The title benzimidazole compounds, namely, 2-(4-methoxynaphthalen-1-yl)-1H-benzo[d]imidazole, C18H14N2O (I) and 2-(4-methoxynaphthalen-1-yl)-1-[(4-methoxynaphthalen-1-yl)methyl]-1H-benzo[d]imidazole ethanol monosolvate, C30H24N2O2·C2H6O (II), were synthesized by the condensation reaction of benzene-1,2-diamine with 4-methoxynaphthalene-1-carbaldehyde in the ratios 1:1 and 1:2, respectively. In I, the mean plane of the naphthalene ring system is inclined to that of the benzimidazole ring by 39.22 (8)°, while in II, the corresponding dihedral angle is 64.76 (6)°. This difference is probably influenced by the position of the second naphthalene ring system in II; it is inclined to the benzimidazole ring mean plane by 77.68 (6)°. The two naphthalene ring systems in II are inclined to one another by 75.58 (6)°. In the crystal of I, molecules are linked by N—H...N hydrogen bonds to form chains propagating along the a-axis direction. Inversion-related molecules are also linked by a C—H...π interaction linking the chains to form layers lying parallel to the ac plane. In the crystal of II, the disordered ethanol molecule is linked to the molecule of II by an O—H...N hydrogen bond. There are a number of C—H...π interactions present, both intra- and intermolecular. Molecules related by an inversion centre are linked by C—H...π interactions, forming a dimer. The dimers are linked by further C—H...π interactions, forming ribbons propagating along the b-axis direction. The interatomic contacts in the crystal structures of both compounds were explored using Hirshfeld surface analysis. The molecular structures of I and II were determined by density functional theory (DFT) calculations at the M062X/6-311+g(d) level of theory and compared with the experimentally determined molecular structures in the solid state. Local and global reactivity descriptors were computed to predict the reactivity of the title compounds. Both compounds were shown to exhibit significant anticorrosion properties with respect to iron and copper.