In the case of air, this ideal limit, should the pump be perfectly hermetic and air an ideal gas, would be given by atmospheric pressure multiplied by the ratio between the total volume of the pump body and that of the clearance volume, according to Boyle's Law.
In all cases the effective limit is far lower and is reached when the difference between the pressure in the pump body when the piston has been lowered completely and the pressure reached in the recipient is insufficient to open the valve.
The machine can also be used as a rarefying pump; it is sufficient to connect the recipient containing the air or other gas we wish to rarefy to the suction pipe and leave the other one open.
In this case there is a limit on the minimum pressure that can be reached when the gas drawn in by the pump and subsequently compressed until it occupies the clearance volume only no longer succeeds in activating the outlet valve.