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Lecture

ESS102H1 Lecture Notes - Aluminosilicate, Titration, Total Dissolved Solids


Department
Earth Sciences
Course Code
ESS102H1
Professor
John Ferris

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4 Acid-Base Relationships
Most reactions in the gas-water-rock system involve or are controlled by the pH of the
system
These include
1. acid-base equilibria, including hydrolysis and polymerization by condensation
2. adsorption, because protons compete with cations and hydroxyl ions compete
with anions for adsorption sites
3. the formation of metal-ligand complexes, again because of competition
4. Oxidation-reduction reactions, because oxidation usually produce protons,
whereas reduction consumes them
5. the solubility and rate of dissolution of many minerals is strongly pH dependent
4.1 Protons and pH
The availability of protons in aqueous solutions is assessed generally in terms of
pH. In principle, pH provides a measure of proton activity {H+} according to the
established relationship
pH = -log{H+} (1)
The value of {H+} is considered within the infinite dilution concept to be equivalent to
proton concentration [H+] in dilute solutions (ionic strength, I < 0.1, therefore activity
coefficient approaches 1, see chapter 2)
Protons, like other ions in aqueous solution, are subject to hydration by water to
form hydronium (H3O+) ions
H+ + H2O = H3O+(2)
By their very nature, hydronium ions themselves tend to become hydrated further through
hydrogen bonds with additional water molecules; however, use of the formula H+ is taken
almost universally to denote all forms of hydrated protons in aqueous solutions.
In all aqueous solutions, the autoprotolysis1 of water must always be considered.
2H2O = H3O+ + OH-(3)
The mass action relationship for the autoprotolysis reaction with the activity of water
equal to unity, and with the formula H+ taken normally to denote all forms of hydrated
protons in aqueous solutions, can be expressed using the equilibrium constant Kw.
1 Autoprotolysis is a proton transfer reaction involving two identical molecules, usually a solvent.
1

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}}{OH{H }}{OHO{H --
3
++ ==
w
K
(4)
At 25 oC and atmospheric pressure, the equilibrium constant Kw = 1.0 x 10-14, which gives
a pH = 7.0 in pure water corresponding to [H+] = [OH-].
4.2 Acid-Base Reactions
An acid refers to a substance that behaves as a proton donor, whereas a base is a
substance that accepts protons2. In a complete acid-base reaction, an exchange of protons
occurs. This process not only satisfies the condition that protons are extensively hydrated
in solution, but also accounts for the familiar changes in pH that are associated
commonly with the introduction of acids and bases to aqueous solutions.
Consider a general reaction for the addition of an acid or base to pure water,
respectively
HA + H2O = H3O+ + A-(5)
B + H3O+ = BH+ + H2O (6)
Each of these reactions consists of two combined parts. For the acid HA
HA = H+ + A-(7)
H2O + H+ = H3O+(8)
and for the base B
H3O+ = H2O + H+(9)
B + H+ = BH+(10)
In the case of the dissociation of the acid (Eqn. 7), the donated protons are accepted by
water (Eqn. 8) resulting in the production of hydronium ions; this tends to decrease pH
(Eqn. 1 and Eqn. 2), as anticipated for an acid. Conversely, the deprotonation of
hydronium ions (Eqn. 9) yield protons that can be accepted by the base (Eqn. 10); this
tends to increase pH (Eqn. 1 and Eqn. 2), as anticipated for a base.
4.3 Mass Action Relationships
2 This definition extends from the Brønsted-Lowry concept of acids and bases.
2

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The strength of an acid is conceived in a generic way by its capacity to donate a
proton. In this context, a weak acid has a poor proton-donating capacity, whereas a
strong base is one that has a strong capacity to accept protons. Herein rests a point of
departure for the establishment of another reasonable reference point, specifically against
which to measure the strength of acids and bases.
A common approach is to adopt a general reaction for an acid-base reaction, such
as that described by Eqn. 5, which is represented formally by two steps as indicated by
Eqn. 7 and Eqn. 8. The respective mass action relationships are
}{
}}{{
1HA
AOH
Ks
+
=
(11)
}{
}}{{
2HA
AH
K+
=
(12)
}{
}{ 3
3+
+
=H
OH
K
(13)
Because the actual equilibrium activity of the hydronium ion and protons are not known
precisely, chemical thermodynamic conventions set G0 for Eqn. 13 to zero, or in terms
of Eqn 11, chapter 2, K3 = 1. As such, the combined mass action expressions yield
}{
}}{{
321 HA
AH
KKKK a
+
===
(14)
where Ka can be recognized as the more familiar acid dissociation constant. From this
formulation it is evident that the strength of acids as measured by acid dissociation
constants are actually referenced in thermodynamic terms against the equilibrium
concentrations of hydronium ions and protons (Eqn. 13). Rearrangement of the final
form of Eqn. 14 with pKa = -log Ka gives
+=
}{
}{
logppH HA
A
Ka
(15)
A compelling result from Eqn. 15 that resonates deeply across the broad fields of
chemistry and biology is that when {HA-} = {A-}, pH = pKa.
For strong acids that give up protons readily, the dissociation constant Ka
anticipated from mass action relationship illustrated by Eqn. 14 will be large and the pKa
value will be small. Conversely, the Ka value of a weak acid will be small and the pKa
value will be large. These basic relationships between Ka and pKa permit evaluations of
the relative strengths of different acids that occur in aqueous systems.
3
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