I have two different after-market fuel caps on my C172. The right tank
cap is vented; the left is not. Should both be vented? Is a properly
functioning vented cap one that only allows air to flow into the tank?

That's probably right. Check your ADs. I seem to recall there being
one from the 1970s that deals with fuel caps. Something to do with
vapor lock above 5000 feet.

Don

To No Name...

There was an AD in '79 which made it mandatory for all Cessnas from the 140A
and beyond to install a half-vented cap, at least one, on either tank, leaving
the other non-vented cap on unless you changed both.

The purpose was to allow inward venting in the event the single point vent was
plugged with bugs or ice. Some have the original single vent on top of the
wing and others behind the strut.

The tanks are interconnected via a tank to tank tube so the original single
vent worked for both, except when the original single vent got plugged.

The half-vented cap has a small "umbrella" silicone vent which will allow air
in whenever the vacuum in the tank exceeds its (never defined) opening
threshold. The cap cannot allow fuel or pressure out, that being the reason it
is called the half-vented cap.

Cessna will sell you replacement half-vented caps but will not sell you the
silicone umbrella-shaped valve in the event it sticks to the seat or if it goes
missing.

Don is mixing problems and solutions in his description of another problem
with the 172's, a venting problem related to using the Both position of the
selector but not related to the cap. Above an xxx altitude using the Both
position, the engine will quit. You are supposed to have a placard that says:
"do not use the Both position above xxxx altitude". The planes which are
subject to the fault are specified in another service note and...maybe..an AD
as well. Find the serial range of the affected planes for the Both position
problem and yours may or may not be in it.

Neal