VII.3 E QUILIBRIUMS IN ELECTROLYTES
VII.3.1 Acids and bases
Acid-base theory of Arrhenius VII.3.1.1
Definition of acids and bases has been altered several times. One of the first classifications of acids and bases was made by Arrhenius (1888). In Arrhenius’s definitions, an acid is any substance that, when dissolved in water, increases the concentration of hydrogen (hydronium) ions, while a base is any substance that, when dissolved in water, increase the concentration of the hydroxide ions.
Identification number:
TÁMOP-4.1.2.A/1-11/1-2011-0016 103
Aqueous solutions of acids have acidic properties, because the hydrogen (hydronium) ion concentration is higher than that of the hydroxide ions. For example, hydrochloric acid (HCl(aq)), sulphuric acid (H2SO4(aq)), nitric acid (HNO3(aq)), etc.
Bases dissociate to hydroxide ions in their aqueous solutions. In aqueous solutions of bases concentration of the hydroxide ions exceeds that of the hydrogen ions. For example, sodium hydroxide (NaOH(aq), potassium hydroxide (KOH(aq)), calcium hydroxide (Ca(OH)2(aq)), etc.
Acids and bases react with each other in neutralization reactions. For example:
HCl(aq) + NaOH(aq) = NaCl(aq) + H2O(l)
HNO3(aq) + KOH(aq) = KNO3(aq) + H2O(l)
Acid-base theory of Brønsted and Lowry VII.3.1.2
J. N. Brønsted and T. M. Lowry extended the acid-base theory of Arrhenius and emphasized the role of hydrogen ion (proton) in the acid-base reactions. According to the Brønsted and Lowry theory, an acids is a species that donates a proton to another species in a proton-transfer reaction. They defined a base as a species that accepts a proton in a proton-transfer reaction.
According to their theory, acids are converted into a base by releasing a proton and a base is transformed to an acid by accepting a proton. (See examples below.) An acid donates a proton only in the presence of a proton acceptor base. Accordingly, conversion of an acid to the respective base and conversion of a base to its respective acid takes place in the same reaction.
Examples:
Acid1 Base2 Base1 Acid2
HCl + H2O = Cl- + H3O+
NH4+
+ H2O = NH3 + H3O+
H3O+ + OH- = H2O + H2O
H2O + NH3 = OH- + NH4+
The corresponding acid-base pairs (e.g. HCl and Cl-, NH4+
and NH3, etc.) are conjugate acid-base pairs. A conjugate acid-base pair consists of two species in an acid-base equilibrium, one acid and one base, which differ by gain or loss of a proton.
Some compounds (for example H2O and NH3 molecules, HCO3
and H2PO4
ions, etc.) can act either as an acid or a base depending on the relative acid-base strength of the reaction partner. These species are amphiprotic (amphoteric) species.
Acid-base theory of Lewis VII.3.1.3
G. N. Lewis realized that the concept of acids and bases can be generalized to include reactions (e.g. reaction of acidic and basic oxides) that do not fit either the Arrhenius or the Brønsted-Lowry concepts.
According to this theory, a Lewis acid is a species (atom, molecule, or ion) that can form a covalent bond by accepting a pair of electrons from another species, while a
104 The project is supported by the European Union and co-financed by the European Social Fund Lewis base is a species (atom, molecule, or ion) that can form a covalent bond by donating an electron pair to another species.
The compounds that are classified as acids or bases according to the Arrhenius or the Brønsted-Lowry theory can also be considered as acids or bases according to the Lewis concept. According to the Lewis concept, however, the group of the compounds considered to be acids or bases further extends and numerous chemical reactions can be interpreted as acid-base reactions.
Examples:
Lewis acid Lewis base Lewis acid-base complex
BF3 + NH3 = F3BNH3
AlCl3 + Cl- = AlCl4
-Fe2+ + 6 H2O = [Fe(H2O)6]2+
SO3 + BaO = BaSO4
Ag+ + 2 NH3 = [Ag(NH3)2]+
Self-ionisation of water, the pH VII.3.1.4
According to the Brønsted-Lowry theory water is an amphoteric compound: it can react either as an acid or a base. Because of this dual acid-base character, water molecules can react with each other in an acid-base reaction. The reaction is a reversible equilibrium process (see VII.3.1.2), in which a proton from one H2O molecule is transferred to another H2O molecule, leaving behind a hydroxide ion and forming a hydronium ion:
H2O + H2O ⇌ H3O+(aq) + OH-(aq)
According to the law of mass action, the equilibrium constant expression can be obtained by multiplying the concentrations of products by each other, dividing their product by the product of concentrations of reactants, rising each concentration term to a power equal to the coefficient in the chemical equation:
[ ][ ]
[
2]
23
O H
OH O Kc H
−
= +
The numerical value of the above equilibrium constant expression is the equilibrium constant of dissociation of water. Since in pure water the extent of the above reaction is very low, the concentration of the non-dissociated water molecules (55.5 M) remains essentially constant. Thus, the above expression for the equilibrium constant can be written in a simpler form.
Rearranging the expression, moving [H2O]2 next to Kd, the ion product equals a constant:
Kc [H2O]2 = [H3O+][OH-] and thus:
Kw = [H3O+][OH-]
Identification number:
TÁMOP-4.1.2.A/1-11/1-2011-0016 105
The equilibrium value of the ion product [H3O+][OH-] is the ion product constant for water, indicated as Kw.
According to the law of mass action, in pure water and in aqueous solutions the product of mol/dm3 concentration of the hydrogen ions (hydronium ions) and the hydroxide ions is constant. The value of the ion product constant of water at 25 °C and on a pressure of 0.1 MPa is 1.0 . 10-14 mol2/dm6. Because of the stoichiometry of the above reactions of the water, in the pure water: [H3O+] = [OH-] = 1.0 . 10-7 M.
Because the concentrations of the hydrogen ions and the hydroxide ions in aqueous solutions are rather low, the negative of the logarithm of their molar concentrations are used for their quantitative description. According to S. P. L.
Sørensen, the pH is defined as the negative logarithm of the mol/dm3 concentration of the hydronium ions. Accordingly,
pH = - log [H3O+] Similarly, we can define pOH as
pOH = -log [OH-]
Based on the above explanation, in pure water at 25 oC pH = pOH = 7. The values under pH 7 (pH 0-7) are acidic, while the values above pH 7 (pH 7-14) characterise the basic solutions.
Equilibrium of the acidic dissociation, the pKa
VII.3.1.5
As it was stated previously, protolysis (electrolytic dissociation) of acids and bases is a reversible, equilibrium process. An acid reacts with water to produce hydronium ion (hydrogen ion) and its conjugate base ion. The process is called acid ionization or acid dissociation. The acid ionization equilibrium of a HA weak acid in aqueous solution is
HA(aq) + H2O(l) ⇌ H3O+(aq) + A-(aq)
For a strong acid, which completely ionizes in solution, concentrations of the formed ions can be calculated based on stoichiometry of the reaction and the initial concentration of the acid. For a weak acid such as acetic acid, however, the concentrations of ions in solution are determined by the acid ionization (dissociation) constant, which is the equilibrium constant for the ionization of the weak acid.
Applying the law of mass action for the above equilibrium:
[ ][ ]
[ ][
HHAOHAO]
Kc
2 3
−
= +
where Kc = equilibrium constant.
Assuming that this is a dilute solution and that the reaction occurs to only a small extent, concentration of water will be nearly constant. Rearranging the equation results
106 The project is supported by the European Union and co-financed by the European Social Fund
[ ][ ]
[ ]
OHA AO H H K Ka c
−
= +
= [ 2 ] 3
[ ][ ]
[ ]
HAAKa H
−
= +
where Ka = acid ionization (dissociation) constant.
The pKa can be defined similar to the pH:
pKa = -log Ka
The higher the Ka or the lower the pKa the stronger the acid against water.
Equilibrium of the basic dissociation, the pKb
VII.3.1.6
Equilibria involving weak bases (B) are treated similarly to those of weak acids. A base reacts with water to produce hydroxide ion and its conjugate acid ion. The process is called base ionization or base dissociation. The base ionization equilibrium of a B weak base in aqueous solution is
B(aq) + H2O = HB+(aq) + OH-(aq)
The corresponding equilibrium constant is
[ ][ ]
[ ][
B HOHO]
Kc HB
2
−
= +
Because the concentration of water is nearly constant, the equation can be rearranged as it was done for acid ionization:
[ ][ ]
[ ]
BOHO HB H K Kb c
−
= +
= [ 2 ]
where Kb is the base ionization (dissociation) constant.
The pKb can be defined similar to the pKa:
pKb = - log Kb
The higher the Kb or the lower the pKb, the stronger the base against to water.