Apparatus for converting feed gas (28) into a product gas (29), comprising at least one reactor (1) with a reaction chamber (15) bounded by the inner wall of an outer tube (4) closed at a first outer end and an inner tube (14) received coaxially in this outer tube (4) and provided at both its outer ends with openings, which reactor (1) is provided with an inlet chamber (11) and with an outlet chamber (10), wherein a first wall (31) of the outlet chamber (10) encloses the outer tube (4) and extends therefrom, and a second wall (12) of the outlet chamber (10) lying opposite the first wall (31) encloses the outer tube (4) and extends therefrom, and the inlet chamber (11) is bounded by the second wall (12) of the outlet chamber (10) and a third wall (47) which lies opposite this second wall (12), encloses the outer tube (4) and extends therefrom.