We will start by determining the mass of the syringe. To correct for the buoyancy in the air we need to seal the end, pull the plunger back, lock it in place and then weigh the syringe.

With the end of the syringe sealed the plunger will be pulled back to evacuate the syringe.
Because there is a vacuum inside we need to lock the syringe plunger in place. Click for a movie.