Apparatus for purifying a liquid, which comprises: - a container provided with at least one inlet opening and with at least one outlet opening, and susceptible of being traversed by a liquid flow to be treated containing ionized particles; - at least one plurality of closed cells, each delimited by at least one anionic membrane and by at least one cationic membrane, and such membranes (6, 7) are perimetrically sealed to each other with interposed first spacing means; - at least one plurality of open cells, susceptible of being traversed by said liquid flow to be treated, each delimited by the anionic membrane and by the cationic membrane of two adjacent closed cells, between which the same open cell is interposed and comprising second spacing means placed to separate said anionic and cationic membranes outside said closed cells; - at least two electrodes (11, 12) associated with two end cells of said container and connected to electrical power supply means adapted to supply them with a direct supply voltage (V A); - a control unit connected to said electrical power supply means, adapted to alternately control the polarity reversal of said electrodes (11, 12) between a first operating polarity, with which it supplies the electrodes (11, 12) with a charge opposite that of the membranes (6, 7) of the closed cells facing the electrodes (11, 12), in order to force the ionized particles present in the treatment liquid contained inside said open cells to pass inside said closed cells through said anionic and cationic membranes, and a second regeneration polarity with which it supplies the electrodes (11, 12) with a charge equal to that of the membranes (6, 7) of the closed cells facing the electrodes (11, 12), in order to force the ionized particles present inside said closed cells to pass inside said open cells through said anionic and cationic membranes; said apparatus being characterized in that it also comprises at least one polymer substance having functional groups with non-zero electric charge, which is contained inside said closed cells and is arranged for creating chemical bonds with the charged particles of said liquid which enters said closed cells by traversing said anionic membranes and said cationic membranes. - a container provided with at least one inlet opening and with at least one outlet opening, and susceptible of being traversed by a liquid flow to be treated containing ionized particles; - at least one plurality of closed cells, each delimited by at least one anionic membrane and by at least one cationic membrane, and such membranes (6, 7) are perimetrically sealed to each other with interposed first spacing means; - at least one plurality of open cells, susceptible of being traversed by said liquid flow to be treated, each delimited by the anionic membrane and by the cationic membrane of two adjacent closed cells, between which the same open cell is interposed and comprising second spacing means placed to separate said anionic and cationic membranes outside said closed cells; - at least two electrodes (11, 12) associated with two end cells of said container and connected to electrical power supply means adapted to supply them with a direct supply voltage (V A); - a control unit connected to said electrical power supply means, adapted to alternately control the polarity reversal of said electrodes (11, 12) between a first operating polarity, with which it supplies the electrodes (11, 12) with a charge opposite that of the membranes (6, 7) of the closed cells facing the electrodes (11, 12), in order to force the ionized particles present in the treatment liquid contained inside said open cells to pass inside said closed cells through said anionic and cationic membranes, and a second regeneration polarity with which it supplies the electrodes (11, 12) with a charge equal to that of the membranes (6, 7) of the closed cells facing the electrodes (11, 12), in order to force the ionized particles present inside said closed cells to pass inside said open cells through said anionic and cationic membranes;