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The simple scheme based on Gran functions for the evaluation of alkalinity does not work very well for seawater because this medium contains a number of other weak electrolytes that contribute measurably to the alkalinity.

Figure 6.9 shows the results of an alkalinity titration of sea water made under similar conditions to that if the lake water in Figure 6.8, except that because the ionic strength of sea water is naturally quite high, a supporting electrolyte does not need to be added.

-150 -100 -50 0 50 100 150 Potential (mV) 1 2 3 4 5 6 7 vHCl (mL) F₂ F1

Figure 6.9: Alkalinity titration of 200 mL of seawater with 0.100 M HCl at 25oC recorded using an automatic titrator. Also shown are the Gran functions F1 and F2 corresponding to equations [6.51] and [6.52]. Drawn using data collected by the author.

The Gran function F2 on the right of the diagram corresponding to excess HCl in equation

[6.52] is reasonably linear, but shows some curvature near the corresponding equivalence point. Although some of the first points can be ignored in fitting the best-fit line, this procedure is not very systematic. Moreover, detailed examination of cases like this shows considerable variation in the results depending on the choice of points that are included. While it is not very obvious from the diagram, the Gran function is noticeably curved.

The Gran function F1 on the left of the diagram corresponding to equation [6.51] is

markedly curved throughout its valid volume range, and it is difficult to see how a reliable estimate of the equivalence point can be obtained.

These problems arise because seawater contains other acids and bases that participate in the titration reactions. Many of these were mentioned in this context in Chapter 4. They include the weak base borate, and the acidic species bisulfate and hydrofluoric acid. As mentioned in Chapter 4, phosphate and silicate can also contribute, although the water sample examined in the present example contains very low concentrations of both these species.

We recall that alkalinity is defined as the ANC of the water with respect to the reference proton condition of pure H2CO3. In this situation, the full definition of the alkalinity for seawater

must include the abovenamed species. The following definition, which achieves this aim, was suggested by Dr Andrew Dickson:

AT = [HCO3 –

] + 2 [CO3 2–

] + [OH–] – [H+]

+ [B(OH)4–] + [HPO42–] + 2[PO43–] + [SiO(OH)3–]

– [HSO4–] – [HF] – [H3PO4] [6.59]

The first line contains the usual alkalinity components seen in earlier definitions. The second line contains the bases specific to seawater that are stronger than HCO3

–

, while the third line contains the corresponding acids stronger than H2CO3. Two additional species could also be

included, NH3 and HS –

, but these are normally not significant in most seawaters.

Equation [6.59] defines what is termed the total alkalinity AT of seawater. The effect of

these minor constituents can be examined by using this equation, together with the relevant equilibrium constants and mass-balance conditions, to calculate the speciation of the seawater system during the titration. For this, zero concentration of phosphate and silicate were assumed, while the concentrations of the other minor species in [6.59] were calculated using the information presented in Chapter 4.

Figure 6.10 shows the calculated seawater speciation near the first equivalence point v1

obtained by this method.

0.05 0.10 0.15

c (mmol L

)

v

(mL)

Figure 6.10: Calculated seawater speciation near the first equivalence point v1 for the

alkalinity titration of sea water, as shown in Figure 6.9.

In interpreting Figure 6.10, we recall that the simple assumption of the Gran function for locating v1 is that for v < v1 the added HCl is consumed through reaction with carbonate ions,

which are all titrated at exactly v = v1.

CO3 2–

+ H+ → HCO3 –

(v1 ) [6.60a]

After this (v > v1), the added HCl reacts only with bicarbonate ions to form H2CO3*

HCO3 –

Therefore, this idealized situation should see the amount of CO3 2–

decrease linearly to zero at v = v1 , after which the amount of H2CO3* should increase linearly from zero. Inspection of

Figure 5.10 shows that this is far from the case4_{. CO}

3 2–

continue to be titrated well after v = v1 ,

and H2CO3* is produced well before, i.e. HCO3 –

begins to be titrated before all of the CO3 2–

has reacted5_.

In addition to these features, which arise from the properties of the CO2 species, it is

apparent that both the borate ion and, to a lesser extent, free OH– are also measurably titrated in the region v < v1. For most of this region, about 1/3 of the HCl is consumed by reaction with

borate ion.

It follows that the derivation of the Gran function F1 in [6.51] is not valid in seawater media

and will not give reliable results.

Figure 6.11 shows the calculated seawater speciation near the second equivalence point v2

obtained by the same calculation method as Figure 6.11.

0.05 0.10 0.15 0.20 0.25 c (mmol L -1) 4.75 5.00 5.25 5.50 5.75 vHCl (mL) HF HSO4- H+ HCO3-

Figure 6.11: Calculated seawater speciation near the second equivalence point v2 for the

alkalinity titration of sea water, as shown in Figure 6.9.

In deriving the Gran function F2 for this equivalence point, equation [6.52], the simplifying

assumption was made that reaction [6.30b] continues to completion at v = v2, after which all

bases have reacted and excess free H+ builds up in solution. Thus, the amount of HCO3 –

should decrease linearly to reach zero at v = v2 , after which the amount of free H

+

should increase linearly from zero.

4

_{Although Figure 6.10 uses concentration, rather than amount, and is therefore}

affected by dilution as the titrant is added, the volume changes are very small because of

the large sample volume (200 mL).

5

This problem is common to all diprotic acids. The two reactions overlap measurably