The replica RISM theory is used to investigate the structure of electrolyte solutions confined in carbonized polyvinylidene chloride (PVDC) nanoporous material, compared to bulk electrolyte solution. Comparisons are made between the models of electrolyte solution sorbed in the carbonized PVDC material and a single carbon nanosphere in bulk electrolyte solution. Particular attention is paid to the chemical potential balance between the species of the sorbed electrolyte solution and the bulk solution in contact with the nanoporous material. As a result of the strong hydrophobicity of the carbonized PVDC material in the absence of activating chemical groups, the densities of water and ions sorbed in the material are remarkably low compared to those in the ambient bulk solution. The interaction between water molecules and cations becomes strong in nanospaces. It turns out that, in carbon nanopores, a cation adsorbed at the carbon surface is fully surrounded by the hydration shell of water molecules which separates the cation and the surface. Distinctively, an anion is adsorbed in direct contact with the carbon surface, which squeezes a part of its hydration shell out. The tendency increases toward smaller cations, which are characterized as "positive hydration" ions. In the bulk, cations are not hydrated so strongly and behave similarly to anions. The results suggest that the specific capacitance of an electric double-layer supercapacitor with nanoporous electrodes is intimately related to the solvation structure of electrolyte solution sorbed in nanopores, which is affected by the microscopic structure of the nanoporous electrode.