Using equilibrium with calcite and co2

Question

Assignment:

K_H = 3.3 x 10^-7

K_a1 = 4.5 x 10^-7 (carbonic acid)

K_a2 = 4.7 x 10^-11 (bicarbonate)

K_sp = 5 x 10^-9 (calcite)

Assuming equilibrium between the atmosphere, seawater, and calcite:

[H⁺]³ =                     K_H²K_a1²K_a2P_CO2²

                                            2K_sp

[HCO₃^-] =                 2K_sp{H⁺]²

                               K_a1²K_a2K_HP_CO2

[CO₃^2-] =               K_a1K_a2K_HP_CO2

                                    [H⁺]²

[Ca²⁺] =                K_sp{H⁺]²

                              K_a1K_a2K_HP_CO2

(a) Predict seawater pH, [CO₃^2-], [Ca²⁺] at an atmospheric concentration of 280 ppmv. Predict seawater pH, [CO₃^2-], [Ca²⁺] at an atmospheric concentration of 840 ppmv.

(b) How would these changes affect the tendency for calcite or aragonite to dissolve or precipitate from seawater? Explain how this affects the carbonate pump for removing CO2 from the atmosphere?

Provide complete and step by step solution for the question and show calculations and use formulas.