The problem of determining the limiting current density of copper electrodeposition on the vertical electrode under the conditions of electrolyte natural convection is solved numerically. The incomplete dissociation of copper sulfate and sulfuric acid by the second stage and the concentration dependences of physicochemical properties of solution are taken into consideration. The effect of incomplete dissociation of copper sulfate and sulfuric acid by the second stage on the ionic transport in the copper electrodeposition and on the limiting current density is estimated by comparing the results, which are calculated taking into account and ignoring the concentration dependences of dissociation constants, and also for the limiting cases of virtually complete dissociation of copper sulfate and sulfuric acid. It is shown that, in excess of supporting electrolyte, incomplete dissociation of copper sulfate and sulfuric acid only slightly affects the limiting current density: the limiting current density changes not more than by 10% with the variation of the dissociation constants by several orders of magnitude. At the moderate and small concentrations of supporting electrolyte, incomplete dissociation should be taken into account, because the error of limiting current density can exceed 50%.