The pH of earth\'s water is controlled by the combination of several equilibria

Question

The pH of earth's water is controlled by the combination of several equilibria found in water, as well as between water and the atmosphere. This problem considers a model for oceanic water. H2CO3 + CO3 yields 2HCO3 1) Calculate the equilibrium constant for this equilibrium using Ka1 and Ka2 of carbonic acid. 3) Starting from a pure solution of HCO3, how are the concentrations of H2CO3 and CO3 related to each other? 4) Ocean water has an average pH of approx. 8.1. How are the concentrations of H2CO3 and CO3 related to each other in ocean water? 4) Do you think modeling ocean water as a pure dilute bicarbonate ion solution a good model

Explanation / Answer

1) the equilibrium will be between

H2CO3 + CO3-2 --> 2HCO3-

Equilibrium constant = K = [HCO3-]^2 / [H2CO3][CO3-2]

The Ka1 and Ka2 for H2CO3 will be

H2CO3 --> H+   + HCO3-

Ka1 = [H+] [ HCO3-] / [H2CO3]

HCO3- --> H+ + CO3-2

Ka2 = [CO3-2][H+] / [HCO3-]

so K =    Ka1 / Ka2

2) Question missing

3) HCO3- + H+ --> H2CO3 (1/Ka1)

1/Ka1 = [H2CO3] / [HCO3-] [H+]

Ka1 = [HCO3-] [H+] / [[H2CO3]

pKa1 = pHCO3- + pH - pH2CO3

pHCO3- = pKa1 - pH + pH2CO3......(1)

HCO3- ---> H+ + CO3-2     (Ka2)

Ka2 = [H+]'[CO3-2] / [HCO3-]

pKa2 = pH' + pCO3-2 - pHCO3-

pHCO3- = pH' + pCO3-2 -pKa2 ... ...(2)

So we can equate (1) and (2)

pKa1 - pH + pH2CO3 = pH' + pCO3-2 -pKa2

So (CO3-2) = {(2Ka)/[H+]} X [HCO3-]

4) Average pH = 8.1

H2CO3 --> H+ + HCO3-

HCO3- --> H+ + CO3-2

[H+] = -antilog 8.1 = 7.94 X 10^-9

So if we know the concentratio of any species we can calcualte concentration of CO3-2 accrodingly

4) yes the modelling water is a good model

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