In the rapidly emerging field of nanotechnology, as well as in biology, where chemical reaction phenomena take place in systems with characteristic length scales ranging from micrometer to the nanometer range, understanding of chemical kinetics in restricted geometries is of increasing interest. In particular, there is a need to develop more accurate theoretical methods. We used a many-particle-density-function formalism (originally developed to study infinite systems) in its simplest form (pair approach) to study a two-species A + B --> 0 reaction-diffusion model in a finite volume. For simplicity reasons, it is assumed that the geometry of the system is one-dimensional (1d) and closed into a ring to avoid boundary effects. The two types of initial conditions are studied with (i) equal initial number of A and B particles, N-0,N-A = N-0,N-B, and (ii) initial number of particles equal on average, = . In both cases, it was assumed that the particles are well mixed in the initial state. It is found that the particle concentration decays exponentially for both types of initial conditions. In the case of the type ii initial condition, the results of the pair-like analytical model agrees qualitatively with computer experiments (Monte Carlo simulation), while less agreement was obtained for the type i initial condition, and the reasons for such behavior are discussed.