the respective tube or double tube and the larger is the residual conversion after said tube or double tube preferred reference values for the total length of the reactor space or gap range from about 2 to about 25 meters preferably from about 5 to 10 meters but can be different of course in certain cases preferred reference values for the length of the insert tubes or double tubes range from about 4 to 90 percent of the total length of the reaction space or gap preferably the reactor is furthermore equipped with two or more more preferably three separate tempering i e cooling or heating jackets which are consecutively in longitudinal direction of the reactor fitted to the reaction tube s of said tubular reactor a or to the outer and inner tube of the annular gap reactor b the first one of said tempering jackets e g being partially or completely located at a position between said second and third location the second one being located directly after said first tempering jacket and partially or completely after said third location and the optional third and further tempering jackets following consecutively after said second tempering jacket in this way it is possible to control the temperature of the reaction mixture independently by liquid cooling or heating media of a suitable temperature present in said two or optionally three or more separate tempering jackets in a way to avoid.