PHlog [HA log [A

Figure 11.2. pH - log C diagram for phosphoric acid.

At higher pH, also

where [H30+] = [A"], log (_) = log ( 2 [H30+]) = -pH + 0.3 = log (2 [A']).

At still higher pH, but with values of pH<pKa, log [A"] dominates.

At pH>pKa, [A"] = C and log [HA] contributes the most to _

At very high pH, log [0H-] will dominate. These considerations are used in the construction of Fig. 11.3

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Figure 11.3. Buffering capacity of sea water as function of pH.

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Figure 11.3. Buffering capacity of sea water as function of pH.

If one is dealing with waters containing very few components, then it is frequently possible to refer to precipitation processes in a stricter sense. Precipitation is a chemical reaction with a relatively fast rate. Thus, in most instances the rate itself is of no direct concern, and there exist no models to describe the rate aspects of the process. The application of the process depends to a large degree upon the equilibrium situation that characterizes this process. Thus, the precipitation process is described by use of the equilibrium or the end-point of the reaction for specified boundary conditions. However, it must be pointed out that for most practical applications such equations derived from thermodynamic principles, have to be modified.

If precipitation is defined as the transformation of two or more dissolved components to a non-dissolved substance, the so-called precipitate, then dissolution processes and precipitation processes are similar reactions but of opposite directions. The solubility of a product, or vice versa the degree to which precipitation will control the dissolved species, is determined by the capacity of the solute to accommodate specific ions. This capacity is controlled by:

- the energy of bonding between the ions under consideration

- the dielectric characteristics of the solute

- the type and number of ions present in the system

The solubility of certain species or the relationship between two or more precipitating partners is furthermore controlled by third partners which lead to so-called side reactions. The solubility is also determined by temperature and ambient pressure.

The mass law describes the solubility and the corresponding precipitation reaction in terms of a solubility product. As seen from the example below the solubility product, Ks, describes the equilibrium concentrations of the precipitating ions, in particular the ion to be removed by precipitation.

The stoichiometric relationship describes how many atoms, molecules or ions of one reaction partner react with corresponding forms of the other partner. Using the above example:

The reaction rate with which the precipitation occurs, or with which a disturbed solubility / precipitation equilibrium is balanced again, is finite. However, in most instances of interest for the practical application of this process, the reaction rate is so large that the available detention time, or reaction time, suffices to reach the equilibrium. It has been indicated above that either in the stage of mixing of chemicals with the waste water stream, or in the transport of the precipitating system from one reactor (mixing reactor) to the next one (in most cases a reactor for the liquid-solid separation) the flow or detention time is large enough. However, there are situations where a change in the stoichiometric parameters in terms of an overdosing of the precipitation causing reagent leads to improved reaction rates and to increased efficiency. Efficiency in this instance is interpreted as reduced remaining concentrations of the ion to be precipitated.

The stoichiometric parameters for practical purposes can also be formulated as a quotient of concentration values. This is indicated in the example below:

On the basis of thermodynamic arguments this quotient should have a value of 1 in this instance shown above. However, practical observations have indicated that increased quotients may increase the reaction rate and the separation of the precipitate. Usually each precipitation reaction is followed in its practical application by a liquid-solid separation step. Depending upon the specific gravity of the solids formed or upon the amount of solids formed, such separation steps can be sedimentation, flotation or filtration.

It has been indicated that the equilibrium concentrations are a function of ambient pressure and temperature. Similarly the reaction rate is strongly affected by these parameters.

One further variable needs be described or defined: the pH value of the precipitating system which is of utmost importance. In aqueous solutions. The role of the process variables presented about will be treated in more detail in Section 11.2.

The application of precipitation as waste water treatment process involves a combination of three unit operations:

1. Addition of chemicals to obtain a precipitation. The process conditions determine the stoichiometric coefficient and thereby the amount of chemicals needed to produce a proper precipitation.

2. Mixing and flocculation of the chemicals to produce floes, which settle or flotate readily.

3. A separation process, whereby the precipitated components are removed from the water. It might be performed either by sedimentation, flotation, centrifugation or filtration.

The first operation has been treated in details above, while the two following processes are presented below.

Colloidal particles often possess an electrical charge, which creates a repelling force and prevents aggregation. Stabilizing ions are adsorbed to an inner fixed layer, which gives its particles its electrical charge, the latter varying with the valence and number of adsorbed ions. Ions of an opposite charge are held near the surface by electrostatic forces. The psi potential is defined as the gradient between the interface of the colloidal particles and the solution, while the zeta potential is defined as the gradient between the slipping plane and the solution. The zeta potential is related to the particle charge and to the thickness of the double layer. It is not possible to measure the psi potential, but the zeta potential can be determined and expressed.

The zeta potential can be used as an expression for the stability. It is possible to measure it on the basis of the following equation:


E = the dielectric constant of the medium p = the viscosity of the medium X = the thickness of the double layer U = the electrophoretic mobility.

The zeta potential is determined by measuring the mobility of the colloidal particles across the electrophoresis cell, viewed through a microscope. Several types of zeta meters are commercially available.

La Mer (1964) distinguished between two types of particle destabilization: coagulation and flocculation.

According to La Mer, coagulation results from compression of the electric double layer surrounding the colloids, while flocculation refers to a destabilization by adsorption of large organic polymers with a subsequent formation of bridges between particles and polymers. These definitions of the two terms - coagulation and flocculation - are not universally accepted, but are useful because they have a practical significance.

Fig. 11.4 is a schematic presentation of destabilization by flocculation.

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