## Carbonate Equilibria

The carbonate equilibria is a function of the ionic strength of water, activity coefficient, and the effective concentrations of the ionic species. The equilibrium coefficients that are calculated from the species concentrations are a function of the temperature. This functionality of the coefficients can, in turn, be calculated using the Van't Hoff equation, to be addressed later.

One of the major cations that can form scales as a result of the instability of water is calcium. Calcium plays an important role in the carbonate equilibria. We will therefore express the carbonate equilibria in terms of the interaction of the calcium ion and the carbonate species which are the reaction products of carbon dioxide and water. In addition, since the equilibria occur in water, the dissociation of the water molecule must also be involved. Using calcium as the cation, the equilibrium equations of the equilibria along with the respective equilibrium constants at 25°C are as follows (Rich, 1963):

The Ks are the values of the respective equilibrium constants. Ksp>CaCO is the equilibrium constant for the solubility of CaCO3. The pair of braces, { }, are read as "the activity of," the meaning of which is explained in the Background Chemistry and Fluid Mechanics chapter in the Background Prerequisites section.

As shown, the equilibrium constants are calculated using the activity. In simple language, activity is a measure of the effectiveness of a given species in its participation in a reaction. It is proportional to concentration; it is an effective or active concentration and has units of concentrations. Because activity bears a relationship to concentration, its value may be obtained using the value of the corresponding concentration. This relationship is expressed as follows:

where sp represents any species involved in the equilibria such as Ca , CO3 , HCO3 and so on. The pair of brackets, [], is read as "the concentration of," y is the activity coefficient.

### 11.1.1 Ionic Strength

As the particle ionizes, the number of particles increases. Thus, it is not a surprise that activity coefficient is a function of the number of particles in solution. The number of particles is characterized by the ionic strength p. This parameter was devised by Lewis and Randall (1980) to describe the electric field intensity of a solution:

i is the index for the particular species and z is its charge. The concentrations are in gmmols/L. In terms of the ionic strength, the activity coefficient is given by the DeBye-Huckel law as follows (Snoeyink and Jenkins, 1980; Rich, 1963):

In 1936, Langelier presented an approximation to the ionic strength p. Letting TDS in mg/L represent the total dissolved solids, his approximation is p = 2.5 (10-5) TDS (11.9)

Also, in terms of the specific conductance, sp conduc (in mmho/cm), Russell, another researcher, presented yet another approximation as f = 1.6( 10-5)sp conduc (11.10)

Example 11.1 The pH of a solution is 7. Calculate the hydrogen ion concentration?

Solution:

Example 11.2 The concentration of carbonic acid was analyzed to be 0.2 mgmol/L. If the pH of the solution is 7, what is the concentration of the bicarbonate ion if the temperature is 25°C?

Solution:

K = 10-635 = {H+}{HC0_} = 10'7{HC0_} 1 {H2C03} 0.2/1000

Example 11.3 A sample of water has the following composition: C02 = 22.0 mg/L, Ca2+ = 80 mg/L, Mg2+ = 12.0 mg/L, Na+ = 46.0 mg/L, HC0_ = 152.5 mg/L, and S04 = 216 mg/L . What is the ionic strength of the sample?

Solution:

Ion mg/L Mol. Mass gmols/L

so2_

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