ppm it is to be stressed that in existing technologies the separation of salts takes up much time of 1 5 to 24 h this necessitates the use of bulky equipment with large capacity for the leaving to stand of the salts nevertheless the effectiveness of the separation of the salts does not exceed 90 therefore for a substantial and certain function of the heat exchanger of the separation columns expensive coalescent filters with special construction must be installed these lower the salt content in the cleavage products to 10 to 20 ppm which according to the invention is achieved without use of filters the acetone possibly after supply of the acetone separated off in the evaporator 3 via the pipe 17 is separated off in column 6 from the cleavage products and passed via pipe 24 to further working up the cleavage products stream viii separated from acetone are removed as sump product from the column 6 and passed via pipe 25 for further rectification the separation of cumene from the cleavage products is carried out in two successively placed columns 7 and 8 in the column 7 as head product there separates the cumene containing fraction which contains not more than 1 ams and 0 3 wt phenol over the head of this column.