The conversion of ammonia (NH_3) to nitrate (NO_3-1) via nitrite uses oxygen not water. Water is a byproduct of the process. The exact reactions differ from bacteria to bacteria. See
here. This is perhaps a bit more complicated than one may need for explanation however.
This may be more "simple".
Because most tanks' pH tend to be below 9 ammonia exists mainly as ammonium (NH_4+) so one would have to add another proton coming loose in the above equations. Because plants maintain a negative electrochemical potential accross their cell walls (i.e. they have a higher concentration of positively charges molecules outside rather than in the cells) the NH_3+ is able to enter the cells without the need for active transport whereas NO_3- has to be pumped accross against the gradient. I am unfortunatly unable to find a nice link to explain this.

So we will have to rely on what I can recall from my plant physiology courses.
By the way, the plant maintains this gradient not to import ammonium but to import calcium, magnesium, potassium etc... The latter salts generally occur as insoluble precipitates. The plants pump H+ out of their stems to lower the pH around themselves. The low pH dissolves the salts. This is also why UG filters are not good as they clear the H+ excess away starving the plant of needed minerals.
I think I have now wondered off topic abit...
tt4n