All species are the following:
[H2CO3], [HCO3], [CO3^2], [H3O+], [OH]
I have no idea how to approach this problem, so steps would be helpful so I can follow. Thanks.
1 Answer

The first step in this question is to observe that H2CO3 is a polyprotic acid. It will have two Ka values, each corresponding to an ionization.
(1) H2CO3 + H2O –> HCO3 + H3O+ [Ka = 4.5E7]
(2) HCO3 + H2O –> CO32 + H3O+ [Ka = 4.7E11]
Observe that the two Ka values differ from each other drastically. This will mean that in terms of pH, ONLY THE FIRST IONIZATION WILL AFFECT pH.
(1) H2CO3 + H2O –> HCO3 + H3O+ [Ka = 4.5E7]
I…..0.165M………………0………….0
C……x………………….+x…………+x
E….0.165x……………..x……………x
4.5E7 = x^2/(0.165x) <– use the appoximation rule because Ka is very small
2.72E4 = x
Thus, from equation (1), we see that the [H3O+] = 2.72E4M, [H2CO3] = 0.165M, and [HCO3]= 2.72E4M. Note that THIS step will determine the pH of the polyprotic acid
To calculate the last species, just transfer these values the next equation
(2) HCO3 + H2O –> CO32 + H3O+ [Ka = 4.7E11]
I….2.72E4………………0………2.72E4
C
E
4.7E11 = (x*2.72E4)/2.72E4
4.7E11 = x = [CO32]
To calculate the OH from H3O+, just find the pH of H3O+, subtract it from 14 to find the pOH, and find the [OH] from that.
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