Does such a pair of substances exist, that in certain physical conditions (temperature, pressure) when both are placed in the same conditions, one will be a liquid, the other - a gas, and the gas density will be higher than that of the liquid?
(let us exclude special states of matter - e.g. don't count superfluid as liquid, or plasma as gas.)
Answer
I've just remembered that there was once a suggestion to use a mixture of xenon and oxygen under high pressure to allow people to float/fly/swim in it. It was also stated that water could be lighter than such a mixture.
According to Smithsonian Physical Tables the critical point for xenon is
$16.6\,\text{C}^{\circ},\quad 60\,\frac{\text{kg}}{\text{cm}^2},\quad 1.155\,\frac{\text{g}}{\text{cm}^3}$
while the density of water is around this conditions according to this online calculator is $1.0015 \frac{\text{g}}{\text{cm}^3}$ and it is still liquid ($60\,\frac{\text{kg}}{\text{cm}^2} \approx 58.84\,\text{bar}$).
One may have a look on phase diagrams of water and xenon on wolfram alpha:
I suppose by lowering a bit the pressure under xenon critical point one can actually have a gas heavier than even water.
The original suggestion on high density xenon-oxygen breathable mixture should be in Ariadne section of New scientist, July 6, 1967. However this issue is not on Google books (yet?).
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