Air is mostly nitrogen, which has a molecular weight of about 28 amu. The presence of oxygen and other gases brings the average up somewhat, so we can take 29-30 g/mol as a reasonable estimate for dry air.
Acetone has a molecular weight of 62.
For two gases at the same temperature and pressure, the density depends only on the molecular mass. So acetone vapor is more than twice as dense as than air at the same temperature and pressure.
Incidentally, applying this same reasoning to methane (molecular weight 16) indicates that it is lighter than air, and a toy balloon filled with natural gas (which is mostly methane) will indeed float ... but only just barely, because the difference in density is small enough that the weight of the balloon itself almost cancels out the buoyancy of the methane.
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