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Calcium Carbonite in a Lake

If a piece of Calcite (Calcium Carbonate) is put into the lake, would it tend to dissolve? Calcium carbonate solubility is 10^-8.35 M2, and the measured concentration of calcium ion is 0.1mM (millimolar)

Information received:
Lake pH=4, and total carbonate concentration of 0.001M.

Carbonate Equilibria:
CO2 + H20 <-> H2CO3 KH= 10^-1.5 mole/(liter.atm)
H2CO3 <-> HCO3- + H+ K1= 10^-6.3 mole/lter
HCO3- <-> CO3^-2 + H+ K2= 10^ -10.3 mole/liter

In a previous question I calculated the concentration of each carbonate species in the lake water, I think they are correct.
H2CO3= 10^-5
HCO3-= 5.012 X 10^-8
CO3^-2= 2.512 X 10^-14

I do not not even know where to begin... My chemistry is a bit rusty. Please help me set the problem up.

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Solution Preview

This is basically a solubility problem, with a few little tricks involved. For one, we are dealing with some acid base chemistry, but do ...

Solution Summary

This solution is provided in 545 words in an attached .rtf file. It discusses acid base chemistry and ionization, and gives step-by-step explanations for solving the problem.