Stochastic models of solid dissolution are numerically studied considering homogeneous and inhomogeneous structures, with local dissolution rates related to reaction energies and temperature. Inhomogeneous solids have a granular lattice structure, with ratio g of intragranular and intergranular lateral sizes, ratio r of the corresponding dissolution rates, and r < 1 to account for enhanced dissolution at the grain boundaries. In homogeneous solids, the maximal deviation from the Faraday law of electrolysis due to the detachment of non-dissolved clusters (chunk effect) is close to 20%, at high temperatures, but the deviation is negligible for typical values of activation energies and room temperature. This justifies the hypothesis of change in the valence of dissolved ions of many experimental works. The surface roughness scales with exponents of the Kardar-Parisi-Zhang class. In inhomogeneous solids, many non-dissolved grains are detached in typical conditions of temperature and activation energies, leading to ratios of detached and dissolved masses of order g, for g >> 1. This suggests that inhomogeneity at the nanoscopic level is essential to observe a significant chunk effect. The global roughness shows oscillations in time due to dominant island detachment at some characteristic times. The dissolved surfaces resemble those of related granular surfaces, but the local roughness scaling shows a crossover scaling with smaller and nontrivial exponents. (C) 2013 Elsevier Ltd. All rights reserved.