# K2 [co32 ih[hco3t

From the second and third equations, respectively, we can express both [H2C03] and

[C032~] in terms of |HC03~| and [h~j, and substitute these relationships solutions into the mass balance equation:

[H2co3] = [HCO3! [H+]/Kx [CO32~] = k2 [HC03~]/[H+]

Thus

([HC031 [H+J/Kj) + ([HC03D + (K2 [HCO3I/[H+D = C

Solving this equation for bicarbonate and substituting the solution into the preceding pair of equations yields the expressions given in the main text for the fraction of each species present at any pH.

Although this salt is almost 'insoluble, a small amount of it dissolves when water passes over it:

CaC03(s) Ca2+ + C032" (4)

Natural waters that are exposed to limestone are called calcareous waters. The dissolved carbonate ion acts as a base, producing its conjugate weak acid, the bicarbonate ion, as well as hydroxide ion in the water:

CXV"" + H20 ^^ HC03" + OH" (5)

These reactions that occur in the natural three-phase (air, water, rock) system are summarized pictorially in Figure 13-7; the reactions of the carbon dioxide-carbonate system are summarized for convenience in Table 13-3.

In the discussions that follow, we analyze the effects on the composition of a body of water of the simultaneous presence of both carbonic acid and calcium carbonate. We shall see that the presence of each of these substances increases the solubility of the other, and that the hydrogen ion and hydroxide ion produced indirectly from their dissolution largely neutralize each other, yielding water with almost neutral pH.

To obtain a qualitative understanding of this rather complicated system, the effect of the carbonate ion alone is first considered.

Water in Equilibrium with Solid Calcium Carbonate

Water

Rock, soil, or sediments

For simplicity, we first consider a (hypothetical) body of water that is in equilibrium with excess solid calcium carbonate and in which all other reactions are of negligible importance. The only process of interest in this case is reaction (4) (see Table 13-3). Recall from introductory chemistry that the appropriate equilibrium constant for processes that involve the dissolution of slightly soluble salts in water is the solubility product, Ksp, which equals the concentrations of the product ions, each raised to its coefficient of the balanced equation. Thus, for reaction (4), JCsp is related to the equilibrium concentration of the ions by the equation figure 13-7 Reactions among the three phases (air, water, rocks) of the carbon dioxide-carbonate system.

Reactions in the C02-Bicarbonate-Carbonate System

Reaction Number |
Reaction |
Equilibrium Constant |
K Value at 25°C |

1 |
H2C03 H+ + HC03" |
KaI (H2C03) |
4.5 X 10"7 |

2 |
HC03" H+ + C032" |
Ka2(H2C03) |
4.7 X 10""11 |

3 |
C02(g) + H20(aq)^H2C03(aq) |
Kh |
3.4 X 10"2 |

4 |
CaC03(s) Ca2+ + C032- |
KP |
4.6 X 10"9 |

5 |
C032" + HC03" + OH" |
Kb (C032") |
2.1 X 1CT4 |

6 |
CaC03(s) + H20(aq) ^^Ca2+ + HCOf + OH" | ||

8 |
CaC03(s) + C02(g) + H20(aq) ;=^Ca2+ + 2 HC03" |
UKW |
1.0 X 10H |

It follows from the stoichiometry of reaction (4) that as many calcium ions are produced as carbonate ions, and that in this simplified system both ion concentrations are equal to S, the solubility of the salt:

S = solubility of CaCO; = [Ca2+] = [C032~]

After substituting S for the ion concentrations in the ksp equation and inserting the Ksp value from Table 13-3, we obtain

Taking the square root of each side of this equation, a value for S can be extracted:

Thus the solubility in water of calcium carbonate is estimated to be 6.8 X 10~5 mol/L, assuming that all other reactions are negligible.

PROBLEM 13-12

Consider a body of water in equilibrium with solid calcium sulfate, CaS04, for which fC = 3.0 X 10~5 at 25°C. Calculate the solubility, in g/L, of calcium sulfate in water, assuming that other reactions are negligible.

According to reaction (5), dissolved carbonate ion acts as a base in water. The relevant equilibrium constant for this process is the base ionization constant, Kb, where

Kb(C032~) = [HC031 [0H~]/[C032~]

Since the equilibrium in this reaction lies to the right in solutions that are not very alkaline, an approximation of the overall effect resulting from the simultaneous occurrence of reactions (4) and (5) can be obtained by adding together the equations for the two individual reactions. The overall reaction is

CaC03(s) + H20(aq) ^^ Ca2+ + HC03 + OH (6)

Thus the dissolution of calcium carbonate in neutral water results essentially in the production of calcium ion, bicarbonate ion, and hydroxide ion.

It is a principle of equilibrium that if several reactions are added together, the equilibrium constant K for the combined reaction is the product of the equilibrium constants for the individual processes. Thus, since reaction (6) is the sum of reactions (4) and (5), its equilibrium constant k6 must equal KspKh, the product of the equilibrium constants for reactions (4) and (5).

Since the acid and base ionization constants for any acid-base conjugate pair such as HCOj" and CO-/* are simply related by the equation

Ka kh = kw = 1.0 X KT14 at 25°c it follows that for the conjugate base C032"

Kj = KyiCO^ ) = Kw/Ka (HCO3 )

Since Ka for HCC)3~ is the Ka2 value for the carbonic acid system, then from Table 13-3,

Kb = 1.0 X 10~l4/4-7 x 10"11 = 2.1 X 10^4

Thus, since K6 for the overall reaction (6) is JC^iCj,, its value is (4.6 X 10"9) X (2.1 X 10~4) = 9.7 X 10~13.

The equilibrium constant for reaction (6) is related to the ion concentrations by the equation k6 = [Ca2+] [HCGf] [OH-]

If we make the approximation that reaction (6) is the only process of relevance in the system, then from its stoichiometry we have a new expression for the solubility of CaC03, namely

S = [Ca2+] = [HC031 = [OH-]

Upon substitution of S for the concentrations, we obtain

Taking the cube root of both sides of this equation, we find

Thus the estimated solubility for CaC03 is 9.9 X 10~5 M, in contrast to the lesser value of 6.8 X 10~5 M that we obtained when the reaction of carbonate ion was ignored. The CaC03 solubility here is greater than estimated from reaction (4) alone, since much of the carbonate ion it produces subsequently disappears by reacting with water molecules. In other words, the equilibrium in reaction (4) is shifted to the right since a large fraction of its product reacts further [reaction (5)].

From these results, it is clear that the saturated aqueous solution of calcium carbonate is moderately alkaline; its pH can be obtained from the hydroxide ion concentration of 9.9 X 10-5 M:

PH = 14 - pOH = 14 - log10[OH"l - 14 - log10(9.9 X 10~5) = 10.0

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