Concept of pH

The Danish scientist Sørensen defined the

concept of pH as follows:

pH equals the inverse of the logarithm to

the base 10 of the hydrogen ion
concentration, as shown by the formula:

pH = -10log [H+] = paH1) (1)

Later Sørensen found this definition to be
incorrect, since more concentrated
solutions appeared to give deviations
between calculated and measured values.

The definition therefore had to be Søren Peder Lauritz Sørensen (1868-

modified to: 1939)
Born in Havrebjerg, Denmark, Sørensen
pH equals the inverse of the logarithm to was a Danish chemist, famous for the
the base 10 of the hydrogen introduction of the concept of pH, a
ion activity2) as shown by the formula: scale for measuring acidity and
basicity. From 1901 to 1938 he was
pH = -10log aH+ = pH3) (2) head of the prestigious Carlsberg
Laboratory, Copenhagen. While
The activity of the hydrogen ions is not working at the Carlsberg Laboratory he
always linear with the concentration, studied the effect of ion concentration
on proteins,and because the
since this activity is not only affected concentration of hydrogen ions was
by the concentration of ions, but also by particularly important, he introduced
other factors, such as: the pH- scale as a simple way of
expressing it in 1909.
 The activity of other ions
present in the solution
 The temperature of the
solution
 The character of the solution.
To facilitate the accurate measurement of pH, and its presentation as a scale, a
range of "standard liquids" or "buffer solutions" are used.

These liquids, whose constituents are accurately defined, have known stable
values.
Although in the preceding text the relationship to hydrogen ions has been made,
research has shown, that the activity of hydroxonium ions (H30+) is more relevant.
In aqueous solutions free H+ ions do not occur, but are always in combination with
water molecules.

H+ + H20 ↔ H30+
Consequently, a more correct definition for pH is:

pH = -
10log
aH30+ (3)
For
clarity,
the
notation
H+ will be
used in
the book
as the

Fig. pH value of pure water against temperature.

hydroxonium ion.

Note 1. The notation -10log .... can also be written p ....

Note 2. See Appendix 2: Definitions.
Note 3. See Chapter 2.8: Buffer solutions.

The pH Scale
Your starting point for the pH scale is pure water which is said to be neutral. Water
dissociates1) into:

H20 ↔ H+ + OH- (4)

Water has an equilibrium constant 2)3):

or:

-log Kw = pKw = -log [H+] + -log [OH-]

= 14 log 10 (6)
Pure water divides to give equal numbers of H+ and OH- ions and consequently, the
concentrations of ions are 10-7 so that:

pH = pOH = 7
The pH value of pure water is 7.

This statement is incomplete, since the equilibrium constant depends on the

temperature. The definition should be: The pH value of pure water is 7 @ 25°C.

Fig. 2.2a. and the table show the pH variation of pure water with temperature.

If the concentration of H+ ions in a solution is increased (e.g. to 10-4), then the

solution has an acid character. In this case the pH value is lower than 7.

Some examples of common solutions with an acid character are:

H2S04 ↔ S042– + 2H+

Sulphuric acid

HCl ↔ Cl– + H+
Hydrochloric acid
If the concentration of OH- ions in a solution is increased (e.g.
T(oC) pKw pH
to 10-10) then the solution is said to have a base character. In
this case the pH value of the solution is a number greater than 0 14,94 7,47
7. 18 14,22 7,11

25 14,00 7,00
Some more examples are:
50 13,22 6,61
NaOH ↔ Na+ + OH-
Caustic soda 100 12,24 6,12
NH3+ H2O ↔ NH4+ + OH-
Ammonia aqueous ammonia

Note 1. See Appendix 2: Definitions

Note 2. The equilibrium constant is the ratio between the rate of
decomposition and the rate of composition.
Note 3. The concentration H2O is supposed to be 1.
pH Table

Some examples of the difference in pH value of various liquids, foods and fruit are
shown in fig. 2.2b. These can be compared with the pH values of common chemical
compounds dissolved in water.

Fig. PH Scale

Measuring the PH Scale

The pH value can be measured by different methods, e.g.:

A. Colorimetric pH measurement
B. Potentiometric pH measurement
2.3.1 Colorometric pH measurement
The principle of colorimetric determination of the pH value is based on the pH
dependance of colour change.

Some examples are:

Litmus paper
When immersed in an acid medium the paper shows red, it changes to blue in a
base medium. "pH paper" consists of pa- per impregnated with a suitable dye.
After immersion in the liquid to be measured the colour of the wet paper can be
compared with a colour disc which shows the relevant pH value for the varying
shades of colour.

Some natural indicators are:

Red cabbage
Red cabbage is red in an acid medium and blue/violet in a natural medium. In an
strongly basic medium the colour changes to green. Mushrooms will whiten
considerably by treating with vinegar (an acid). In a base medium the mushrooms
will turn brown.

2.3.2 Potentiometric pH measurement

The most often used pH sensing element
is a pH sensitive glass sensor. Other pH
sensors are used if a glass sensor is not
acceptable (e.g. antimon sensor, ISFET).
Accurate potentiometric pH will be
discussed in more depth in later chapters.

2.3.3 The semiconductor sensor method

(ISFET)
ISFET is a, non-glass, ion-sensitive
semiconductor device (or transistor) used
to measure the changes in ion
concentrations within a solution. The
current that passes through the transistor
will change in response to the ion
concentration change.
Walther Hermann Nernst (1864-
1941)
Principle of
Born in Briesen, West Prussia, in 1864.
Potentiometric pH He spent his early school years
(Gymnasium) at Graudentz, and
Measurement subsequently went to the Universities
of Zurich, Berlin and Graz (Ludwig
The principle of potentiometric pH Boltzmann and Albert von
measurement can be explained by Ettinghausen), studying physics and
mathematics.
Nernst's law.

Nernst found that a potential difference

occurs between a metal object and a
solution containing ions of the same metal when the object is immersed in the
solution. The potential difference E, caused by the exchange of metal ions between
metal and liquid, was defined by Nernst as follows:
R = Gas constant (R=8.314J/mol.K)
F = Faraday number (F = 96493 C/ mol.)
n = Valency of the metal
[Mn+] = Metal ion concentration
T = Absolute temperature in Kelvin
Eo = "Normal potential"
The "normal potential" is the potential difference arising between metal and
solution when this solution contains 1 mol Mn+/litre.

Since the behavior of the gas Hydrogen has a certain degree of conformity with a
metal (both have a positive ion formation), Nernst's law can also be applied to a
"hydrogen electrode"1) immersed into a solution containing hydrogen ions.

The formula can be re-written as follows:

or

With the constants:

E = Eo + 0,059 Ln [H+] (volt)

The Effect of Temperature

2.6.1 Temperature effect on the glass and the reference electrode
The glass and the reference electrodes have a number of temperature dependent
contact potentials; it is obvious then that the voltage supplied by the measuring
system is temperature dependent.

This temperature dependency is shown by the factor in the Nernst equation

The voltage supplied by the measuring system is:

Fig. 2.6 Temperature effect on the mV/pH ratio.

pHinner is standardised at pH 7.

T is the temperature in °C. If the glass and the reference electrodes are immersed
in liquids of equal temperatures, the potential variations of similar reference
systems will be equal and opposite.

E3 = -E4
Consequently, the system will be unaffected by temperature variations. The
temperature effect on the contact potential of the junction on the reference
electrode is kept to a minimum by correct selection of the junction and electrolyte.
The temperature effects obtained by immersing the electrodes in different
standard solutions and then by varying the temperature of these standard
solutions, are shown in the graphs of fig. 2.6.
This graph shows that:

a. the mV/pH ratio increases as the temperature of the measuring system

increases.
At 25°C the mV/pH ratio is 59.16 and at 20°C this ratio is 58.16 mV/pH.
At 80°C the mV voltage per pH unit is increased to 70.08 mV.
b. the various isothermal lines intersect at one point S (the isothermal
point of intersection)
c. the intersection point is dependent on the pH of the buffer solution
used in the glass electrode (this is usually pH 7).
It is important that the isothermal lines intersect at only one point. So
selection of the correct buffer solution is essential in order to obtain an
accurate isothermal point of intersection S, shown in figure 2.6.
In general, when a pH measurement is made in a process at widely fluctuating pH
and temperature levels, automatic temperature compensation is necessary. To
achieve this the electrode system is completed with a temperature sensing
elements, packaged in a similar construction to an electrode, that compensates for
slope variations of the mV/pH ratio of the electrode system.

Note 1. The isothermal point of intersection of the standard electrodes of

Yokogawa is at pH 7. Depending on the buffer solution used this point may,
for special applications be at another value pH 3.

Buffer Solutions
Buffer solutions are needed as indispensable tool for maintaining an accurate pH
measurement. Buffer solutions are used as references points for calibration and
adjustment of pH measurements to compensate aging and deterioration.

Buffer solutions are mixtures of weak acids and the salt of these acids with a
strong base, or mixtures of weak bases and the salt of these bases with a strong
acid. Consequently, if the buffers are not accurate themselves, the calibration
serves no useful purpose.

Buffers are classified in three categories. The main difference between the
different types of buffers is the accuracy and buffer capacity.

Primary reference buffer

These buffers are not commercial buffer and mainly used in metrological
institutes. These buffers show the lowest uncertainty in pH values, ±0.003.
Standard Buffer (secondary reference buffer)
Standard buffer solutions are used as standards for accurate measurements
especially in laboratories and production of technical buffers. They are traceable to
the primary standards. The constituents of these buffers are defined by
international standards like DIN19266, IeC 726 and NIST. The uncertainty is 0.002
and 0.004 pH units (at 25°C), depending on the buffer.

Technical buffer
They are commercial buffers and used mainly for calibration of industrial pH
measurements. The buffer values of technical buffers are traceable to standard
buffer. The DIN19267 defines standards for these solutions. The uncertainty is 0.02
a pH units (at 25°C), depending on the buffer examples of preferred buffer by
Yokogawa are shown in the table below. Buffer solutions prepared from these
substances conform to the recommendations of the DIN Standards Committee
and the National Institute of Standards and Technology (NIST). The substances
were chosen for their particular suitability as calibration standards for precision pH
meters.

Standard Buffer Solutions1)

COMPOSITIONS Molarity pH at 25°C Dilution value (pH1/2

Potassium trihydrogen dioxalate (Tetroxalate)

0.0496 1.679 +0,186
KH3(C2O4)2 • 2H20

Borax Na2B4O7 • 10H2O 0.00997 9.180 +0,010

Potassium dihydrogen phosphate+ Disodium hydrogen phosphate 0.02490+ 6.865 +0.080

Na2HPO4 • 2H2O + KH2PO4 0.02490

Potassium hydrogen phtalate

0.05 4.008 +0.052
KHC8H4O4
Note 1. N.B.S. national Bureau of Standards of the U.S.A.
Note 2,3. See Appendix 2: Definitions.
Temperature dependence

The temperature dependence of the pH of a buffer solution is generally specified

in terms of measured pH values at certain discrete temperatures.

Many buffer tables are pre-programmed in Yokogawa Analyzers. So if during

calibration the temperature compensator is immersed in the buffer liquid, an
automatic adjustment for temperature variations will be done. Any stated pH value
is only meaningful if the measuring temperature is also specified.

Be Aware

Buffers with a pH above 7 are particularly sensitive to atmospheric CO2. Buffer

showing any sign of turbidity must be discarded immediately.

For accuracy it is recommended that a buffer should not be used for more than a
month after opening. Buffers should be stored in tightly sealed, preferably air-
tight bottles made of polyethene or borosilicate glass. Buffers should not be
returned to the bottles once removed.