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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:

calcium carbonate                  -> calcium oxide     + carbon dioxide
calcium oxide     + water          -> calcium hydroxide
calcium hydroxide + carbon dioxide -> calcium carbonate + water

$\ce{CaCO3 -> CaO + CO2}$
$\ce{CaO + H2O -> Ca(OH)2}$
$\ce{Ca(OH)2 + CO2 -> CaCO3 + H2O}$

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?

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The chemistry you have posted is for non-hydraulic cement, which requires air drying for precisely the reasons you enumerated. The kind of cement that sets underwater uses silicates and various oxides (primarily calcium, aluminum and iron oxides). The basic chemical process that is occurring is hydration, whereby the mixture of oxides and silicates incorporates several water molecules directly into the crystal lattice. The fact that the setting process both uses water, and also produces a structure that is insoluble and robust to attack by water, is what makes underwater setting of hydraulic cement possible.

With regard to teaching your high school class, it's probably better to stick to the lime cycle for non-hydraulic cement as far as detailed chemical reactions are concerned. One interesting point that you can tell them about hydraulic cement is that its chemistry is still not completely understood, and even the molecular crystal structure was only very recently sorted out by MIT scientists in 2009.

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