1.3 Direct Current Conductivity and pH of Water
25
Fig. 1.18 The temperature
dependencies of the
electro-kinetic parameters of
water: the specific
conductivities, σ dc ; the
equivalent conductivity, 0
w ;
and the coefficient of the
autoionization constant,
pK w , derived from them.
The dotted lines mark T =
25 ◦ C, the temperature at
which the concept of pH is
determined and pK w = 14,
pH = 7. Experimental data
from [72]
Table 1.2 Parameters of (1.11) for room-temperature water
n H 2 O (M) w (S· m 2 /mol)
H 3 O + (S · m 2 /mol) OH − (S · m 2 /mol) 0
w (S · m 2 /mol)
55.5
9.90·10 −7
349.8
198.5
548.3
pH
σ dc (S/cm)
α
n H 3 O + (M)
pK w
7
5.5·10 −8
1.8·10 −9
1.0·10 −7
14
where α = w //
0
w is the degree of H 2 O dissociation; w = σ dc /n H 2 O is the molar
conductivity; and
0
w =
0
H 3 O + +
0
O H − is the equivalent conductivity, defined by
the sum of the mobilities of H 3 O
+ and OH
− ions as obtained from experiments with
infinite dilution. Table 1.2 shows different quantitative estimates of the parameters
of (1.11) at room temperature as the concept of pH is adjusted for room temperature (see black arrow in Fig. 1.18). However, the ratio represented by the last term
in (1.11) is not conserved when the temperature changes. The DC conductivity values
change faster than those for
0
w (see Fig. 1.18) which leads (see yellow arrow) to the
anomalous temperature behavior of pK w , and, as a consequence, pH.
Summarizing, the concept of pH is based on the poorly defined notion of the
activity of hydronium ions in water and aqueous solutions. It reflects the diffusionaveraged concentration of ions, and does not account for the fluctuation-borne shortlived ions, the concentration of which is much higher [15, 73] in comparison with
the long-lived ions detected by glass electrode, or conductometric techniques (see
Chaps. 3 and 4). However, the short lifetime makes them “invisible” to static conductivity measurements. Let us consider the following abstract analogy. Figure 1.19
shows the photo of the Paris boulevard at the midday taken in 1838.
23 It looks empty,
23 This photo is the first known photo of a human.
25
Fig. 1.18 The temperature
dependencies of the
electro-kinetic parameters of
water: the specific
conductivities, σ dc ; the
equivalent conductivity, 0
w ;
and the coefficient of the
autoionization constant,
pK w , derived from them.
The dotted lines mark T =
25 ◦ C, the temperature at
which the concept of pH is
determined and pK w = 14,
pH = 7. Experimental data
from [72]
Table 1.2 Parameters of (1.11) for room-temperature water
n H 2 O (M) w (S· m 2 /mol)
H 3 O + (S · m 2 /mol) OH − (S · m 2 /mol) 0
w (S · m 2 /mol)
55.5
9.90·10 −7
349.8
198.5
548.3
pH
σ dc (S/cm)
α
n H 3 O + (M)
pK w
7
5.5·10 −8
1.8·10 −9
1.0·10 −7
14
where α = w //
0
w is the degree of H 2 O dissociation; w = σ dc /n H 2 O is the molar
conductivity; and
0
w =
0
H 3 O + +
0
O H − is the equivalent conductivity, defined by
the sum of the mobilities of H 3 O
+ and OH
− ions as obtained from experiments with
infinite dilution. Table 1.2 shows different quantitative estimates of the parameters
of (1.11) at room temperature as the concept of pH is adjusted for room temperature (see black arrow in Fig. 1.18). However, the ratio represented by the last term
in (1.11) is not conserved when the temperature changes. The DC conductivity values
change faster than those for
0
w (see Fig. 1.18) which leads (see yellow arrow) to the
anomalous temperature behavior of pK w , and, as a consequence, pH.
Summarizing, the concept of pH is based on the poorly defined notion of the
activity of hydronium ions in water and aqueous solutions. It reflects the diffusionaveraged concentration of ions, and does not account for the fluctuation-borne shortlived ions, the concentration of which is much higher [15, 73] in comparison with
the long-lived ions detected by glass electrode, or conductometric techniques (see
Chaps. 3 and 4). However, the short lifetime makes them “invisible” to static conductivity measurements. Let us consider the following abstract analogy. Figure 1.19
shows the photo of the Paris boulevard at the midday taken in 1838.
23 It looks empty,
23 This photo is the first known photo of a human.