#It Depends...
It Depends...
...on which kind of mask your character finds, and if they know the difference.
A standard mask used to administer oxygen, air and anesthetics:
A standard mask used to administer only oxygen:
If you character knows what to look for (and where in a hospital to find one), the first will do well enough, if properly sized and worn. This kind of mask is designed to work with the coaxial gas delivery / evacuation tubing that's attached to an anesthesia machine. The hose attaches to the opening at the top, a rubber head-band attaches to the four prongs, holding the mask on the face. At the bottom is a soft plastic balloon that surrounds the nose and mouth.
The second mask is designed to provide "blow-by" oxygen. This mask is a slightly harder plastic whose rubber band attachment is quite flimsy and weak (by design). This kind of mask can be found almost everywhere in a hospital and is designed to hook up either to the central O2 system or to any portable O2 tank. This kind of mask rests lightly on the face and is, by design, very leaky.
Problems:
Obviously, the second mask will admit aerosol poison along with oxygen or air from the tank. Ungood, that. This could, however, be the cause for several hectic MacGyver moments as your character realises that the mask isn't going to be quite up to the task. This is why God invented Tegaderm film dressings. Just glom a bunch of those all over the face and mask, taking care to seal up the O2 delivery tube and Bob's your uncle.
Should your character obtain the first kind of mask, they'll need a "converter" to go from the O2 tank's small gauge hose to the large opening. Part of the anesthesia supplies is an ambu bag which will do the conversion. Still, this mask isn't perfect! These masks are designed to keep anesthetic gasses inside the circuit (OR staff headaches from leaking anesthetics are not uncommon); but they're not designed for long term use and they certainly aren't designed to keep poisons out. Even when strapped to a person's face, they often leak, especially at the bridge of the nose. Your character will have to carry the O2 tank in one hand and jam the mask to their face with the other.
The tank can provide 15 lpm maximum, which should be more than enough to get your character through the Zone of Yuck. Using a standard hospital E tank, your character should be good for about 45 minutes or so at maximum flow. Tanks are notorious being not quite full...so, make sure they check the gauge before grabbing a random tank!
Reality Check = PASS!
Even so, it will be a harrowing and exciting venture with a very high risk of failure. For example, do note that the mask won't protect the eyes, and they, being mucus membranes, are susceptible to noxious fumes.