Florida International University ?pH Buffering in Natural Waters Worksheet

pH Buffering in Natural Waters:

We have seen that the carbonic acid system plays a critical role in providing natural waters with both acid- and base-neutralizing capacity, i.e., in resisting changes in pH when strong acids or bases are added and maintaining a stable pH environment. The reasons that carbonic acid is so critical are because:

it is a weak acid (with pK₁ = 6.35 and pK₂ = 10.33), so it exhibits chemical speciation, and

it is an abundant species in natural waters (acetic acid and phosphoric acid would also contribute to pH buffering but are present at very low concentrations in natural waters)

What I want you to do for this quiz is to plot the fractions of the three carbonic acid species as a function of pH using a spreadsheet.

Unknown concentrations: [H₂CO₃], [HCO₃^–] and [CO₃^2–]

So we need three equations:

(1)First acid dissociation constant, K₁ = 10^-6.35 = [H⁺][HCO₃^–]/ [H₂CO₃]

(2)Second acid dissociation constant, K₂ = 10^-10.33 = [H⁺][CO₃^2–]/ [HCO₃^–]

(3)Mass balance equation, C_T = [H₂CO₃] + [HCO₃^–] + [CO₃^2–]

I suggest keeping pH as the “master” variable, i.e., define pH values in the range 0 to 14 in the first column of the spreadsheet; keep the second column for values of [H⁺] = 10^-pH.

Then write the molar concentrations of each species as a function of hydrogen ions [H⁺]. Use equations (1) and (2) to write the [H₂CO₃] and [CO₃^2–] in terms of [HCO₃^–]:

[H₂CO₃] = [H⁺][HCO₃^–] /K₁ (4)

[CO₃^2–] = K₂[HCO₃^–] /[H⁺] (5)

Now substitute for [H₂CO₃] and [CO₃^2–] using equations (4) and (5) in the mass balance equation (3):

C_T = [H₂CO₃] + [HCO₃^–] + [CO₃^2–] = [H⁺][HCO₃^–] /K₁ + [HCO₃^–] + K₂[HCO₃^–] /[H⁺]

C_T = [HCO₃^–]

So that F₁ = [HCO₃^–]/ C_T = 1 /

Substitute for K₁ and K₂ to get values for F₁ in the third column of your spreadsheet. Now use equations (4) and (5) to calculate the F₀ and F₂ fractions in columns four and five.

Here’s a fragment of what your spreadsheet should look like: