Editing PH (section)

=== pH ===
The pH of a solution is defined as the decimal [[logarithm]] of the reciprocal of the [[hydrogen ion]] [[Activity (chemistry)|activity]], ''a''<sub>H</sub>+.<ref name="covington3"/> Mathematically, pH is expressed as:
: <math chem="">\ce{pH} = - \log_{10}(a_\ce{H+}) = \log_{10}\left(\frac 1 {a_\ce{H+}} \right) </math>

For example, for a solution with a hydrogen ion activity of {{val|5|e=−6|ul=mol|upl=L}} (i.e., the concentration of hydrogen ions), the pH of the solution can be calculated as follows:
: <math chem="">\ce{pH} = - \log_{10}(5\times10^{-6}) = 5.3 </math>

The concept of pH was developed because [[ion-selective electrodes]], which are used to measure pH, respond to activity. The electrode potential, ''E'', follows the [[Nernst equation]] for the hydrogen ion, which can be expressed as:
: <math chem=""> E = E^0 + \frac{RT}{F} \ln(a_\ce{H+}) = E^0 - \frac{RT\ \ln{10}}{F} \ce{pH} \approx E^0 - \frac{2.303\ RT}{F} \ce{pH} </math>
where ''E'' is a measured potential, ''E''<sup>0</sup> is the standard electrode potential, ''R'' is the [[molar gas constant]], ''T'' is the thermodynamic temperature, ''F'' is the [[Faraday constant]]. For {{chem2|H+}}, the number of electrons transferred is one. The electrode potential is proportional to pH when pH is defined in terms of activity.

The precise measurement of pH is presented in International Standard [[ISO 31-8]] as follows:<ref>Quantities and units – Part 8: Physical chemistry and molecular physics, Annex C (normative): pH. [[International Organization for Standardization]], 1992.</ref> 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 [[Saturated calomel electrode|calomel electrode]], and the hydrogen-ion selective electrode is a [[standard hydrogen electrode]].
: {{math|Reference electrode {{!}} concentrated solution of KCl {{!}}{{!}} test solution {{!}} H<sub>2</sub> {{!}} Pt}}

Firstly, the cell is filled with a solution of known hydrogen ion activity and the electromotive force, ''E''<sub>S</sub>, is measured. Then the electromotive force, ''E''<sub>X</sub>, of the same cell containing the solution of unknown pH is measured.
: <math chem="">\ce{pH(X)} = \ce{pH(S)}+\frac{E_\ce{S} - E_\ce{X} }{z}</math>

The difference between the two measured electromotive force values is proportional to pH. This method of calibration avoids the need to know the [[standard electrode potential]]. The proportionality constant, 1/''z'', is ideally equal to <math>\frac{F}{RT\ln{10}}\ </math>, the "Nernstian slope".

In practice, a [[glass electrode]] is used instead of the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against [[Buffer solution]]s of known hydrogen ion ({{chem2|H+}}) activity proposed by the International Union of Pure and Applied Chemistry ([[IUPAC]]).<ref name="covington3"/> Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To calibrate the electrode, it is first immersed in a standard solution, and the reading on a [[pH meter]] is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted using the "slope" control to be equal to the pH for that solution. Further details, are given in the [[IUPAC]] recommendations.<ref name="covington22" >{{cite journal |last1=Covington |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |year=1985 |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |url-status=live |journal=Pure Appl. Chem. |volume=57 |issue=3 |pages=531–542 |doi=10.1351/pac198557030531 |s2cid=14182410 |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref> When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values. Commercial standard buffer solutions usually come with information on the value at 25&nbsp;°C and a correction factor to be applied for other temperatures.

The pH scale is logarithmic and therefore pH is a [[dimensionless quantity]].<ref>{{Cite book |url=https://goldbook.iupac.org/ |title=The IUPAC Compendium of Chemical Terminology: The Gold Book |date=2019 |publisher=International Union of Pure and Applied Chemistry (IUPAC) |editor-last=Gold |editor-first=Victor |edition=4 |location=Research Triangle Park, NC |language=en |doi=10.1351/goldbook.p04525}}</ref>