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{{Other uses|PH (disambiguation)}}
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{{Lowercase title}}
[[File:216 pH Scale-01.jpg|thumb|right|pH values of some common substances]]
{{Acids and bases}}

In [[chemistry]], '''pH''' ({{IPAc-en|p|iː|ˈ|eɪ|tʃ}}) is a scale used to specify how [[acidic]] or [[Base (chemistry)|basic]] a [[Aqueous solution|water-based solution]] is. Acidic solutions have a lower pH, while basic solutions have a higher pH. At room temperature (25°C or 77°F), [[pure water]] is neither acidic nor basic and has a pH of 7.

The pH scale is [[logarithmic scale|logarithmic]] and inversely indicates the [[concentration]] of [[hydrogen ion]]s in the solution (a lower pH indicates a higher concentration of hydrogen ions). This is because the formula used to calculate pH approximates the [[Negative number|negative]] of the [[base 10 logarithm]] of the [[molar concentration]]{{efn|Measured in units of [[mole (unit)|moles]] per liter.}} of hydrogen ions in the solution. More precisely, pH is the negative of the base 10 logarithm of the [[activity (chemistry)|activity]] of the hydrogen ion.<ref name="Bates">Bates, Roger G. ''Determination of pH: theory and practice''. Wiley, 1973.</ref>

At 25&nbsp;°C, solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases. The pH value can be less than 0 for very strong acids, or greater than 14 for very strong bases.<ref>{{cite journal | last1 = Lim | first1 = Kieran F. | year = 2006 | title = Negative pH Does Exist | journal = Journal of Chemical Education | volume = 83 | issue = 10 | pages = 1465 | doi=10.1021/ed083p1465| bibcode = 2006JChEd..83.1465L }}</ref>

The pH scale is [[Measurement traceability|traceable]] to a set of standard solutions whose pH is established by international agreement.<ref name="covington" /> Primary pH standard values are determined using a [[galvanic cell|concentration cell with transference]], by measuring the potential difference between a [[hydrogen electrode]] and a standard electrode such as the [[silver chloride electrode]]. The pH of aqueous solutions can be measured with a [[glass electrode]] and a [[pH meter]], or a color-changing [[pH indicator|indicator]]. Measurements of pH are important in chemistry, [[agronomy]], medicine, water treatment, and many other applications.

==History==
The concept of  pH was first introduced by the [[Danish people|Danish]] chemist [[Søren Peder Lauritz Sørensen]] at the [[Carlsberg Laboratory]] in 1909<ref>{{cite journal | last1 = Sørensen | first1 = S. P. L. | year = 1909 | title = Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen | url = | journal = Biochem. Zeitschr | volume = 21 | issue = | pages = 131–304 }} Two other publications appeared in 1909, one in French and one in Danish.</ref> and revised to the modern pH in 1924 to accommodate definitions and measurements in terms of electrochemical cells. In the first papers, the notation had the "H" as a subscript to the lowercase "p", as so: p<sub>H</sub>.

The exact meaning of the "p" in "pH" is disputed, as Sørensen did not explain why he used it.<ref>{{Cite journal|last=Francl|first=Michelle|date=August 2010|title=Urban legends of chemistry|url=https://www.nature.com/articles/nchem.750.epdf|journal=Nature Chemistry|volume=2|issue=8|pages=600–601|doi=10.1038/nchem.750|issn=1755-4330}}</ref> He describes a way of measuring it using ''potential'' differences, and it represents the negative ''power'' of 10 in the concentration of hydrogen ions. All the words for these start with ''p'' in [[French language|French]], [[German language|German]] and [[Danish language|Danish]], all languages Sørensen published in: Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish. He also used "q" in much the same way elsewhere in the paper. So the "p" could stand for the French ''puissance,'' German ''Potenz,'' or Danish ''potens'', meaning "power", or it could mean "potential". He might also just have labelled the test solution "p" and the reference solution "q" arbitrarily; these letters are often paired.<ref>{{cite journal|last1=Myers|first1=Rollie J.|year=2010|title=One-Hundred Years of pH|journal=Journal of Chemical Education|volume=87|issue=1|pages=30–32|bibcode=2010JChEd..87...30M|doi=10.1021/ed800002c}}</ref> There is little to support the suggestion that "pH" stands for the [[Latin language|Latin terms]] ''pondus hydrogenii'' (quantity of hydrogen) or ''potentia hydrogenii'' (power of hydrogen).

Currently in [[chemistry]], the p stands for "decimal [[cologarithm]] of", and is also used in the term p''K''<sub>a</sub>, used for [[acid dissociation constant]]s<ref name="Jens">{{cite journal|author=Nørby, Jens|year=2000|title=The origin and the meaning of the little p in pH|journal=Trends in Biochemical Sciences|volume=25|issue=1|pages=36–37|doi=10.1016/S0968-0004(99)01517-0|pmid=10637613}}</ref> and pOH, the equivalent for [[hydroxide]] ions.

Bacteriologist [[Alice Catherine Evans|Alice C. Evans]], famed for her work's influence on [[dairy]]ing and [[food safety]], credited William Mansfield Clark and colleagues (of whom she was one) with developing pH measuring methods in the 1910s, which had a wide influence on laboratory and industrial use thereafter. In her memoir, she does not mention how much, or how little, Clark and colleagues knew about Sørensen's work a few years prior.<ref name="Evans-Memoirs">{{cite web |last1=Evans |first1=Alice C. |author-link=Alice Catherine Evans |year=1963 |title=Memoirs |url=https://history.nih.gov/archives/downloads/aliceevans.pdf |website=NIH Office of History |publisher=National Institutes of Health Office of History |accessdate=2018-03-27}}</ref>{{rp|10<!-- 12 of 65 in PDF-->}} She said: 
<blockquote>In these studies [of bacterial metabolism] Dr. Clark's attention was directed to the effect of acid on the growth of bacteria. He found that it is the intensity of the acid in terms of hydrogen-ion concentration that affects their growth. But existing methods of measuring acidity determined the quantity, not the intensity, of the acid. Next, with his collaborators, Dr. Clark developed accurate methods for measuring hydrogen-ion concentration. These methods replaced the inaccurate titration method of determining acid content in use in biologic laboratories throughout the world. Also they were found to be applicable in many industrial and other processes in which they came into wide usage.<ref name="Evans-Memoirs"/>{{rp|10<!-- 12 of 65 in PDF-->}}</blockquote>

The first [[electronics|electronic]] method for measuring pH was invented by [[Arnold Orville Beckman]], a professor at [[California Institute of Technology]] in 1934.<ref>{{cite web|title=ORIGINS: BIRTH OF THE PH METER|url=https://eands.caltech.edu/origins-birth-of-the-ph-meter/|website=CalTech Engineering & Science Magazine|accessdate=11 March 2018}}</ref> It was in response to local citrus grower [[Sunkist Growers, Incorporated|Sunkist]] that wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.<ref>{{cite web|last1=Tetrault|first1=Sharon|title=The Beckmans|url=https://books.google.com/?id=nf0DAAAAMBAJ&pg=PA96&lpg=PA96&dq=ph+caltech+beckman+sunkist#v=onepage&q=ph%20caltech%20beckman%20sunkist&f=false|website=Orange Coast|publisher=Orange Coast Magazine|accessdate=11 March 2018|date=June 2002}}</ref>

==Definition and measurement==
===pH===

pH is defined as the decimal [[logarithm]] of the reciprocal of the [[hydrogen ion]] [[activity (chemistry)|activity]], ''a''<sub>H</sub>+, in a solution.<ref name=covington>{{cite journal|doi=10.1351/pac198557030531|last1=Covington|url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf|first1=A. K.|last2=Bates|first2=R. G.|last3=Durst|first3=R. A.|title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology|journal=Pure Appl. Chem.|year=1985|volume=57|pages=531–542|issue=3|url-status=live|archiveurl=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf|archivedate=24 September 2007|df=dmy-all}}</ref>

:<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 {{math|5&times;10<sup>−6</sup>}} (at that level, this is essentially the number of moles of hydrogen ions per liter of solution) there is {{math|1/(5&times;10<sup>−6</sup>) {{=}} 2&times;10<sup>5</sup>}}, thus such a solution has a pH of {{math|log<sub>10</sub>(2&times;10<sup>5</sup>) {{=}} 5.3}}.  For a commonplace example based on the facts that the masses of a mole of water, a mole of hydrogen ions, and a mole of [[hydroxide ion]]s are respectively 18 g, 1 g, and 17 g, a quantity of 10<sup>7</sup> moles of pure (pH 7) water, or 180 tonnes (18&times;10<sup>7</sup> g), contains close to 1 g of [[Dissociation (chemistry)|dissociated]] hydrogen ions (or rather 19 g of H<sub>3</sub>O<sup>+</sup> [[hydronium]] ions) and 17 g of hydroxide ions.

Note that pH depends on temperature. For instance at 0&nbsp;°C the pH of pure water is 7.47. At 25&nbsp;°C it's 7.00, and at 100&nbsp;°C it's 6.14.

This definition was adopted because [[ion-selective electrode]]s, 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

:<math chem> E = E^0 + \frac{RT}{F} \ln(a_\ce{H+})=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 [[gas constant]], ''T'' is the temperature in [[kelvin]]s, ''F'' is the [[Faraday constant]]. For H<sup>+</sup> 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:<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]]. The hydrogen-ion selective electrode is a [[standard hydrogen electrode]].

:<span class="texhtml">Reference electrode | concentrated solution of KCl || test solution | H<sub>2</sub> | Pt</span>{{clarify|date=October 2014}}

Firstly, the cell is filled with a solution of known hydrogen ion activity and the emf, ''E''<sub>S</sub>, is measured. Then the emf, ''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 emf 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{1}{2.303RT/F}\ </math> the "Nernstian slope".

To apply this process in practice, a [[glass electrode]] is used rather than 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 activity. [[IUPAC]] has proposed the use of a set of buffer solutions of known H<sup>+</sup> activity.<ref name=covington/> Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To implement this approach to calibration, the electrode 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=covington/> 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]].

===p[H]===
This was the original definition of Sørensen in 1909,<ref name="Sor">{{cite web|url=http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx|title=Carlsberg Group Company History Page|publisher=Carlsberggroup.com|archiveurl=https://web.archive.org/web/20140118043012/http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx|archivedate=18 January 2014|url-status=live|accessdate=7 May 2013|df=dmy-all}}</ref> which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [H<sup>+</sup>] in modern chemistry, which appears to have units of concentration. More correctly, the thermodynamic activity of H<sup>+</sup> in dilute solution should be replaced by [H<sup>+</sup>]/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.

However, it is possible to measure the concentration of hydrogen ions directly, if the electrode is calibrated in terms of hydrogen ion concentrations. One way to do this, which has been used extensively, is to [[titration|titrate]] a solution of known concentration of a strong acid with a solution of known concentration of strong alkaline in the presence of a relatively high concentration of background electrolyte. Since the concentrations of acid and alkaline are known, it is easy to calculate the concentration of hydrogen ions so that 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| doi=10.1021/ed042p375| last=Rossotti| first=F.J.C.|author2=Rossotti, H.|year=1965|title=Potentiometric titrations using Gran plots: A textbook omission|journal=J. Chem. Educ.|volume=42|pages=375–378| issue=7|bibcode = 1965JChEd..42..375R }}</ref> The calibration yields a value for the standard electrode potential, ''E''<sup>0</sup>, and a slope factor, ''f'', so that the Nernst equation in the form
:<math chem>E = E^0 + f\frac{2.303RT}{F} \log[\ce{H+}]</math>
can be used to derive hydrogen ion concentrations from experimental measurements of ''E''. The slope factor, ''f'', is usually slightly less than one. A slope factor of less than 0.95 indicates that the electrode is not functioning correctly. The presence of background electrolyte ensures that the hydrogen ion activity coefficient is effectively constant during the titration. As it is constant, its value can be set to one by defining the [[standard state]] as being the solution containing the background electrolyte. Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration.

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, as detailed below.

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

===pH indicators===
{{main|Universal indicator}}
[[Image:Universal indicator paper.jpg|thumb|300px|Chart showing the variation of color of universal indicator paper with pH]]
Indicators may be used to measure pH, by making use of the fact that their color changes with pH. Visual comparison of the color of a test solution with a standard color chart provides a means to measure pH accurate to the nearest whole number. More precise measurements are possible if the color is measured spectrophotometrically, using a [[Colorimeter (chemistry)|colorimeter]] or [[spectrophotometer]].
[[Universal indicator]] consists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. Another method of measuring pH is using an electronic [[pH meter]].

===pOH===
[[Image:PHscalenolang.svg|thumb|300px|Relation between p[OH] and p[H] (red = acidic region, blue = basic region)]]
pOH is sometimes used as a measure of the concentration of hydroxide ions. OH<sup>−</sup>. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by

:<math chem>[\ce{OH^-}] = \frac{K_\ce{W}}{[\ce{H^+}]}</math>

where ''K''<sub>W</sub> is the [[self-ionization of water|self-ionisation]] 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]].

===Extremes of pH===
Measurement of pH below about 2.5 (ca. 0.003&nbsp;[[mole (unit)|mol]] dm<sup>−3</sup> acid) and above about 10.5 (ca. 0.0003&nbsp;mol dm<sup>−3</sup> alkaline) requires special procedures because, when using the glass electrode, the [[Nernst equation|Nernst law]] breaks down under those conditions. Various factors contribute to this. It cannot be assumed that [[liquid junction potential]]s are independent of pH.<ref name=Feldman>{{cite journal|doi=10.1021/ac60120a014|title=Use and Abuse of pH measurements|journal=Analytical Chemistry|author=Feldman, Isaac |volume=28|pages=1859–1866|year=1956|issue=12}}</ref> Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by [[ionic strength]] variation. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as Na<sup>+</sup> and K<sup>+</sup> in the solution.<ref>{{VogelQuantitative}}, Section 13.19 The glass electrode</ref> Specially constructed electrodes are available which partly overcome these problems.

Runoff from mines or mine tailings can produce some very low pH values.<ref>{{cite journal |last1=Nordstrom |first1=D. Kirk |last2=Alpers |first2=Charles N. |title=Negative pH, efflorescent mineralogy, and consequences for environmental restoration at the Iron Mountain Superfund site, California |date=March 1999 |pmid=10097057 |doi=10.1073/pnas.96.7.3455 |volume=96 |issue=7 |pages=3455–62 |pmc=34288 |journal=Proceedings of the National Academy of Sciences of the United States of America |bibcode = 1999PNAS...96.3455N |url=http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1495&context=usgsstaffpub }}</ref>

===Non-aqueous solutions===
Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents. pH values based on these measurements belong to a different scale from aqueous pH values, because [[activity (chemistry)|activities]] relate to different [[standard state]]s. Hydrogen ion activity, ''a<sub>H<sup>+</sup></sub>'', can be defined<ref name="GoldBook">{{GoldBookRef|title=activity (relative activity), ''a''|file=A00115}}</ref><ref name="GreenBook">{{GreenBookRef2nd|pages=49–50}}</ref> as:
:<math chem>a_\ce{H+} = \exp\left (\frac{\mu_\ce{H+} - \mu^{\ominus}_\ce{H+}}{RT}\right )</math>
where ''μ''<sub>H<sup>+</sup></sub> is the [[chemical potential]] of the hydrogen ion, <math chem>\mu^{\ominus}_\ce{H+}</math> is its chemical potential in the chosen standard state, ''R'' is the [[gas constant]] and ''T'' is the [[thermodynamic temperature]]. Therefore, pH values on the different scales cannot be compared directly due to different solvated proton ions such as lyonium ions, requiring an intersolvent scale which involves the transfer activity coefficient of [[lyonium ion|hydronium/lyonium ion]].

pH is an example of an [[acidity function]]. Other acidity functions can be defined. For example, the [[Hammett acidity function]], ''H''<sub>0</sub>, has been developed in connection with [[superacid]]s.

===Unified absolute pH scale===
The concept of "unified pH scale" has been developed on the basis of the absolute chemical potential of the proton. This model uses the [[Lewis acids and bases|Lewis acid–base]] definition. This scale applies to liquids, gases and even solids.<ref name="Krossing">{{cite journal | last1 = Himmel | first1 = D. | last2 = Goll | first2 = S. K. | last3 = Leito | first3 = I. | last4 = Krossing | first4 = I. | year = 2010 | title = A Unified pH Scale for all Phases | url = | journal = [[Angew. Chem. Int. Ed.]] | volume = 49 | issue = 38| pages = 6885–6888 | doi = 10.1002/anie.201000252 | pmid = 20715223 }}</ref>
In 2010, a new "unified absolute pH scale" has been proposed that would allow various pH ranges across different solutions to use a common proton reference standard.<ref>{{Cite journal|last=Himmel|first=Daniel|last2=Goll|first2=Sascha K.|last3=Leito|first3=Ivo|last4=Krossing|first4=Ingo|date=2010-08-16|title=A Unified pH Scale for All Phases|journal=Angewandte Chemie International Edition|volume=49|issue=38|pages=6885–6888|doi=10.1002/anie.201000252|pmid=20715223|issn=1433-7851}}</ref>

==Applications==
<!-- [[File:PH scale 2.png|thumb|right|Another visual representation of the pH scale.]]
[[File:Hydrangea macrophylla - Hortensia hydrangea.jpg|right|thumb|''[[Hydrangea macrophylla]]'' blossoms vary from [[pink]] to [[blue]], according to a pH-dependent mobilization and uptake of soil aluminium into the plants.]] -->

Pure water is neutral. When an [[acid]] is dissolved in water, the pH will be less than 7 (25&nbsp;°C). When a [[base (chemistry)|base]], or [[alkali]], is dissolved in water, the pH will be greater than 7. A solution of a strong acid, such as [[hydrochloric acid]], at concentration 1&nbsp;mol dm<sup>−3</sup> has a pH of 0. A solution of a strong alkali, such as [[sodium hydroxide]], at concentration 1&nbsp;mol dm<sup>−3</sup>, has a pH of 14. Thus, measured pH values will lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible. Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration.

The pH of neutrality is not exactly 7 (25&nbsp;°C), although this is a good approximation in most cases. Neutrality is defined as the condition where [H<sup>+</sup>] = [OH<sup>−</sup>] (or the activities are equal). Since [[self-ionization of water]] holds the product of these concentration [H<sup>+</sup>]&times;[OH<sup>−</sup>] = K<sub>w</sub>, it can be seen that at neutrality [H<sup>+</sup>] = [OH<sup>−</sup>] = {{radic|K<sub>w</sub>}}, or pH = pK<sub>w</sub>/2. pK<sub>w</sub> is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution of [[sodium chloride|NaCl]] in pure water are both neutral, since [[Self-ionization of water|dissociation of water]] produces equal numbers of both ions. However the pH of the neutral NaCl solution will be slightly different from that of neutral pure water because the hydrogen and hydroxide ions' activity is dependent on [[ionic strength]], so K<sub>w</sub> varies with ionic strength.

If pure water is exposed to air it becomes mildly acidic. This is because water absorbs [[carbon dioxide]] from the air, which is then slowly converted into [[bicarbonate]] and hydrogen ions (essentially creating [[carbonic acid]]).
:<chem>CO2 + H2O <=> HCO3^- + H+</chem>

===pH in soil===

====Classification of soil pH ranges====

The United States Department of Agriculture [[Natural Resources Conservation Service]], formerly Soil Conservation Service classifies soil pH ranges as follows:
<ref>{{cite web|author=Soil Survey Division Staff|url=http://soils.usda.gov/technical/manual/contents/chapter3.html |title=Soil survey manual.1993. Chapter 3, selected chemical properties. |publisher=Soil Conservation Service. U.S. Department of Agriculture Handbook 18 |accessdate=2011-03-12 |url-status=dead |archiveurl=https://web.archive.org/web/20110514151830/http://soils.usda.gov/technical/manual/contents/chapter3.html |archivedate=14 May 2011 |df=dmy-all}}</ref>
[[Image:Soil pH effect on nutrient availability.svg|thumb|500px|right|Nutritional elements availability within soil varies with pH. Light blue color represents the ideal range for most plants.]]

{|class="wikitable" style="align: center;"
|-
!scope="col"|Denomination
!scope="col"|pH range
|-
|Ultra acidic|| < 3.5
|-
|Extremely acidic|| 3.5–4.4
|-
|Very strongly acidic|| 4.5–5.0 <!-- BTW to which range belong the value 4.45? was the article written by scientists or by record clerks? -->
|-
|Strongly acidic|| 5.1–5.5
|-
|Moderately acidic|| 5.6–6.0
|-
|Slightly acidic|| 6.1–6.5
|-
|Neutral|| 6.6–7.3
|-
|Slightly alkaline|| 7.4–7.8
|-
|Moderately alkaline|| 7.9–8.4
|-
|Strongly alkaline|| 8.5–9.0
|-
|Very strongly alkaline|| > 9.0
|-
|}
In Europe, Topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map <ref>{{Cite journal|last=Ballabio|first=Cristiano|last2=Lugato|first2=Emanuele|last3=Fernández-Ugalde|first3=Oihane|last4=Orgiazzi|first4=Alberto|last5=Jones|first5=Arwyn|last6=Borrelli|first6=Pasquale|last7=Montanarella|first7=Luca|last8=Panagos|first8=Panos|date=2019|title=Mapping LUCAS topsoil chemical properties at European scale using Gaussian process regression|url=https://linkinghub.elsevier.com/retrieve/pii/S0016706119304768|journal=Geoderma|language=en|volume=355|pages=113912|doi=10.1016/j.geoderma.2019.113912|via=}}</ref> of topsoil pH in Europe shows the alkaline soils in  Mediterranean, Hungary, East Romania, North France. Scandinavian countries, Portugal, Poland and North Germany have more acid soils.

===pH in nature===
[[File:Lemon.jpg|thumb|[[Lemon juice]] tastes sour because it contains 5% to 6% [[citric acid]] and has a pH of 2.2. (high acidity)]]
pH-dependent [[plant pigment]]s that can be used as [[pH indicator]]s occur in many plants, including [[hibiscus]], [[red cabbage]] ([[anthocyanin]]) and [[red wine]]. The juice of [[citrus]] fruits is acidic mainly because it contains [[citric acid]]. Other [[carboxylic acid]]s occur in many living systems. For example, [[lactic acid]] is produced by [[muscle]] activity. The state of [[protonation]] of [[phosphate]] derivatives, such as [[Adenosine triphosphate|ATP]], is pH-dependent. The functioning of the oxygen-transport enzyme [[hemoglobin]] is affected by pH in a process known as the [[Root effect]].

===Seawater===
{{See also|Ocean acidification}}

The pH of [[seawater]] is typically limited to a range between 7.5 and 8.4.<ref name="Chester Marine Geochem">{{cite book|last=Chester, Jickells|first=Roy, Tim|title=Marine Geochemistry|date=2012|publisher=Blackwell Publishing|isbn=978-1-118-34907-6}}</ref> It plays an important role in the ocean's [[Carbon cycle#In the ocean|carbon cycle]], and there is evidence of ongoing [[ocean acidification]] caused by [[Carbon dioxide emission#Greenhouse gas emissions|carbon dioxide emissions]].<ref name=raven05>{{cite book|author=Royal Society|url=http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf|year=2005|title=Ocean acidification due to increasing atmospheric carbon dioxide|isbn=978-0-85403-617-2|url-status=live|archiveurl=https://web.archive.org/web/20100716000207/http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf|archivedate=16 July 2010|df=dmy-all}}</ref> However, pH measurement is complicated by the [[chemical property|chemical properties]] of seawater, and several distinct pH scales exist in [[chemical oceanography]].<ref name=zeebe>Zeebe, R. E. and Wolf-Gladrow, D. (2001) ''CO<sub>2</sub> in seawater: equilibrium, kinetics, isotopes'', Elsevier Science B.V., Amsterdam, Netherlands {{ISBN|0-444-50946-1}}</ref>

As part of its [[operational definition]] of the pH scale, the [[IUPAC]] defines a series of [[buffer solution]]s across a range of pH values (often denoted with [[National Bureau of Standards|NBS]] or [[National Institute of Standards and Technology|NIST]] designation). These solutions have a relatively low [[ionic strength]] (≈0.1) compared to that of seawater (≈0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes in [[standard electrode potential|electrode potential]]. To resolve this problem, an alternative series of buffers based on [[artificial seawater]] was developed.<ref>{{cite journal|doi=10.1016/0011-7471(73)90101-0|author=Hansson, I.|year=1973|title=A new set of pH-scales and standard buffers for seawater|journal=Deep-Sea Research|volume=20|pages=479–491|issue=5|bibcode=1973DSROA..20..479H}}</ref> This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the 'total scale', often denoted as pH<sub>T</sub>. The total scale was defined using a medium containing [[sulfate]] ions. These ions experience protonation, H<sup>+</sup> + SO{{su|b=4|p=2−}} {{eqm}} HSO{{su|b=4|p=−}}, such that the total scale includes the effect of both [[proton]]s (free hydrogen ions) and hydrogen sulfate ions:

:[H<sup>+</sup>]<sub>T</sub> = [H<sup>+</sup>]<sub>F</sub> + [HSO{{su|b=4|p=−}}]

An alternative scale, the 'free scale', often denoted 'pH<sub>F</sub>', omits this consideration and focuses solely on [H<sup>+</sup>]<sub>F</sub>, in principle making it a simpler representation of hydrogen ion concentration. Only [H<sup>+</sup>]<sub>T</sub> can be determined,<ref>{{cite journal| doi=10.1016/0016-7037(84)90225-4| author=Dickson, A. G.|year=1984|title=pH scales and proton-transfer reactions in saline media such as sea water|journal=Geochim. Cosmochim. Acta|volume=48|pages=2299–2308|issue=11|bibcode = 1984GeCoA..48.2299D }}</ref> therefore [H<sup>+</sup>]<sub>F</sub> must be estimated using the [SO{{su|b=4|p=2−}}] and the stability constant of HSO{{su|b=4|p=−}}, {{nowrap|1=K{{su|b=S|p=*}}}}:

:[H<sup>+</sup>]<sub>F</sub> = [H<sup>+</sup>]<sub>T</sub> − [HSO{{su|b=4|p=−}}] = [H<sup>+</sup>]<sub>T</sub> ( 1 + [SO{{su|b=4|p=2−}}] / K{{su|b=S|p=*}} )<sup>−1</sup>

However, it is difficult to estimate K{{su|b=S|p=*}} in seawater, limiting the utility of the otherwise more straightforward free scale.

Another scale, known as the 'seawater scale', often denoted 'pH<sub>SWS</sub>', takes account of a further protonation relationship between hydrogen ions and [[fluoride]] ions, H<sup>+</sup> + F<sup>−</sup> ⇌ HF. Resulting in the following expression for [H<sup>+</sup>]<sub>SWS</sub>:

:[H<sup>+</sup>]<sub>SWS</sub> = [H<sup>+</sup>]<sub>F</sub> + [HSO{{su|b=4|p=−}}] + [HF]

However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.

The following three equations summarise the three scales of pH:

:pH<sub>F</sub> = − log [H<sup>+</sup>]<sub>F</sub>
:pH<sub>T</sub> = − log ( [H<sup>+</sup>]<sub>F</sub> + [HSO{{su|b=4|p=−}}] ) = − log [H<sup>+</sup>]<sub>T</sub>
:pH<sub>SWS</sub> = − log ( [H<sup>+</sup>]<sub>F</sub> + [HSO{{su|b=4|p=−}}] + [HF] ) = − log [H<sup>+</sup>]<sub>SWS</sub>

In practical terms, the three seawater pH scales differ in their values by up to 0.12 pH units, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean's [[Total inorganic carbon|carbonate system]].<ref name=zeebe /> Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.

===Living systems===
:{| class="wikitable"
|+pH in living systems<ref>{{cite book|title=Medical Physiology: A Cellular And Molecular Approach|last=Boron|first=Walter, F.|publisher=Elsevier/Saunders|year=2004|isbn=978-1-4160-2328-9|author2=Boulpaep, E.L.}}</ref>
|-
! Compartment
! pH
|-
| [[Gastric acid]] || 1.5-3.5<ref>{{cite book |vauthors=Marieb EN, Hoehn K |title=Human anatomy & physiology |publisher=Benjamin Cummings |location=San Francisco |year=2010 |pages= |isbn=978-0-8053-9591-4}}</ref>
|-
| [[Lysosome]]s || 4.5
|-
| [[Human skin]] || 4.7<ref>{{Cite journal|last=Lambers|first=H.|last2=Piessens|first2=S.|last3=Bloem|first3=A.|last4=Pronk|first4=H.|last5=Finkel|first5=P.|date=2006-10-01|title=Natural skin surface pH is on average below 5, which is beneficial for its resident flora|journal=International Journal of Cosmetic Science|volume=28|issue=5|pages=359–370|doi=10.1111/j.1467-2494.2006.00344.x|issn=1468-2494|pmid=18489300}}</ref>
|-
| Granules of [[chromaffin cell]]s || 5.5
|-
| [[Urine]] || 6.0
|-
| [[Cytosol]] || 7.2
|-
| [[Blood]] (natural pH) || 7.34–7.45
|-
| [[Cerebrospinal fluid]] (CSF) || 7.5
|-
| [[Mitochondrial matrix]] || 7.5
|-
| [[Pancreas]] secretions || 8.1
|}

The pH of different cellular compartments, [[body fluid]]s, and organs is usually tightly regulated in a process called [[acid-base homeostasis]]. The most common disorder in acid-base homeostasis is [[acidosis]], which means an acid overload in the body, generally defined by pH falling below 7.35. [[Alkalosis]] is the opposite condition, with blood pH being excessively high.

The pH of blood is usually slightly basic with a value of pH 7.365. This value is often referred to as physiological pH in biology and medicine. [[Dental plaque|Plaque]] can create a local acidic environment that can result in [[tooth decay]] by demineralization. [[Enzyme]]s and other [[protein]]s have an optimum pH range and can become inactivated or [[denaturation (biochemistry)|denatured]] outside this range.
<!-- <div class="noprint">
[[File:Blood values sorted by mass and molar concentration.png|thumb|900px|[[Reference ranges for blood tests]], showing concentration of protons (purple) at left. It can be seen that the ranges are kept in a narrow range, and that free protons are among the compounds with the very smallest mass concentrations.]]
</div> -->

==Calculations of pH==
The calculation of the pH of a solution containing acids and/or bases is an example of a chemical speciation calculation, that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution. The complexity of the procedure depends on the nature of the solution. For strong acids and bases no calculations are necessary except in extreme situations. The pH of a solution containing a weak acid requires the solution of a [[quadratic equation]]. The pH of a solution containing a weak base may require the solution of a [[cubic equation]]. The general case requires the solution of a set of [[non-linear]] [[simultaneous equation]]s.

A complicating factor is that water itself is a weak acid and a weak base (see [[amphoterism]]). It [[self-ionization of water|dissociates]] according to the equilibrium
:<chem>2H2O <=> H3O+ (aq) + OH^-(aq)</chem>
with a [[acid dissociation constant|dissociation constant]], {{mvar|K<sub>w</sub>}} defined as
:<math chem>K_w = \ce{[H+][OH^-]}</math>
where [H<sup>+</sup>] stands for the concentration of the aqueous [[hydronium ion]] and [OH<sup>−</sup>] represents the concentration of the [[hydroxide ion]]. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.

===Strong acids and bases===
[[Strong acid]]s and [[Strong base|bases]] are compounds that, for practical purposes, are completely dissociated in water. Under normal circumstances this means that the concentration of hydrogen ions in acidic solution can be taken to be equal to the concentration of the acid. The pH is then equal to minus the logarithm of the concentration value. [[Hydrochloric acid]] (HCl) is an example of a strong acid. The pH of a 0.01M solution of HCl is equal to −log<sub>10</sub>(0.01), that is, pH = 2. [[Sodium hydroxide]], NaOH, is an example of a strong base. The p[OH] value of a 0.01M solution of NaOH is equal to −log<sub>10</sub>(0.01), that is, p[OH] = 2. From the definition of p[OH] above, this means that the pH is equal to about 12. For solutions of sodium hydroxide at higher concentrations the self-ionization equilibrium must be taken into account.

Self-ionization must also be considered when concentrations are extremely low. Consider, for example, a solution of hydrochloric acid at a concentration of 5×10<sup>−8</sup>M.  The simple procedure given above would suggest that it has a pH of 7.3. This is clearly wrong as an acid solution should have a pH of less than 7. Treating the system as a mixture of hydrochloric acid and the [[amphoteric]] substance water, a pH of 6.89 results.<ref>{{cite web|last=Maloney|first=Chris|title=pH calculation of a very small concentration of a strong acid.|url=http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html|accessdate=13 March 2011|url-status=live|archiveurl=https://web.archive.org/web/20110708062942/http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html|archivedate=8 July 2011|df=dmy-all}}</ref>

===Weak acids and bases===

A weak acid  or the conjugate acid of a weak base can be treated using the same formalism.
:<math chem>\begin{cases}
\ce{Acid:} & \ce{HA <=> H+ + A^-}\\
\ce{Base:} & \ce{HA+ <=> H+ + A}
\end{cases}</math>
First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality
:<math chem>K_a = \frac \ce{[H] [A]}\ce{[HA]}</math>
and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H<sup>+</sup>] and [A<sup>−</sup>] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law of  [[mass conservation]] in terms of the two "reagents" H and A.
:<math chem>C_\ce{A} = \ce{[A]}  +  \ce{[HA]}</math>
:<math chem>C_\ce{H} = \ce{[H]}  +  \ce{[HA]}</math>
C stands for [[analytical concentration]]. In some texts, one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining K<sub>a</sub>, there are now three equations in three unknowns. When an acid is dissolved in water C<sub>A</sub> = C<sub>H</sub> = C<sub>a</sub>, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
:<math chem>[\ce H]^2 + K_a[\ce H] - K_a C_a = 0</math>
Solution of this [[quadratic equation]] gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an [[ICE table]] which can also be used to calculate the pH when some additional  (strong) acid or alkaline has been added to the system, that is, when C<sub>A</sub> ≠ C<sub>H</sub>.

For example, what is the pH of a 0.01M solution of [[benzoic acid]], pK<sub>a</sub> = 4.19?

* Step 1: <math>K_a = 10^{-4.19} = 6.46\times10^{-5}</math>
* Step 2: Set up the quadratic equation. <math chem>[\ce{H}]^2 + 6.46\times 10^{-5}[\ce{H}] - 6.46\times 10^{-7} = 0 </math>
* Step 3: Solve the quadratic equation. <math chem>[\ce{H+}] = 7.74\times 10^{-4};\quad \mathrm{pH} = 3.11</math>
For alkaline solutions an additional term is added to the mass-balance equation for hydrogen. Since addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to <math chem>\frac{K_w}\ce{[H+]}</math>
:<math chem>C_\ce{H} = \frac{[\ce H] + [\ce{HA}] -K_w}\ce{[H]}</math>
In this case the resulting equation in [H] is a cubic equation.

===General method===
Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations.<ref>{{cite book |last1=Billo |first1=E.J. |title= EXCEL for Chemists|edition= 3rd |year= 2011|publisher= Wiley-VCH|isbn= 978-0-470-38123-6}}</ref> With three or more reagents or when many complexes are formed with general formulae such as A<sub>p</sub>B<sub>q</sub>H<sub>r</sub>,the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.
:<math chem>[\ce{A}_p\ce{B}_q\ce{H}_r] =\beta_{pqr}[\ce A]^{p}[\ce B]^{q}[\ce H]^{r}</math>
Next, write down the mass-balance equations for each reagent:
:<math chem>\begin{align}
C_\ce{A} &= [\ce A] + \Sigma p \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^{r} \\
C_\ce{B} &= [\ce B] + \Sigma q \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^r \\
C_\ce{H} &= [\ce H] + \Sigma r \beta_{pqr}[\ce A]^p[\ce B]^q[\ce H]^r - K_w[\ce H]^{-1}
\end{align}</math>
Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.

There are 3 [[non-linear]] [[simultaneous equation]]s in the three unknowns, [A], [B] and [H]. Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this formalism, is a key element in the [[determination of equilibrium constants]] by potentiometric titration.

== See also ==
* [[Alkaline diet]]
* [[Arterial blood gas]]
* [[decibel|Bel]]
* [[Chemical equilibrium]]
* [[pCO2]]

==Notes==
{{notelist}}

==References==
{{reflist|30em}}

==External links==
{{Commons category|pH}}
*[http://www.science.uwaterloo.ca/~cchieh/cact/c123/ph.html The pH Scale]
*[http://www.chem1.com/acad/webtext/pdf/c1xacid2.pdf Chem1 Virtual Textbook, Acid-base Equilibria and Calculations]
*[http://chemistry.about.com/library/weekly/aa012803a.htm Red Cabbage pH Indicator]
*[http://www.engineeringtoolbox.com/food-ph-d_403.html Food and Foodstuff – pH Values]
*[http://www.aqion.onl Online pH Calculator for about 100 inorganic Acids, Bases, and Salts]

{{Wastewater}}{{Use dmy dates|date=March 2012}}

{{DEFAULTSORT:Ph}}
[[Category:Acid–base chemistry]]
[[Category:Equilibrium chemistry]]
[[Category:Units of measurement]]
[[Category:Water quality indicators]]
[[Category:Logarithmic scales of measurement]]
[[Category:General chemistry]]