I hope I'm right in picturing this "chemical mixing vessel" as a box. If so, and if it is filled with a liquid or gas (or mixture of liquids or gases, such as air) then the movement of some of the molecules in a certain direction within the box will instantly cause an equal number of molecules to move in the opposite direction to take their place. An example of this is if there was a helicopter hovering inside the box, or the fan in the question. Whether the helicopter was sitting on the floor or hovering, the downward force it exerts on the bottom of the box would be the same, so the load cells (whatever they may be) should show a relatively steady reading.
If there was some liquid (water, for example) in the bottom of this sealed box and you then heated it to evaporate some or all of the water, the overall mass of liquid water + gaseous water would be the same. The overall weight would also, therefore, be the same. It sounds strange because, obviously, if you tried to weigh (with an ordinary scale) a cubic metre of air that was simply mixed in with a whole room full of air, the scale would read zero. This is because all weighing scales used in our atmosphere have been calibrated to account for the constant downward force that gravity is causing the air to push with. I think that placing the scale in a vacuum (still on Earth, just in a room with no air) would make it possible to 'weigh' air, water vapour etc. You would just have to make sure that the scale was supporting the full weight of the gas (e.g. with a vertical tube or something). I hope I've come close to answering the question.