Editing PH (section)

== Definition ==
=== pH ===
The pH of a solution is defined as the decimal [[logarithm]] of the reciprocal of the [[Hydron|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 cations), 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 cation, 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>

=== p[H] ===
This was the original definition of Sørensen in 1909,<ref name="Sor2">{{cite web |title=Carlsberg Group Company History Page |url=http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |url-status=live |archive-url=https://web.archive.org/web/20140118043012/http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |archive-date=18 January 2014 |access-date=7 May 2013 |publisher=Carlsberggroup.com}}</ref> which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [{{chem2|H(+)}}] in modern chemistry. More correctly, the [[thermodynamic activity]] of {{chem2|H(+)}} (''a''<sub>H</sub>+) in dilute solution should be replaced by [{{chem2|H(+)}}]/''c''<sub>0</sub>, where the standard state concentration ''c''<sub>0</sub> = 1&nbsp;mol/L. This ratio is a pure number whose logarithm can be defined.

It is possible to measure the concentration of hydrogen cations directly using an electrode calibrated in terms of hydrogen ion concentrations. One common method is to [[Titration|titrate]] a solution of known concentration of a strong acid with a solution of known concentration of strong base in the presence of a relatively high concentration of background electrolyte. By knowing the concentrations of the acid and base, the concentration of hydrogen cations can be calculated and the measured potential can be correlated with concentrations. The calibration is usually carried out using a [[Gran plot#Electrode calibration|Gran plot]].<ref>{{cite journal |last=Rossotti |first=F.J.C. |author2=Rossotti, H. |year=1965 |title=Potentiometric titrations solution containing the background electrolyte. |journal=J. Chem. Educ. |volume=42 |doi=10.1021/ed042p375}}</ref> This procedure makes the activity of hydrogen cations equal to the numerical value of concentration of these ions.

The glass electrode (and other [[Ion selective electrode]]s) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition.

The difference between p[H] and pH is quite small, and it has been stated that pH = p[H] + 0.04.<ref>{{VogelQuantitative}}, Section 13.23, "Determination of pH"</ref> However, it is common practice to use the term "pH" for both types of measurement.

=== pOH ===
[[File:PHscalenolang.svg|thumb|Relation between pH and pOH. Red represents the acidic region. Blue represents the basic region.]]
pOH is sometimes used as a measure of the concentration of hydroxide ions, {{chem2|OH−}}. By definition, pOH is the negative logarithm (to the base 10) of the hydroxide ion concentration (mol/L). pOH values can be derived from pH measurements and vice-versa. The concentration of hydroxide ions in water is related to the concentration of hydrogen cations by
: <math chem="">[\ce{OH^-}] = \frac{K_\ce{W}}{[\ce{H^+}]}</math>
where ''K''<sub>W</sub> is the [[Self-ionization of water|self-ionization]] constant of water. Taking [[logarithm]]s,
: <math chem="">\ce{pOH} = \ce{p}K_\ce{W} - \ce{pH}.</math>

So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of [[Alkaline soils|soil alkalinity]].