# Calculate the concentration of all species in a 0.165 M solution of H2CO3?

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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.

• 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 = 4.5E-7]

(2) HCO3- + H2O –> CO32- + H3O+ [Ka = 4.7E-11]

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 = 4.5E-7]

I…..0.165M………………0………….0

C……-x………………….+x…………+x

E….0.165-x……………..x……………x

4.5E-7 = x^2/(0.165-x) <– use the appoximation rule because Ka is very small

2.72E-4 = x

Thus, from equation (1), we see that the [H3O+] = 2.72E-4M, [H2CO3] = 0.165M, and [HCO3-]= 2.72E-4M. 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 = 4.7E-11]

I….2.72E-4………………0………2.72E-4

C

E

4.7E-11 = (x*2.72E-4)/2.72E-4

4.7E-11 = 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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