thus, a four-dimensional mathematical analysis is performed, which allows the computation of state-to-state reactive probabilities and cross sections. The bending vibrational levels of the acetylene C2H2 molecule are calculated on the basis of a one single degenerate bending expansion, i.e., just one H (the attacked one) is considered to bend, the remainder being frozen. Present results show that the product acetylene is formed in highly excited vibrational states, particularly if either the reacting asymmetric CH or symmetric C-2 stretches are involved. Finally, rate constant results are compared with two other theoretical treatments and with experiments.