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The weight of the gas is gone once it's burned
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Well, no. The weight of the gas is no longer IN THE TANK when its burned. It is, instead, in the weight of all of the waste products put off by the car. The air we breathe out, with all of those CO2 molecules, has weight. So does everything we excrete (including sweat). So the weight is never "gone" - it just goes into the waste products.
Heather - I don't know if you'd notice the difference or not, but I'd assume it'd be measurable, even if it wasn't really something you could pick up on yourself. If your body is actively metabolizing fat and you're losing weight, you'll be breathing out more weight (so you can get out the extra CO2 you're producing) and excreting more water (so you can get the extra H20 out), and if you were REALLY paying attention and carefully standardizing your water intake/activity levels/moisture intake from food/room humidity, you might be able to notice. But so many things go into the amounts of water we excrete that it would be really hard to tell where the effect was from.