Fractional Composition Equations

We now derive equations that give the fraction of each species of acid or base at a given pH. These equations will be useful for acid-base and EDTA titrations, as well as for electrochemical equilibria. They will be of key value in Chapter 13. 

Our goal is to find an expression for the fraction of an acid in each form (HA and A ) as a function of pH. We can do this by combining the equilibrium constant with the mass balance. Consider an acid with formal concentration F  

Rearranging the mass balance gives [A ] = F — [HA], which can be plugged into the Ka expression to give 

In a similar manner, the fraction in the form A, designated A-, can be obtained  

The fraction denoted here as aA is the same thing we called the fraction of dissociation (a) previously. 

Fixing the pH invalidates the original charge balance because we added unspecified ions to the solution to fix the pH. There exists a new charge balance, but we do not know enough to write an equation for it. 

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The derivation of fractional composition equations for a diprotic system follows the same pattern used for the monoprotic system. 

Now we use the fractional composition equations from Chapter 10. Equation 10-18 told us that... 

Step 1 Write a fractional composition equation from Section 10-5 for each acid or base that appears in the charge balance. 

Here is a recap of the fractional composition equations from Section 10-5 for any mono-protic acid HA and any diprotic acid H2A. 

A bigger nuisance when considering ion pairs is that the fractional composition equations for [H2T], [HT ], and [T2-] also are changed because the mass balance for H2T now has five species in it instead of three ... 

The new fractional composition equations are somewhat messy, so we reserve this case for Problem 13-18. The end result is that adding the ion-pair equilibria 13-12 and 13-13 changes the calculated pH from 4.30 to 4.26. This change is not large, so neglecting ion pairs with small equilibrium constants does not lead to serious error. We find that 7% of sodium is tied up in ion pairs. Our ability to compute the distribution of species in a solution is limited by our knowledge of relevant equilibria. 

Our strategy is to substitute expressions into the charge balance to obtain an equation in which the only variable is [H+l. For this purpose, we use the fractional composition equations for the triprotic acid, H,P04, which we abbreviate as H3P ... 

Now for our old friends, the fractional composition equations. Abbreviating oxalic acid as H2Ox, we can write... 

To convert [A] or [B] into FA or FB, we use fractional composition equations (Section 10-5), which relate the formal (that is, total) concentration of all forms of an acid or a... 

Give a physical interpretation of Equations 23-6 and 23-7 in terms of the fractional composition equations for a monoprotic acid discussed in Section 10-5. 

We have seven equations and seven chemical species. Fractional composition equations ... 

In this problem, we construct the fractional composition graph in Figure 11-1. From the mass balance and the equilibrium expressions, we can derive fractional composition equations for a diprotic system, H2A ... 

For the diprotic acid FljedH2, we use the following equation to express [FlredH2] in terms of the formal concentration of FljejH2. To do this, the fractional composition equation or (o equation) is used to convert the form of an acid or base to its concentration in a particular form ... 

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