Electrolytic dissociation of water
The water molecules dissociates according to the reaction:
H3O+ + HO-
H2O + H2O
The equilibrium is shifted far to the left. Experimentally, it
was determined that at 25°C, only one molecule of water, out of
556,000,000 is dissociated, which means the dissociation
degree of water is α = 18·10-10.
The equilibrium constant for the dissociation reaction of
water is:
K
c H O   cOH 
3
c H2 2O
1
K  c H2 2O  c H O   cOH   K W
3
Kw is called the ionic product of water
The
ionic
product
of
water
depends
on
the
temperature. At 25°C, the value of KW is 10-14 mol L-1.
In pure water the concentration of the H3O+ ions is
equal to that of the HO-, which means that at 25°C:
c H O  cOH   KW  10 7 mol L-1
3
2
To express the concentration of the hydrogen ions in
aqueous solutions, the notion of pH was introduced by
Sörensen (1909):
pH   lg c H O 
3
The relation was modified by Bates by replacing the
concentration of the hydronium ions with their activity:
pH   lg a H O 
3
or
pH   lg aH 
For diluted solutions, the activity can be considered equal to
the concentration
3
Similar to the pH notion the term of pOH was
introduced, that is a measure of the concentration of the
hydroxyl ions:
pOH   lg c HO
It is easily demonstrated that, at the temperature of 25°C:
pH + pOH = -lg KW = 14
4
Acid – base equilibrium
Acids are substances that, in aqueous solutions,
release hydrogen ions H+. For example, the hydrochloric
acid dissociates in H+ and Cl- ions:
HCl
H+ + Cl-
Bases are substances that, in aqueous solutions,
produce hydroxyl ions, like the case of sodium hydroxide,
that dissociates in Na+ and HO- ions:
NaOH
Na+ + HO5
Strong acids are completely dissociated,
the dissociation degree α = 1
ACIDS
Ex: HCl, H2SO4, HNO3
Weak acids are partially dissociated,
the dissociation degree α << 1
Ex: CH3COOH, HCN, H2S
Strong bases are completely dissociated,
the dissociation degree α = 1
BASES
Ex: NaOH, KOH
Weak bases are partially dissociated,
the dissociation degree α << 1
Ex: NH3, organic amines R-NH2
6
The dissociation degree is defined as the ratio
between the number of dissociated molecules and the total
number of dissolved molecules:
number of dissociate d molecules

total number of dissolved molecules
7
Acidity constant
HA
the acidity constant is:
Base constant
the base constant is:
BOH
H+ + A-
[H  ]  [A  ]
Ka 
[HA]
B+ + HO-
[B  ]  [HO  ]
Kb 
[BOH]
8
Very weak acids: the first acidity constant lower than 10-7.
Acid
Constant K1
HClO (hypochlorous acid)
3.2·10-8
H3BO3 (boric acid)
5.8·10-10
Weak acids: the first acidity constant between 10-7 and 10-2.
Acid
Constant K1
H3PO4 (phosphoric acid)
7.5·10-3
CH3COOH (acetic acid)
1.8·10-5
H2CO3 (carbonic acid)
0.45·10-6
Strong acids are completely dissociated in aqueous solution;
one can not distinguish between their acidity constants. 9
Weak bases, like ammonia, aniline, have the base constant
below 10-3:
Base
Constant Kb
Ammonia NH3
1.7·10-5
Aniline C6H5 – NH2
3.8·10-10
Strong bases, like sodium hydroxide, calcium hydroxide, are
completely dissociated in water, like in case of strong acids,
one can not distinguish between their base constants.
10
Calculation of pH for acid and base solutions
Strong acids are completely dissociated in aqueous
solutions so the hydronium ions concentration is equal to the
concentration of the acid. For example, for a 10-3 mol L-1
solution of HCl, the concentration of the hydronium ions is
[H3O+] = 10-3 mol L-1. The pH of the solution is:
pH = -lg[H+] = -lg 10-3 = 3
For a strong base, for example 10-3 mol L-1 KOH the
concentration of hydroxyl ions is [HO-] = 10-3 mol L-1. It results
that the pOH of the solution is: pOH = -lg[HO-] = -lg 10-3 = 3
Considering the relation between pOH and pH one obtains:
pH = 14 – pOH = 14 – 3 = 11
11
For concentrations higher than 10-3 mol L-1 the pH is
calculated using the Bates relation because the activity
differs from the concentration
At very low acid concentrations to calculate pH it is
necessary to consider the hydronium ions coming from the
dissociation of both acid as well as water molecule.
12
For example, the pH of a 10-7 mol L-1 solution of HCl is
not 7 because the hydronium ions result not only from the
dissociation of the acid, but from the dissociation of water as
well:
HCl
H+ + Cl-
H2O
H+ + HO-
Considering that the concentration of hydrochloric acid in
the solution is c = 10-7 and the concentration of hydronium,
respectively hydroxyl ions is x, the total hydronium ions
concentration will be c+x. The ionic product of water, at the
temperature of 25°C, will be:
(x + c)x = 10-14
13
One obtains a second degree equation:
x2 + cx - 10-14 = 0
Solving the equation one obtains:
 c  c 2  4  10 14  10 7  10 14  4  10 14
x

=6.1810-8
2
2
The solution with “minus” in front of the square root has no
meaning, since it is negative.
The concentration of the hydronium ions will be:
[H+] = 10-7 + 6,1810-8 = 1.61810-7
Thus, the pH of a 10-7 mol L-1 solution of HCl, will be:
pH = -lg[H3O+] = -lg 1.61810-7 = 6.79
14