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6-10   WATER AND WASTEWATER ENGINEERING

                            and O’Melia, 1968). In water treatment applications the mechanism is hypothesized to be nucle-
                            ation of the precipitate on a particle surface followed by growth of an amorphous precipitate that
                            entraps other particles.


                              CHEMISTRY OF COAGULATION
                              The chemistry of coagulation is extremely complex. The following discussion is limited to the
                            basic chemistry. Because metal coagulants hydrolyze to form acid products that affect pH that
                            in turn affects the solubility of the coagulant, it is useful to begin with a review of a few basic
                            concepts that will help explain the interaction of coagulants and pH.


                                  Buffer Solutions.  A solution that resists large changes in pH when an acid or base is added or
                            when the solution is diluted is called a  buffer  solution. A solution containing a weak acid and
                            its salt is an example of a buffer. Atmospheric carbon dioxide (CO  2  ) produces a natural buffer
                            through the following reactions:

                                                                                             2


                                   CO g ()    CO 2   H O    H CO 3    H   HCO 3     2 H    CO 3         (6-2)
                                      2              2       2
                            where    H  2  CO  3        carbonic acid

                                  HCO 3       bicarbonate ion
                                     2
                                  CO 3        carbonate ion
                                This is perhaps the most important buffer system in water and wastewater treatment.
                            It will be referred to several times in this and subsequent chapters as the  carbonate buffer
                            system.
                                 As depicted in  Equation 6-2 , the CO  2   in solution is in equilibrium with atmospheric CO  2  (g).
                            Any change in the system components to the right of CO  2   causes the CO  2   either to be released
                            from solution or to dissolve.
                                One can examine the character of the buffer system in resisting a change in pH by assuming
                            the addition of an acid or a base and applying the law of mass action (Le Chatelier’s principle).
                            For example, if an acid is added to the system, it unbalances it by increasing the hydrogen ion
                            concentration. Therefore, the carbonate combines with it to form bicarbonate. Bicarbonate reacts
                            to form more carbonic acid, which in turn dissociates to CO  2   and water. The excess CO  2   can be
                            released to the atmosphere in a thermodynamically open system. Alternatively, the addition of a
                            base consumes hydrogen ions, and the system moves to the right with the CO  2   being replenished
                            from the atmosphere. When CO  2   is bubbled into the system or is removed by passing an inert
                            gas such as nitrogen through the liquid (a process called  stripping ), the pH will change more dra-
                            matically because the atmosphere is no longer available as a source or sink for CO  2  .  Figure 6-7
                            summarizes the four general responses of the carbonate buffer system. The first two cases are
                            common in natural settings when the reactions proceed over a relatively long period of time. In a
                            water treatment plant, the reactions can be altered more quickly than the CO  2   can be replenished
                            from the atmosphere. The second two cases are not common in natural settings. They are used in
                            water treatment plants to adjust the pH.
                                In natural waters in equilibrium with atmospheric CO  2  , the amount of CO  2   in solution is

                                                                                         2
                            quite small in comparison to the HCO 3  in solution. The presence of Ca    in the form of lime-
                            stone rock or other naturally occurring sources of calcium results in the formation of calcium
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