1. Buffers Complexation

2. The Tableau Method of Morel & Hering
In determining alkalinity, we need to correctly write the TOTH equation.
To do so, we need to decide on a proper system of components (as usual, we want the minimum number of components) and then decide which species are formed by adding H+ and which are formed by subtracting H+.
The Morel & Hering method is to produce a matrix-like table (a ‘tableau’) with components across the top and species listed vertically.
Entries in the Tableau are the stoichiometric coefficient of each component needed to form each species.
Consider a solution containing H3SiO4–, H4SiO4, B(OH)3, B(OH)4–, H2S, HS–, HPO42-, H2CO3, HCO3–, CO32–, and, H+, and OH–. We also recall that we always chose H2O as a component.

3. H+
H2O
CO2
H2PO4–
H4SiO4
B(OH)3
H2S 1
OH– -1
H2CO3
HCO3–
CO32– -2
HPO42-
H3SiO4–
B(OH)4–
HS–
Alk = -TOTH = -{[H+] - [OH-] - [HCO3–] - 2[CO32-] - [HPO42-] - [H3SiO4-] - [HS-]}

4. Titration Determination of Alkalinity
We have learned how to calculate alkalinity, but it can also be measured by titration.
Titration is the process of progressively adding a strong acid or base to a solution until a specified pH, known as an end-point, is reached.
In the case of the determination of alkalinity, this end-point is the CO2 equivalence point, as the definition suggests.
The analytical definition of alkalinity is its acid neutralizing capacity when the end-point of the titration is the CO2 equivalence point.

5. [Na+] + [H+] = [Cl–] + [ HCO3–] + 2[CO32- ] + [OH–]
Titration Example
Consider a solution containing sodium carbonate (Na2CO3). Because the carbonate ion can act as a proton acceptor, Na2CO3 is a base.
We assume ideal behavior, complete dissociation, and a volume of solution large enough that the titration results in trivial dilution.
The charge balance equation during the titration is:
[Na+] + [H+] = [Cl–] + [ HCO3–] + 2[CO32- ] + [OH–]
Since the Cl– concentration is conservative, it will be equal to the total amount of HCl added.
Using equilibrium constant expressions to eliminate some species, e.g.,
and noting mass balance requires 2[Na]=ΣCO2, we derive the following:

6. Titrating Alkalinity
This plot shows the how carbonate species in a 5 mM Na2CO3 solution change with pH as HCl is added during titration.
Notice how the HCl curve flattens at the equivalence points - pH changes rapidly with small additions of HCl.
This means we don’t have to hit the pH of the E.P. with great precision to obtain the alkalinity.
In practice, a solution indicator or pH meter would be used.
The end-point is reached here at 10 mM HCl.

7. Calculated and Titrated Alkalinity
In this example, titration yielded an alkalinity of 10 mM.
Can we obtain the same result from calculation?
TOTH = [H+] - [OH-] - [HCO3–] - 2[CO32-]
Charge balance is (before addition of HCl):
[Na+] + [H+] = [HCO3–] + 2[CO32-] + [OH–]
Solving the two equations, we find:
Alk = -TOTH = [Na+] = 10 mM

8. Buffer Intensity
The carbonate system is a good example of a pH buffer - a system of reactions that tends to maintain constant pH. If we add acid (H+), carbonate is converted to bicarbonate and bicarbonate is converted to carbonic acid, both reactions consuming H+ and driving pH higher.
We define the buffer intensity of a solution as the inverse of change in pH per amount of strong base (or acid) added:
where CB and CA are the concentrations, in equivalents*, of strong base or acid respectively.
*Equivalents are the number of moles of an acid (base) times the number of H+ (OH-) ions it will release upon complete dissociation. A 1M solution of HCl is a 1N solution, but a 1M solution of H2SO4 is a 2N solution, as is a 1M solution of Ca(OH)2.

9. Buffer Intensity
The buffer capacity of the carbonate system depends strongly on pH and also on the concentration of the carbonate species and the concentration of other ions in solution.
In pure water containing no other ions and only carbonate in amounts in equilibrium with the atmosphere, the buffering capacity is negligible near neutral pH. Natural solutions, however, can have substantial buffering capacity.
“Hard water” is an example of water with a substantial buffering capacity due to the presence of dissolved carbonates.
How adversely lakes and streams are impacted by “acid rain” depends upon their buffering intensity.
βCT fixed total dissolved CO2, βPCO2 water in equilibrium with atmospheric CO2, βCaCO3(s) water in equilibrium with calcite, and βAn-Kaol. water in equilibrium with anorthite and kaolinite.

10. Complexation and Speciation
Ions in solution often associate with other ions, forming new species called complexes. Complex formation is important because it affects the solubility and reactivity of ions, as we will see in the following section. In some cases, complex formation is an intermediate step in the precipitation process. In other cases, ions form stable, soluble complexes that greatly enhance the solubility of the one or both of the ions.

11. Complexes & Ligands
Complexation is usually described in terms of a central ion, generally a metal, and ion(s) or molecule(s) that bind to it, or coordinate it, referred to as ligands.

12. Aquo-Complexes
The simplest and most common complexes are those formed between metals and water or its dissociation products.
As we found earlier a solvation shell, typically consisting of 6 or so water molecules that are loosely bound to the ion through electrostatic forces, surrounds ions in aqueous solutions. Truly “free” ions do not exist.
This solvation shell is referred to as an aquo-complex. Water molecules are the ligands in aquo-complexes.
The existence of these complexes is implicitly assumed (and accounted for through the activity coefficient) and not usually explicitly considered.

13. Other Complexes
Ion pairs, where ions of opposite charge associate with one another through electrostatic attraction, yet each ion retains part or all of its solvation sphere. Two possibilities:
the two solvation spheres are merely in contact
the water molecules are shared between the two solvation spheres.
Ion pairs are also called outer sphere complexes.
Complexes (sensu stricto), where the two ions are in contact and a bond forms between them that is at least partly covalent in nature. These are often called inner sphere complexes.