1. A system for delivering a liquid or air to an extracorporeal blood circuit in a hemodialysis apparatus comprising: (1) A pump cassette having a top plate and an opposing bottom plate, the bottom plate having pneumatic ports for connection to a source of pneumatic pressure, the pump cassette comprising: (a) a reciprocating membrane-based blood pump in which a pumping chamber of the blood pump is separated from a control chamber of the blood pump by a blood pump membrane operated by pneumatic pressure applied to the blood pump control chamber via at least one of said pneumatic ports, the blood pump fluidly connecting an inlet to an outlet of the pump cassette through a blood flow-path between the top plate and bottom plate of the pump cassette; (b) a metering pump having a pumping chamber in valved fluid communication with: a liquid flow-path between the top plate and bottom plate of the pump cassette, the liquid flow-path fluidly connected to the blood flow-path; a hollow spike on the top plate of the pump cassette, the hollow spike configured to fluidly connect a liquid-containing container to the metering pump through a passageway in the top plate; and an air vent on the top plate of the pump cassette, the air vent configured to fluidly connect to the metering pump through a passageway in the top plate; and (c) a first metering pump valve interposed between the metering pump and the hollow spike, a second metering pump valve interposed between the metering pump and the air vent, and a third metering pump valve interposed between the metering pump and the blood flow-path; and (2) a controller configured to control each of said valves and said metering pump to draw a volume of a liquid from the container via the hollow spike and to deliver the liquid to the blood flow-path via the liquid flow-path, or to draw a volume of air via the air vent and to deliver the volume of air to the container via the hollow spike or to the blood flow-path via the liquid flow-path.