An apparatus for extracorporeal treatment of blood (1) comprising a treatment unit (2), a blood withdrawal line (6), a blood return line (7), a preparation line (19) and a spent dialysate line (13); a non-invasive blood volume sensor (50) for determining an additional property of blood is active on a tube segment (61) of the blood withdrawal line or of the blood return line; the sensor includes one source (53) for directing a signal towards the blood, a plurality of detectors (57) for receiving the signal, and a controller (65) receiving the output signals from the detectors (57) and determining a blood volume variation and a value of sodium concentration in the blood (Napl) both based on the output signals. A process of determining at least one parameter and on property of blood circulating an extracorporeal blood circuit is also disclosed.