Device for the treatment of blood for single needle mode with means for collecting blood (11) comprising a closed volume, means for storing gas (18) comprising a closed volume, means for establishing a connection (19, 21) between the means for collecting blood (11) and the means for storing gas (18), where the means for collecting blood (11) and the means for storing gas (18), together with the means for establishing a connection (19, 21) between the means for collecting blood (11) and the means for storing gas (18), they form a closed volume in which gas cannot enter or from which gas cannot escape, means for transporting blood (6) to the means for collecting blood (11) in an extracorporeal blood circuit, where the extracorporeal blood circuit has a blood supply conduit (8) that extends into an inlet (4A) of a blood treatment unit (2) and a blood conduit return of blood (9) that starts from an outlet (4B ) of the blood treatment unit, means for compressing gas (20), and a control and calculation unit (27) that interacts with the means for collecting blood (11), with the means for storing gas (18), with the means to establish a connection (19, 21) between the means for collecting blood (11) and the means for storing gas (18), and with the means for compressing gas (20), so that in an arterial phase, by filling the means to collect blood, gas that is displaced from the means to collect blood is transferred to the means to store gas and, in a venous phase, to empty the means to collect blood, gas that has been stored in the means to storing gas is transferred to the means to collect blood by means of compressing gas, so that in the arterial phase blood can be supplied to the extracorporeal blood circuit and in the venous phase blood can be discharged from the extracorporeal blood circuit, characterized why The control and calculation unit (27) is designed in such a way that to initialize the successive arterial and venous phases, a max air pressure pressure is calcula
