Ummm...OK...Got most of that. It does mean however that a ship running out of air could be no issue if there is fuel stored as water.
The issue is running out of N2, more than O2. Crack a ton of ammonia, tho... (NH3) and it's 14/17ths Nitrogen by mass... liquid amonia is 683kg/kL at boil (-33.5°C at 1013mB, gas is 0.73 kg/kL at NTP (1013mB 20°C).
Liquid nitrogen is 808.4kg/kL in liquid at Std pressure and -195.8°C, 1.1651kg/kL as a gas at NTP.
So a Td of ammonia is 9.562Mg, of which 1.687Mg is hydrogen, and 7.875Mg is Nitrogen. Storing both as cryogenics... we get 1.687 Td H2, and 0.454 Td of Liquid N2. Expanding that to NTP we get some 6759kL, or 482Td, which, at 79% (the only trace gas really essential is CO2, and the life aboard will make that...) is sufficient for 611 Td of Std atmosphere... (1 Td of cryogenic N2 is sufficient for 1346 Td of standard mix, but needs 5267kg of 02, 4.617 kL cryogenic O2 or 0.33 Td.
In other words, we can store 901 Td of standard mix per Td as cryogenics...
And we then need 5kg more O2 per man-week...
Stashing spare atmosphere as water and ammonia is highly efficient by volume... but not by mass. Storing fuel as water and/or ammonia is efficient by volume, but again, not by mass.
Unless you need the nitrogen and oxygen...
http://www.engineeringtoolbox.com/ammonia-d_971.html
http://www.engineeringtoolbox.com/nitrogen-d_1421.html
http://www.engineeringtoolbox.com/gas-density-d_158.html