Observations of 18 different molecules toward the Orion Bar are presented and analyzed to determine the chemical composition of this dense photon dominated region (PDR). In addition to molecules commonly found in dark clouds, the CO+ ion has definitely been identified. In contrast, no HOC+ is found, indicating an abundance ratio HCO+/HOC+ > 500. Chemical models are developed to explain the observed molecular column densities across the Orion Bar. These models include the geometrical, clumped structure derived in Paper I (Hogerheijde et al. 1995), which suggests that across the Bar, the PDR changes from a face-on to an edge-on geometry and back. It is found that the clumped structure does not affect the chemistry since the clumps contain only 10% of the material. The simplest model combining chemistry and geometry is therefore an one-dimensional homogeneous PDR at the face-on positions, and the same PDR convolved with the inferred geometry at the edge-on positions. This model produces column densities which are in good agreement with those derived from the observations. In particular, the observed trend that radicals such as CN and C2H have larger column densities close to the ionization front is well reproduced because these lines of sight sample a larger portion of the outer PDR where the radical abundances peak. In contrast, species such as SO are more prominent away from the ionization front, where the line of sight intersects more of the inner, shielded cloud. Only the column densities of H2S, SiO and CO+ cannot be reproduced by our models; all other species are well fitted. The results from two-dimensional calculations, which take the actual geometry and the clumps explicitly into account, are in good agreement with the one-dimensional case, justifying our simple approach. The most important difference between these models is the temperature structure, which is affected by the presence of dense clumps in the two-dimensional case and by scattering of photons from the wall of the cavity. The temperature is high - of order 1000K - at the outer PDR layers, and drops rapidly inward.