Understanding Chemical Reactions: From Mg and O2 to CO2 and H2CO3

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ldixon
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We lit a piece of Mg so the formula is:
2Mg(s) + O2(g) HEAT-- 2MgO(s)

We then dissolved this in water so it would then be:
MgO(s) + H2O(l) -- Mg(OH)2(l)

Next we blew into the solution which made it:
CO2(g) + H2O(l) -- H2CO3(l)

Is this all correct? Should I have (Aq) after the H2CO3?
 
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Look up the solubility of Mg(OH)2, if it's completely soluble then it may be more appropriate to subscript an "(aq)" term after it. The H2CO3 should be designated with the aqueous symbol.