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Can you smell what's being cooked on the gas stove? If so, the combustion products from the stove are also reaching your nose.
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That’s a good point, and obvious now you point it out.

On the other hand, when water turns into steam at standard atmospheric pressure, it expands in volume by about 1,700 times.

Whereas the gas in your stove is already a vapour, mostly methane, turning in to mostly water vapour and carbon dioxide. So the expansion ratio isn’t going to be anywhere near as high as that.

I’d say you’re still right.

Still, I wonder to what extent an exhaust fan does help.

If the exhaust fan can vent x cubic feet per minute and the room is y cubic feet in volume then it takes z minutes to full ventilate the room, etc etc.

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Air molecules move randomly at over 300 meters per second (not coincidentally close to the speed of sound).
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That’s a hyper local measurement, and temperature dependant.

You’d sure notice if the air in your kitchen was swooshing around at 671 miles per hour.

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It squeezes me with approximately the weight of an elephant sitting on my chest. But humans are adapted to this and don't notice. It helps that the insides of my lungs are being squeezed outwards by the same force. Otherwise I surely couldn't breathe.
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I’ve never once been in a property that had an exhaust fan sufficient. I’ve had the exhaust on full blast and the spike on the air quality sensor on another floor of the house is rapid and massive.

I suspect a sufficient ventilation would require something more like a lab fume hood that can pull a negative pressure on the area around the stove.

And from what I have seen, a good number of exhaust fans are straight up fake and just ventilate back in to the room rather than ducted outside.

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> And from what I have seen, a good number of exhaust fans are straight up fake and just ventilate back in to the room rather than ducted outside.

Culinary Cargo Cult.

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