The effects caused by the chemical reactions on the transport coefficients of a mixture of ideal gases which undergo a simple reversible symmetric reaction of the type A+A--> <--B+B are analyzed within the framework of a kinetic theory based on the Boltzmann equation. The analyzed system is closed to the final stage of a chemical reaction where the affinity is considered to be a small quantity and the system tends to the chemical equilibrium. This kind of reaction is known as "fast" reactions, because the reactive processes are of the same order as the elastic ones. The internal degrees of freedom of the molecules of the gas are not taken into account. This enables to represent the gas molecules as rigid spheres and therefore to determine the coefficients of thermal conductivity, diffusion, thermal-diffusion ratio, shear viscosity, and the forward reaction rate analytically. It was verified that some factors-among others, the concentration of the reagents (or products of the reaction), the activation energy, the heat of reaction, and the steric factor-can affect in a significant way the transport coefficients in reactive gas mixtures.