In an electrical discharge reactor for facilitating chemical reactions, power consumption and yield of chemical reactions are optimized, and heat dissipation is improved, by filling an interspace between a first electrode (1) and a second electrode (2) of the discharge reactor with a block (4) of rigid, open-pored dielectric material. The material preferably has a porosity of 80-90%. The skeleton of the block can consist of glass, quartz or ceramic. The diameter of the pores in the block, in which micro-discharges occur, represents an effective gap width that is critical for the progress of the silent discharge. The diameter of the pores can, for example, be between 0.05 millimeters and 0.2 millimeters to optimize power consumption. As a safeguard against breakdown, a barrier layer (5) of a nonconductive, solid material can be provided between the electrodes (1, 2). To facilitate a reaction of CO.sub.2 and H.sub.2 to form methanol and water, or to facilitate a reaction of CO.sub.2 and CH.sub.4 to form synthesis gas, the skeleton of the block can be coated with a suitable catalyst. The catalyst can include, for example, Cu and ZrO.sub.2, or Cu and ZnO, or nickel compounds.