How do you calculate the pH of water when adding carbonates to water?

[Dennis1590]

They are doing a bad job in explaining how the pH changes when adding carbonates to water. Either sodium bicarbonate or another carbonate.  I tried to understand it by myself and google searches but still haven't found a way. This is the problem: 

So the water has a pH of 6.35. Which is the pKa value of H₂CO₃/HCO₃^-. So in solution at this pH there should be 50% H₂CO₃, 50% HCO₃^- and 0% CO₃^2-.

So in general they now start calculating stuff with the electroneutrality equation which is:

H⁺= HCO₃^- + 2*CO₃^2- + OH^- .

Lets assume that the total of carbonates species is 0.03 mol/L at a pH of 6.35. Than 50%*0,03 = 0.015 mol/L of H₂CO₃ and 0.015 mol/L of HCO₃^- in solution. There is also kw/10^-6.35=10^-7.65 mol/L OH^- present in solution.

So filling this in the electroneutrality equation: H⁺= 0.015 + 10^-7.65 = 0.015 mol/L.

So this is a bit confusing. Since pH is 6,35 it should be H⁺= 10^-6.35 mol/L. Not 0.015 mol/L. 

My question is. What am I missing here. Can somebody help clear the confusion.

 

 

[John Cuthber]

5 hours ago, Dennis1590 said:

They are doing a bad job 

Who?

[chenbeier]

7 hours ago, Dennis1590 said:

My question is. What am I missing here.

You missing it's a weak acid.

The dissociation of carbonic acid is not half H2CO3 half HCO3-. This is only valid if you have a buffer of carbonic acid and (sodium) hydrogencarbonate half half. Then pH is pKa according Hendersson Hasselbalch.

pH = 0.5* (pka-logc) for weak acid.

 

Edited May 19 by chenbeier