pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution.[4]
pH
=
−
log
10
(
a
H
+
)
=
log
10
(
1
a
H
+
)
{\displaystyle {\ce {pH}}=-\log _{10}(a_{{\ce {H+}}})=\log _{10}\left({\frac {1}{a_{{\ce {H+}}}}}\right)}
For example, for a solution with a hydrogen ion activity of 5×10−6 (at that level, this is essentially the number of moles of hydrogen ions per litre of solution) there is 1/(5×10−6) = 2×105, thus such a solution has a pH of log10(2×105) = 5.3. Consider the following example: a quantity of 107 moles of pure (pH 7) water, or 180 metric tonnes (18×107 g), contains close to 18 g of dissociated hydrogen ions.
Note that pH depends on temperature. For instance at 0 °C the pH of pure water is about 7.47. At 25 °C it is 7.00, and at 100 °C it is 6.14.
This definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. Ideally, electrode potential, E, follows the Nernst equation, which, for the hydrogen ion can be written as
E
=
E
0
+
R
T
F
ln
(
a
H
+
)
=
E
0
−
2.303
R
T
F
pH
{\displaystyle E=E^{0}+{\frac {RT}{F}}\ln(a_{{\ce {H+}}})=E^{0}-{\frac {2.303RT}{F}}{\ce {pH}}}
where E is a measured potential, E0 is the standard electrode potential, R is the gas constant, T is the temperature in kelvins, F is the Faraday constant. For H+ number of electrons transferred is one. It follows that electrode potential is proportional to pH when pH is defined in terms of activity. Precise measurement of pH is presented in International Standard ISO 31-8 as follows:[12] A galvanic cell is set up to measure the electromotive force (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a silver chloride electrode or a calomel electrode. The hydrogen-ion selective electrode is a standard hydrogen electrode.
Reference electrode | concentrated solution of KCl || test solution | H2 | Pt[clarification needed]
Firstly, the cell is filled with a solution of known hydrogen ion activity and the emf, ES, is measured. Then the emf, EX, of the same cell containing the solution of unknown pH is measured.
pH
(
X
)
=
pH
(
S
)
+
E
S
−
E
X
z
{\displaystyle {\ce {pH(X)}}={\ce {pH(S)}}+{\frac {E_{{\ce {S}}}-E_{{\ce {X}}}}{z}}}
