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Also, in case an environment with equal density of air and water can be made:
Will it be possible for a human to breathe in that environment?

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up vote 6 down vote accepted

One way to discuss the maximum density of a gas is to look at its phase diagram. In a PT phase diagram, we will obviously seek a point on the boundary of the gas region where the temperature is low and the pressure is high. For at least the Oxygen and Nitrogen phase diagrams, it looks like the critical point would be a good candidate for these maximum gas density conditions. Thus, identifying the density of air at its critical point would be a good possibility to get us its maximum density or close to its maximum density.

The critical point for air has a specific volume of $92.35 cm^3/mol$, and a density of $0.31 g/cm^3$ (by using its average formula mass). This is less than the density of water, which is $1.0 g/cm^3$ by definition.

Because of this, there seems to be a good case that the answer to your question is no. If the conditions are low enough temperature and high enough pressure to make the substance of air the same density of water (if possible at all), it will no longer be a gas, and most people's layman concept of "air" requires that it is a gas. To answer your second part, the critical point of air is at $-221^{\circ} F$ and the pressure is $37.25 atm$, so no, a human could not withstand these conditions.


Update:

I was unaware of how useful Wolfram Alpha has become. Here is air at conditions sufficient to produce a density greater than water:

http://www.wolframalpha.com/input/?i=air+at+2500+bar+and+-130+degrees+C

Here is another example, at $0^{\circ} C$:

http://www.wolframalpha.com/input/?i=air+at+5000+bar+and+0+degrees+C

diagram

(Image copyright Wolfram alpha, use believed consistent with terms)

Both of these lie squarely in the supercritical liquid region. Is that a gas, no, but it's not fully a liquid either. I suppose the next question is if you can breathe such a fluid. Well, for these conditions we're talking about 2,500 and 5,000 times atmosphere pressure. The deepest trench in the ocean has a pressure of 1,000 times atmosphere at the bottom (and no human has been there). Super cold temperatures are completely intolerable for humans, but pressure can be increased dramatically. In order to have breathable air the same density of water, we would have to create pressures many orders of magnitude times the world record of what has been withstood by a human. Whether or not it is absolutely impossible or not is kind of our of our scope. All I can say is that it seems unlikely.

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You could imagine replacing the nitrogen with some other biologically inactive gas. Argon would get you to half of water's density. Krypton gets to 90% of water's STP density. I believe I've read that xenon is an anesthetic, so I guess krypton is as good as we could do. –  dmckee Jun 4 '12 at 17:06
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Actually, my xenon link shows that this idea is a non-starter: all the heavy noble gasses cause bad narcosis at high pressure. So, scratch the above... –  dmckee Jun 4 '12 at 17:08
    
Okay, interesting. My take is that the answer depends on the interpretation of the question. I agree that the construct of "air" may be fungible to allow alterations that you suggest, but it is not the definition I've used in my answer. Whether or not some conception of air may exist as a heavier-than-water gas remains and open question although the answer is likely to be "no". –  Alan Rominger Jun 4 '12 at 17:25
    
According to peacesoftware.de/einigewerte/stickstoff_e.html a pressure of 1000 bar at 0°C gets you to a relative density of 0.6 while staying in the gas phase. The site won't allow pressures greater than 1000 bar, so maybe the nitrogen solidifies above that. –  John Rennie Jun 4 '12 at 18:39
    
@JohnRennie Unless I have the wrong thing, the critical pressure of Nitrogen gas is 33 bar. I'm not sure about the supercritical region, it might be gas-like, although not fully a gas (formerly, a supercritical liquid). The conditions that you give look to be in that region. wolframalpha.com/input/… –  Alan Rominger Jun 4 '12 at 19:36

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