Abstract: The shaft seal between a fixed housing wall (2) and a revolving shaft (1) consists of a collar (6) fixedly connected to the shaft (1), respectively one leg of the U-shaped sealing rings (69, 71) pressing against this collar. The cavities (14, 15) of the sealing rings (69, 71) can be acted upon, via connections, by a pressure medium, wherein respectively one of the legs of the sealing rings (69, 71) is pressed sealingly against the collar (6). The annular chamber (17) coaxial to the end face of the collar (6) can be filled with a lubricant and/or a coolant by way of an inlet and outlet. This structurally simple shaft seal is arranged in compact fashion. This seal operates in a safe and reliable manner. For the prevention of chemical accidents, a circulating pressure medium can be provided to act only on the sealing ring (69) located closest to the reaction chamber (3), and this pressure medium can be continuously monitored for traces from the reaction chamber (3) by way of an indicator.