# How can concrete set underwater?

I'm about to teach concrete to some high school children. I'm not a chemist but as I understand it the limestone cycle is this:

\begin{align} \ce{CaCO3 &-> CaO + CO2}\tag{R1}\\ \ce{CaO + H2O &-> Ca(OH)2}\tag{R2}\\ \ce{Ca(OH)2 + CO2 &-> CaCO3 + H2O}\tag{R3} \end{align}

Two questions:

1. The water has to go somewhere or the concrete will stay wet. Air drying I could understand but how can concrete set underwater? And, assuming concrete dries from the outside in, wouldn't osmosis predict more water would be drawn into the concrete?

2. Making kilograms of calcium carbonate will take kilograms of calcium hydroxide and kilograms of carbon dioxide. How can such a large amount of carbon dioxide reach the concrete? There isn't a lot of it in water, is there? I could imagine some reaction might produce carbon dioxide in the concrete, but then wouldn't it end up frothy/honeycombed?