pH of water in a limestone quarry with carbonate equilibrium

[coookiemonste]

Homework Statement

Find the pH of water in limestone (CaCO3) quarry.
H2CO3 pk1=6.37, pk2=10.32

Homework Equations

pH=pKa + log [conjugate base]/[acid]
Kw=10^-14

The Attempt at a Solution

CO3 2- + H2O -> HCO3- + OH-
Ka= [HCO3-][OH-]/[CO3 2-]
10^-10.32=x^2/[10^-6.37]
[OH-]=x=.01059
-log[OH-]=1.98
14-1.98=12.02
is this correct?

 

[wallace13]

since its a salt, I think you can do pH= 1/2 (pKa1 + pKa2)

 

[Borek]

since its a salt, I think you can do pH= 1/2 (pKa1 + pKa2)

No, that would work for solution of amphiprotic salt, here you start with fully neutralized carbonate.

A lot depends on the initial cncentration of carbonates - and this depends on the calcium carbonate solubility product. Besides, solubility will increase due to carbonates hydrolyzis, so finding an exact answer can be tricky. No idea how deep you are expected to get into it.

Ka= [HCO3-][OH-]/[CO3 2-]
10^-10.32=x^2/[10^-6.37]

Why do you think [CO₃^2-] = K_a1?

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