Deffeyes diagram

Such a graph, also known as a Deffeyes diagram, may be derived from the electroneutrality equation, written with Aik in place of the difference between... 

The Deffeyes diagram of Fig. 2-15 is a family of such straight-line relationships, plotted for each of several pH values. Note that very similar graphs can be drawn in which PC02 is used in place of CT in this case, the carbonate species concentrations in the electroneutrality equation are equal to PCOl multiplied by a constant which is a function of pH. 

The effects of additions of Aik or Cx to a water are easy to determine graphically using a Deffeyes diagram, as shown below in Example 2-10. For further detail on the acid-base chemistry of natural waters, the reader is referred to Stumm and Morgan (1996) or Morel and Hering (1993). 

In the Deffeyes diagram coordinate system, the addition of strong acid (Ca, moles/liter) and strong base (Cb, moles/liter) can be represented by... 

In general, natural waters contain alkalinity as well as weak acids and weak bases. Calculation of the pH of a water from Aik and weak acid and weak base concentrations requires that mass conservation equations, the electroneutrality condition, and mass action equations for all weak acids and weak bases be solved simultaneously. In natural waters, however, the weak acids of the carbonate system are often present at significantly higher concentrations than other weak acids or weak bases. Cj is the sum of the concentration of dissolved CO2, carbonic acid, and the concentrations of the two anions produced when carbonic acid ionizes (HCOs and COa ). Various tools have been developed to simplify the analysis of waters dominated by Aik and Cj. One of these tools is the Deffeyes diagram... 

The solution is based on the Deffeyes diagram of Fig. 2.20. For the early morning scenario, follow the horizontal line from 6 x 10 eq/liter on the Aik axis until it intersects pH 7.5 (point B). Then follow the vertical line to the Ct axis, to find that Cx is 6.4 x 10 M. 

Graphs using variables with conservative properties (Cj, [Aik], or [Acy]> as coordinates can be used expediently to show contours of pH, [H2CO3], [HCO ], and so on. On such diagrams, as shown by DefFeyes (1965), the addition or removal of base, acid, CO2, HCO, or CO is a vector property. These graphs can be used to facilitate equilibrium calculations. 

The relationship between alkalinity, Ct.coj and pH has been used by Deffeyes to construct a diagram relating alkalinity toCi-.coa cil a series of constant pH values. This diagram, shown in Fig. 4-21, can be used for a wide variety of calculations involving the addition and removal of various species from the carbonate system. 

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