Weakly acceptor-doped ceria ceramics were characterized structurally and compositionally with advanced transmission electron microscopy (TEM) techniques and electrically with electrochemical impedance spectroscopy (EIS). The grain boundaries studied with TEM were found to be free of second phases. The impedance spectra, acquired in the range 703 <= T/K <= 893 in air, showed several arcs that were analyzed in terms of bulk, grain-boundary, and electrode responses. We ascribed the grain-boundary resistance to the presence of space-charge layers. Continuum-level simulations were used to calculate charge-carrier distributions (of acceptor cations, oxygen vacancies, and electrons) in these space-charge layers. The acceptor cations were assumed to be mobile at high (sintering) temperatures but immobile at the temperatures of the EIS measurements. Space-charge formation was assumed to be driven by the segregation of oxygen vacancies to the grain-boundary core. Comparisons of data from the simulations and from the EIS measurements yielded space-charge potentials and the segregation energy of vacancies to the grain-boundary core. The space-charge potentials from the simulations are compared with values obtained by applying the standard, analytical (Mott-Schottky and Gouy-Chapman) expressions. The importance of modelling space-charge layers from the thermodynamic level is demonstrated.