Yes, indeed. A combination of low temperatures and high pressures results in the different components of air condensing out as liquids. Air is about 78% nitrogen and 22% oxygen (the remaining components are mostly carbon dioxide, water and argon, all in very small quantities and can be neglected). First, the oxygen condenses into the liquid at 90.2 K (which is negative 182.9 degrees C,) and then nitrogen condenses into the liquid at 77.4 K (which is negative 195.75 degrees C). This process of condensation is in fact used industrially to separate nitrogen and oxygen. When cooled further, these liquids freeze into solids.

Air is made up of several different gases, which all freeze at different temperatures. If you were to place an air-tight box into an incredibly cold freezer, the gases would freeze at different times as the box cooled, and so theoretically, you would get layers of different frozen gases. However, there are so few molecules of any gas in air relative to the volume it occupies, you probably wouldn't be able to see the layers. Instead, when you opened the box (assuming you could do so without melting the crystals or freezing yourself), you would probably just see a few crystals sprinkled on the bottom of the box.

The first gas to freeze would be water vapor. This is why the air is so dry in very cold places. Then carbon dioxide would freeze, and then nitrogen. The last gases to freeze would be oxygen and argon. At absolute zero, all the atoms in the different gas molecules would merge into one atom (see the question this week on absolute zero ).

For scientists living at the South Pole in the dead of winter it can get as cold as minus 80 degrees Celsius. This makes it very hard for them to breath outside without a special air supply. At such cold temperatures, the carbon dioxide freezes and drops out of the air. (Remember that it is the amount of carbon dioxide in our blood, not the amount of oxygen, that triggers our brain to take a breath. The scientists would pass out simply by "forgetting" to breathe.)

Yes, you can freeze air, and yes, each ingredient of air will freeze at a different temperature, so that if you were to take a jar of air and slowly make it colder and colder, each different ingredient would freeze into a different layer, just as you suggest.

Water, for example (which is often present in air as humidity), freezes at 32 degrees Fahrenheit, or 0 degrees Celsius. You can see this happen sometimes on cold nights, when there is frost on the windows. This frost is moisture which used to be in the air and then froze in a layer onto your window. If your windows got really cold: about -200 Celsius or -330 Fahrenheit, then the nitrogen in the air would liquefy on your window, and at about -220 Celsius or -365 Fahrenheit, it would freeze solid, giving you a layer of solid nitrogen. The other ingredients of air freeze at intermediate temperatures.

The only gas which doesn't freeze solid is Helium. It liquefies at -270 Celsius or -450 Fahrenheit, but it will never freeze solid unless you squeeze quite hard on it.