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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 $\ce{CaCO3 -> Ca^{2+} + CO3^{2-}}$ .

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 $\ce{CaCO3 -> Ca(OH)2 + CO3^{2-}}$ and then calculate the concentrations, but is that what this question is even asking? Thanks!

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    $\begingroup$ You need to write the precipitation reaction. If something precipitates, what is happening? $\endgroup$ – SendersReagent Apr 10 '16 at 1:23
  • $\begingroup$ Using a graph to plot a solubility curve or use already obtained data to then determine the solubility of CaCO3 at ph 8 may help? $\endgroup$ – Technetium Apr 10 '16 at 4:21
  • $\begingroup$ I doubt that aragonite will precipitate at all unless additional conditions are met (e.g. presence of magnesium ions). Under normal conditions I would expect calcite to be formed since it is less soluble than aragonite and is the thermodynamically more stable modification. $\endgroup$ – aventurin Apr 10 '16 at 16:27
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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.

           Hägg diagram of carbonic acid (Leyo, Wikipedia)

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

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