We consider a model of a two-component solution that consists of chemically reacting solutes and a chemically inert solvent. The particles interact via Lennard-Jones potentials. In addition, a directional associative interaction between the solute molecules promotes the formation of dimers, The theory for association in fluids of Wertheim is used to study the dimerization equilibrium. A multidensity Ornstein-Zernike equation is solved with the associative mean spherical approximation and, in some cases, with the hypernetted chain approximation, Some quantitative characteristics of dimerization in solution are obtained. We discuss the pair distribution functions, the solute-solvent coordination numbers, the partial molar volumes, and the compressibility, under varying conditions, Our particular concern is near-critical mixtures. The results, obtained with an explicit allowance for the chemical association between the reactants, show an enhanced solute-solvent clustering in near-critical solutions. The states distant from the critical region are characterized by more usual solvation of the solute molecules.