1.3 Direct Current Conductivity and pH of Water
23
of pondus hydrogenii (quantity of hydrogen), or simply pH.
19 The conductivity of
pure water σ dc = 5.5·10
−8 S/cm used in (1.8) n = [H
+ ] = 1/2·σ dc k B T /(q
2 D p N a ),
where D p = 9.3·10
−9 m
2 /s is the proton self-diffusion coefficient [66], gives n ≈
10
−7 M, which is better known as pH = 7.
The concept of pH appeared as a result of the adaptation of the notion of the
ionic product of water K w = [H
+ ]×[OH
− ], where [H
+ ] and [OH
− ] are effective
concentrations of hydronium and hydroxide ions, in a form that is more convenient
for practical applications.
20 The ionic product is connected with pH by the formula
pH = 1/2 × pK w , where p is the decimal logarithm.
According to the definition [69], pH is a measure of activity of hydronium ions.
When we assume pH = 7 for the pure water, it means that the effective concentration
of hydroxyl ions is n ± = 10
− pH
= 10
−7 mol/l, or 3·10
19 m
−3 , or 10
−7 %.
21 For an
aqueous solution, pH values vary from 0 to 14, where pH = 0 corresponds to a very
strong acid with seven orders of magnitude higher concentration of active H 3 O
+ ions
than in the pure water, and pH = 14 is for a very strong base with seven orders of
magnitude higher concentration of active OH
− ions. Salts do not alter the pH value
of water, as they do not bring any hydroxyl or hydronium ions to water, although
they significantly increase its electrical conductivity [11] and decrease its dielectric
constant (see Sect. 5.1 of Chap. 5 for explanation).
There is no direct way to determine the concentration of ions or the autoionization
constant, pK w . In order to detect the ions, one can use indicators, such as dyes or
litmus paper, which change color depending on the activity
22 of hydronium ions
and the intensity of the corresponding chemical reaction with water. Color indicators
cover the whole pH range between 0 and 14 and, together with spectroscopic methods,
allow a resolution better than 0.1 of the pH units. A more modern and precise method
for pH measurements is based on the glass-electrode galvanic cell. This method
measures the electromotive force between a reference electrode and an electrode
sensitive to the hydronium ion activity when they are both immersed in the same
aqueous solution [68]. Although this method is accurate, it requires calibration, and
is very sensitive to impurities and experimental conditions.
The activity of hydronium ions can be also tested by nuclear magnetic resonance
(NMR). The proton exchange broadens the line of the so-called chemical shift, which
represents the resonant frequency of a nucleus relative to a standard in a magnetic
19 In chemistry, pH (also known as “the potential of hydrogen” or “the power of hydrogen”) is a
scale used to specify the acidity or basicity of an aqueous solution. The pH scale is the negative of
the base 10 logarithm of the “activity” of the H + ion.
20 Interestingly, pH was originally developed in beer brewing [67] and apart from the modern
definition had very pragmatic meaning.
21 This value is several orders of magnitude lower than concentrations of such impurities in natural
water as HDO, H 2 O 2 , CO 2 , O 2 , and N 2 in natural water, which are 10 −2 , 10 −7 , 10 −4 , 10 −4 , and
10 −3 %, respectively.
22 In chemical thermodynamics, activity a is a measure of the “effective concentration” of a species
in a mixture, in the sense that the species’ chemical potential depends on the activity of a real
solution in the same way that it would depend on concentration for an ideal solution. The term
“activity” in this sense was coined by Lewis in 1907.
23
of pondus hydrogenii (quantity of hydrogen), or simply pH.
19 The conductivity of
pure water σ dc = 5.5·10
−8 S/cm used in (1.8) n = [H
+ ] = 1/2·σ dc k B T /(q
2 D p N a ),
where D p = 9.3·10
−9 m
2 /s is the proton self-diffusion coefficient [66], gives n ≈
10
−7 M, which is better known as pH = 7.
The concept of pH appeared as a result of the adaptation of the notion of the
ionic product of water K w = [H
+ ]×[OH
− ], where [H
+ ] and [OH
− ] are effective
concentrations of hydronium and hydroxide ions, in a form that is more convenient
for practical applications.
20 The ionic product is connected with pH by the formula
pH = 1/2 × pK w , where p is the decimal logarithm.
According to the definition [69], pH is a measure of activity of hydronium ions.
When we assume pH = 7 for the pure water, it means that the effective concentration
of hydroxyl ions is n ± = 10
− pH
= 10
−7 mol/l, or 3·10
19 m
−3 , or 10
−7 %.
21 For an
aqueous solution, pH values vary from 0 to 14, where pH = 0 corresponds to a very
strong acid with seven orders of magnitude higher concentration of active H 3 O
+ ions
than in the pure water, and pH = 14 is for a very strong base with seven orders of
magnitude higher concentration of active OH
− ions. Salts do not alter the pH value
of water, as they do not bring any hydroxyl or hydronium ions to water, although
they significantly increase its electrical conductivity [11] and decrease its dielectric
constant (see Sect. 5.1 of Chap. 5 for explanation).
There is no direct way to determine the concentration of ions or the autoionization
constant, pK w . In order to detect the ions, one can use indicators, such as dyes or
litmus paper, which change color depending on the activity
22 of hydronium ions
and the intensity of the corresponding chemical reaction with water. Color indicators
cover the whole pH range between 0 and 14 and, together with spectroscopic methods,
allow a resolution better than 0.1 of the pH units. A more modern and precise method
for pH measurements is based on the glass-electrode galvanic cell. This method
measures the electromotive force between a reference electrode and an electrode
sensitive to the hydronium ion activity when they are both immersed in the same
aqueous solution [68]. Although this method is accurate, it requires calibration, and
is very sensitive to impurities and experimental conditions.
The activity of hydronium ions can be also tested by nuclear magnetic resonance
(NMR). The proton exchange broadens the line of the so-called chemical shift, which
represents the resonant frequency of a nucleus relative to a standard in a magnetic
19 In chemistry, pH (also known as “the potential of hydrogen” or “the power of hydrogen”) is a
scale used to specify the acidity or basicity of an aqueous solution. The pH scale is the negative of
the base 10 logarithm of the “activity” of the H + ion.
20 Interestingly, pH was originally developed in beer brewing [67] and apart from the modern
definition had very pragmatic meaning.
21 This value is several orders of magnitude lower than concentrations of such impurities in natural
water as HDO, H 2 O 2 , CO 2 , O 2 , and N 2 in natural water, which are 10 −2 , 10 −7 , 10 −4 , 10 −4 , and
10 −3 %, respectively.
22 In chemical thermodynamics, activity a is a measure of the “effective concentration” of a species
in a mixture, in the sense that the species’ chemical potential depends on the activity of a real
solution in the same way that it would depend on concentration for an ideal solution. The term
“activity” in this sense was coined by Lewis in 1907.