Question

You have solid calcium carbonate and inorganic carbon in equilibrium in a lake at pH 7. Use equilibrium calculations to show that due to this equilibrium the calcium concentration is ~0.5 mM.

Answer 1

Calcium Carbonate and Water

Minerals containing calcium carbonate have different solubilities in water. Two types of carbonate minerals are listed in the table above. An average value for the K_sp of calcium carbonate is about 5 x 10^-9.

K_sp = [Ca²⁺][CO₃^2-] = 5 x 10^-9

There must be net neutrality so the number of positive charges must equal the number of negative charges in solution.

2 [Ca²⁺] + [H⁺] = 2 [CO₃^2-] + [HCO₃^-] + [HO^-]

In any basic solution of calcium carbonate, the concentration of protons is much less than the concentration of calcium ions and the concentration of bicarbonate anions is greater than either carbonate or hydroxide anions, so:

2 [Ca²⁺] = [HCO₃^-]

Effect of Caco3 on pH :

1. Henry's Law tells us the concentration of dissolved CO₂.
   • K_H/p_CO2 = [CO₂] = 10^-4.88
   
   
2. We can treat the dissolved CO₂ as an acid.
   • K_a1 = [HCO₃^-][H⁺]/[CO₂] = 10^-6.37
   
   
3. Bicarbonate is also an acid.
   • K_a2 = [CO₃^2-][H⁺]/[HCO₃^-] = 10^-8.4
   
   
4. The concentration of calcium carbonate is governed by the solubility product constant of the mineral.
   • K_sp = [Ca²⁺][CO₃^2-] = 10^-8.3
   
   

Using the equations above, it is possible to calculate the concentration of any of the species in solution.

• 
  
• 
  
• 
  
• [CO₂] = K_H/p_CO2
  
  {[H⁺]}³ = [CO₂]²(K_a1)²(K_a2)/2(K_sp)
  
  [HCO₃^-] = [CO₂](K_a1)/[H⁺] = 2 (K_sp)([H⁺]²)/(K_a1)(K_a2)[CO₂]
  
  [CO₃^2-] = (K_a1)(K_a2)[CO₂]/[H⁺]

• In general, there are two different values of the pHs of calcium carbonate equilibrium for waters of the same total alkalinity AlkT, calcium concentration, temperature Tand ionic strength of water I. However, in the pH range from 6.5 to 9.5 there is onlyone value of pHs calculated from the system of equations .For the investigations into the calcium carbonate equilibrium presented herea more complex model was adapted. In this model, both the total alkalinity and theconcentration of calcium were modified in the computations based on the concentra-tions known from the chemical analyses of water by subtracting the ions involved ininorganic complexes (the so-called ion pairs effect):

  [Ca2+] = [Ca]T – [CaOH]+ – [CaHCO3]+ – [CaCO3] – [CaSO4]

  AlkT = [CO32–]T – [CaCO3]0 – [MgCO3]0 + 0.5 [HCO3–]T –0.5 [CaHCO3]+– 0.5 [MgHCO3]+ – 0.5 [H3O+] + 0.5 [OH–].