Precipitaiton of aragonite I'm not positive what this questions is asking.  The prompt says "Write balanced equations for the following processes.  Chemical species should be the dominant ones at the given $\mathrm{pH}$. Show your work in deriving these equations."  Then the actual question is: 


  Precipitation of aragonite ($\ce{CaCO3}$;  $K_\mathrm{sp} = 4.8 \times 10^{-9}$), at $\mathrm{pH}~8$.


The balanced equation would just be $\ce{CaCO3 -&gt; Ca^{2+} + CO3^{2-}}$ .

I know that in an acid-base reaction I can use the $\mathrm{pH}$ as the $K_\mathrm{sa}$ to find the concentrations of the reactants and products, but I'm not sure where the $\ce{H+}$ would come in here.  I'm also not sure what finding the concentrations has to do with writing a balanced equation.  Does $\ce{Ca(OH)2}$ have something to do with this?  

I could change the equation to $\ce{CaCO3 -&gt; Ca(OH)2 + CO3^{2-}}$  and then calculate the concentrations, but is that what this question is even asking?  Thanks!
I think the question aims at the composition of carbonic acid solutions. The concentration of carbonate ions ($\ce{CO3^{2-}}$) depends on the pH of the solution. At low pH values the concentration is low, at high pH values the concentration is high. So the question is if the concentration of $\ce{CO3^{2-}}$ at pH 8 is high enough to precipitate calcium carbonate.

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$\ce{H2CO3}$: black, $\ce{HCO3^{-}}$: violet, $\ce{CO3^{2-}}$: turquoise, $\ce{H+}$ and $\ce{OH-}$: grey