PH

PH

Overview
In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, pH is a measure of the acid
Acid
An acid is a substance which reacts with a base. Commonly, acids can be identified as tasting sour, reacting with metals such as calcium, and bases like sodium carbonate. Aqueous acids have a pH of less than 7, where an acid of lower pH is typically stronger, and turn blue litmus paper red...

ity or basicity
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...

 of an aqueous solution
Aqueous solution
An aqueous solution is a solution in which the solvent is water. It is usually shown in chemical equations by appending aq to the relevant formula, such as NaCl. The word aqueous means pertaining to, related to, similar to, or dissolved in water...

. Pure water is said to be neutral, with a pH close to 7.0 at 25 °C (77 °F). Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...

 or alkaline. pH measurements are important in medicine
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....

, biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, agriculture
Agriculture
Agriculture is the cultivation of animals, plants, fungi and other life forms for food, fiber, and other products used to sustain life. Agriculture was the key implement in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that nurtured the...

, forestry
Forestry
Forestry is the interdisciplinary profession embracing the science, art, and craft of creating, managing, using, and conserving forests and associated resources in a sustainable manner to meet desired goals, needs, and values for human benefit. Forestry is practiced in plantations and natural stands...

, food science
Food science
Food science is a study concerned with all technical aspects of foods, beginning with harvesting or slaughtering, and ending with its cooking and consumption, an ideology commonly referred to as "from field to fork"...

, environmental science
Environmental science
Environmental science is an interdisciplinary academic field that integrates physical and biological sciences, to the study of the environment, and the solution of environmental problems...

, oceanography
Oceanography
Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

, civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

 and many other applications.

In a solution pH approximates but is not equal to p[H], the negative logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 (base 10) of the molar concentration of dissolved hydronium ions ; a low pH indicates a high concentration of hydronium ions, while a high pH indicates a low concentration.
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Encyclopedia
In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, pH is a measure of the acid
Acid
An acid is a substance which reacts with a base. Commonly, acids can be identified as tasting sour, reacting with metals such as calcium, and bases like sodium carbonate. Aqueous acids have a pH of less than 7, where an acid of lower pH is typically stronger, and turn blue litmus paper red...

ity or basicity
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...

 of an aqueous solution
Aqueous solution
An aqueous solution is a solution in which the solvent is water. It is usually shown in chemical equations by appending aq to the relevant formula, such as NaCl. The word aqueous means pertaining to, related to, similar to, or dissolved in water...

. Pure water is said to be neutral, with a pH close to 7.0 at 25 °C (77 °F). Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are basic
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...

 or alkaline. pH measurements are important in medicine
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....

, biology
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, agriculture
Agriculture
Agriculture is the cultivation of animals, plants, fungi and other life forms for food, fiber, and other products used to sustain life. Agriculture was the key implement in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that nurtured the...

, forestry
Forestry
Forestry is the interdisciplinary profession embracing the science, art, and craft of creating, managing, using, and conserving forests and associated resources in a sustainable manner to meet desired goals, needs, and values for human benefit. Forestry is practiced in plantations and natural stands...

, food science
Food science
Food science is a study concerned with all technical aspects of foods, beginning with harvesting or slaughtering, and ending with its cooking and consumption, an ideology commonly referred to as "from field to fork"...

, environmental science
Environmental science
Environmental science is an interdisciplinary academic field that integrates physical and biological sciences, to the study of the environment, and the solution of environmental problems...

, oceanography
Oceanography
Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

, civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

 and many other applications.

In a solution pH approximates but is not equal to p[H], the negative logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 (base 10) of the molar concentration of dissolved hydronium ions ; a low pH indicates a high concentration of hydronium ions, while a high pH indicates a low concentration. This negative of the logarithm matches the number of places behind the decimal point, so, for example, 0.1 molar hydrochloric acid
Hydrochloric acid
Hydrochloric acid is a solution of hydrogen chloride in water, that is a highly corrosive, strong mineral acid with many industrial uses. It is found naturally in gastric acid....

 should be near pH 1 and 0.0001 molar HCl should be near pH 4 (the base 10 logarithms of 0.1 and 0.0001 being −1, and −4, respectively). Pure (de-ionized) water is neutral, and can be considered either a very weak acid or a very weak base, giving it a pH of 7 (at 25 °C (77 °F)), or 0.0000001 M H+. The pH scale has no upper or lower limit and can therefore be lower than 0 or higher than 14. For an aqueous solution
Aqueous solution
An aqueous solution is a solution in which the solvent is water. It is usually shown in chemical equations by appending aq to the relevant formula, such as NaCl. The word aqueous means pertaining to, related to, similar to, or dissolved in water...

 to have a higher pH, a base must be dissolved in it, which binds away many of these rare hydrogen ions. Hydrogen ions in water can be written simply as H+ or as hydronium
Hydronium
In chemistry, a hydronium ion is the cation , a type of oxonium ion produced by protonation of water. This cation is often used to represent the nature of the proton in aqueous solution, where the proton is highly solvated...

 (H3O+) or higher species (e.g., H9O4+) to account for solvation
Solvation
Solvation, also sometimes called dissolution, is the process of attraction and association of molecules of a solvent with molecules or ions of a solute...

, but all describe the same entity. Most of the Earth's freshwater bodies surface are slightly acidic due to the abundance and absorption of carbon dioxide; in fact, for millennia in the past, most fresh water bodies have had a slightly acidic pH.

However, pH is not precisely p[H], but takes into account an activity factor
Activity (chemistry)
In chemical thermodynamics, activity is a measure of the “effective concentration” of a species in a mixture, meaning that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution.By convention, activity...

. This represents the tendency of hydrogen ions to interact with other components of the solution, which affects among other things the electrical potential read using a pH meter
PH meter
A pH meter is an electronic instrument used for measuring the pH of a liquid...

. As a result, pH can be affected by the ionic strength
Ionic strength
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts...

 of a solution—for example, the pH of a 0.05 M potassium hydrogen phthalate
Potassium hydrogen phthalate
Potassium hydrogen phthalate, often called simply KHP, is an acidic salt compound. It forms white powder, colorless crystals, a colorless solution, and an ionic solid that is the monopotassium salt of phthalic acid...

 solution can vary by as much as 0.5 pH units as a function of added potassium chloride
Potassium chloride
The chemical compound potassium chloride is a metal halide salt composed of potassium and chlorine. In its pure state, it is odorless and has a white or colorless vitreous crystal appearance, with a crystal structure that cleaves easily in three directions. Potassium chloride crystals are...

, even though the added salt is neither acidic nor basic.

Hydrogen ion activity coefficient
Activity coefficient
An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture, the interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed...

s cannot be measured directly by any thermodynamically sound method, so they are based on theoretical calculations. Therefore, the pH scale is defined in practice as traceable to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined by the Harned cell, a hydrogen gas electrode, using the Bates–Guggenheim Convention.

History


The concept of p[H] was first introduced by Danish chemist
Chemist
A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...

 Søren Peder Lauritz Sørensen at the Carlsberg Laboratory
Carlsberg Laboratory
The Carlsberg Laboratory in Copenhagen, Denmark was created in 1875 by J. C. Jacobsen, the founder of the Carlsberg brewery, for the sake of advancing biochemical knowledge, especially relating to brewing. It featured a Department of Chemistry and a Department of Physiology...

 in 1909 and revised to the modern pH in 1924 after it became apparent that electromotive force in cells depends on activity rather than concentration of hydrogen ions. In the first papers, the notation had the "H" as a subscript to the lowercase "p", like so: pH.

It is unknown what the exact definition of "p" in "pH" is. Some references suggest the "p" stands for "power
Exponentiation
Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...

",others refer to the German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

 Potenz (meaning "power"), others refer to French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

 puissance (also meaning "power", based on the fact that the Carlsberg Laboratory was French-speaking); others refer to "potential".
According to the Carlsberg Foundation pH stands for "power of hydrogen". A common definition used in schools is "percentage". Jens Norby published a paper in 2000 arguing that "p" is a constant and stands for "negative logarithm"; "H" then stands for hydrogen. Other suggestions have surfaced over the years that the "p" stands for the Latin terms pondus hydrogenii or potentia hydrogenii.

It is also suggested that Sørensen used the letters "p" and "q" (commonly paired letters in mathematics) simply to label the test solution (p) and the reference solution (q).

Mathematical definition


pH is defined as a negative decimal logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 of the hydrogen ion
Hydrogen ion
Hydrogen ion is recommended by IUPAC as a general term for all ions of hydrogen and its isotopes.Depending on the charge of the ion, two different classes can be distinguished: positively charged ions and negatively charged ions....

 activity in a solution.


where aH+ is the activity
Activity (chemistry)
In chemical thermodynamics, activity is a measure of the “effective concentration” of a species in a mixture, meaning that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution.By convention, activity...

 of hydrogen ion
Hydrogen ion
Hydrogen ion is recommended by IUPAC as a general term for all ions of hydrogen and its isotopes.Depending on the charge of the ion, two different classes can be distinguished: positively charged ions and negatively charged ions....

s in units of mol/L (molar concentration). Activity has a sense of concentration, however activity is always less than the concentration and is defined as a concentration (mol/L) of an ion multiplied by activity coefficient. The activity coefficient for diluted solutions is a real number between 0 and 1 (for concentrated solutions may be greater than 1) and it depends on many parameters of a solution, such as nature of ion, ion force, temperature, etc. For a strong electrolyte, activity of an ion approaches its concentration in diluted solutions. Activity can be measured experimentally by means of an ion-selective electrode that responds, according to the Nernst equation
Nernst equation
In electrochemistry, the Nernst equation is an equation that can be used to determine the equilibrium reduction potential of a half-cell in an electrochemical cell. It can also be used to determine the total voltage for a full electrochemical cell...

, to hydrogen ion activity. pH is commonly measured by means of a glass electrode
Glass electrode
A glass electrode is a type of ion-selective electrode made of a doped glass membrane that is sensitive to a specific ion. It is an important part of the instrumentation for chemical analysis and physico-chemical studies. In modern practice, widely used membranous ion-selective electrodes are part...

 connected to a milli-voltmeter with very high input impedance, which measures the potential difference, or electromotive force
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...

, E, between an electrode sensitive to the hydrogen ion activity and a reference electrode, such as a calomel electrode
Saturated calomel electrode
The Saturated calomel electrode is a reference electrode based on the reaction between elemental mercury and mercury chloride. The aqueous phase in contact with the mercury and the mercury chloride is a saturated solution of potassium chloride in water...

 or a silver chloride electrode
Silver chloride electrode
A silver chloride electrode is a type of reference electrode, commonly used in electrochemical measurements. For example, it is usually the internal reference electrode in pH meters...

. Quite often, glass electrode is combined with the reference electrode and a temperature sensor in one body. The glass electrode can be described (to 95–99.9% accuracy) by the Nernst equation:


where E is a measured potential, E0 is the standard electrode potential, that is, the electrode potential for the standard state in which the activity is one. R is the gas constant
Gas constant
The gas constant is a physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. It is equivalent to the Boltzmann constant, but expressed in units of energy The gas constant (also known as the molar, universal,...

, T is the temperature in kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...

s, F is the Faraday constant, and n is the number of electrons transferred (ion charge), one in this instance. The electrode potential, E, is proportional to the logarithm of the hydrogen ion activity.

This definition, by itself, is wholly impractical, because the hydrogen ion activity is the product of the concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...

 and an activity coefficient
Activity coefficient
An activity coefficient is a factor used in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances. In an ideal mixture, the interactions between each pair of chemical species are the same and, as a result, properties of the mixtures can be expressed...

. To get proper results, the electrode must be calibrated using standard solutions of known activity.

The operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

 of pH is officially defined by International Standard ISO 31-8
ISO 31-8
ISO 31-8 is the part of international standard ISO 31 that defines names and symbols for quantities and units related to physical chemistry and molecular physics.-Quantities and units:-Notes:...

 as follows: For a solution X, first measure the electromotive force EX of the galvanic cell
Galvanic cell
A Galvanic cell, or Voltaic cell, named after Luigi Galvani, or Alessandro Volta respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell...

reference electrode|concentrated solution of KCl || solution X|H2|Pt

and then also measure the electromotive force ES of a galvanic cell that differs from the above one only by the replacement of the solution X of unknown pH, pH(X), by a solution S of a known standard pH, pH(S). The pH of X is then


The difference between the pH of solution X and the pH of the standard solution depends only on the difference between two measured potentials. Thus, pH is obtained from a potential measured with an electrode calibrated against one or more pH standards; a pH meter
PH meter
A pH meter is an electronic instrument used for measuring the pH of a liquid...

 setting is adjusted such that the meter reading for a solution of a standard is equal to the value pH(S). Values pH(S) for a range of standard solutions S, along with further details, are given in the IUPAC recommendations. The standard solutions are often described as standard buffer solution. In practice, it is better to use two or more standard buffers to allow for small deviations from Nernst-law ideality in real electrodes.
Note that, because the temperature occurs in the defining equations, the pH of a solution is temperature-dependent.

Measurement of extremely low pH values, such as some very acidic mine waters, requires special procedures. Calibration of the electrode in such cases can be done with standard solutions of concentrated sulfuric acid, whose pH values can be calculated with using Pitzer parameters to calculate activity coefficients.

pH is an example of an acidity function
Acidity function
An acidity function is a measure of the acidity of a medium or solvent system, usually expressed in terms of its ability to donate protons to a solute . The pH scale is by far the most commonly used acidity function, and is ideal for dilute aqueous solutions...

. Hydrogen ion concentrations can be measured in non-aqueous solvents, but this leads, in effect, to a different acidity function, because the standard state for a non-aqueous solvent is different from the standard state for water. Superacid
Superacid
According to the classical definition superacid is an acid with an acidity greater than that of 100% pure sulfuric acid, which has a Hammett acidity function of −12. According to the modern definition, superacid is a medium, in which the chemical potential of the proton is higher than in pure...

s are a class of non-aqueous acids for which the Hammett acidity function
Hammett acidity function
The Hammett acidity function is a measure of acidity that is used for very concentrated solutions of strong acids, including superacids. It was proposed by the physical organic chemist Louis Plack Hammett and is the best-known acidity function used to extend the measure of acidity beyond the...

, H0, has been developed.

pH in its usual meaning is a measure of acidity of (dilute) aqueous solutions only. Recently the concept of "Unified pH scale" has been developed on the basis of the absolute chemical potential of the proton. This concept proposes the "Unified pH" as a measure of acidity that is applicable to any medium: liquids, gases and even solids.

p[H]


This was the original definition of Sørensen, which was superseded in favour of pH in 1924. 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 titrate a solution of known concentration of a strong acid with a solution of known concentration of strong alkali in the presence of a relatively high concentration of background electrolyte. Since the concentrations of acid and alkali 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. The calibration yieds a value for the standard electrode potential, E0, and a slope factor, f, so that the Nernst equation in the form
can be used to derive hydrogen ion concentrations from experimental measurements of E. The slope factor 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
Standard state
In chemistry, the standard state of a material is a reference point used to calculate its properties under different conditions. In principle, the choice of standard state is arbitrary, although the International Union of Pure and Applied Chemistry recommends a conventional set of standard states...

 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 difference between p[H] and pH is quite small. It has been stated that pH = p[H] + 0.04. It is common practice to use the term "pH" for both types of measurement.

pOH


pOH is sometimes used as a measure of the concentration of hydroxide ions, OH, or alkalinity
Alkalinity
Alkalinity or AT measures the ability of a solution to neutralize acids to the equivalence point of carbonate or bicarbonate. The alkalinity is equal to the stoichiometric sum of the bases in solution...

. pOH is not measured independently, but is derived from pH. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
[OH] = KW /[H+]


where KW is the self-ionisation constant of water. Taking logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

s
pOH = pKW − pH.


So, at room temperature pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity
Alkali soils
Alkali, or alkaline, soils are clay soils with high pH , a poor soil structure and a low infiltration capacity. Often they have a hard calcareous layer at 0.5 to 1 metre depth. Alkali soils owe their unfavorable physico-chemical properties mainly to the dominating presence of sodium carbonate...

.

Applications


Pure (neutral) water has a pH around 7 at 25 °C (77 °F); this value varies with temperature. When an acid
Acid
An acid is a substance which reacts with a base. Commonly, acids can be identified as tasting sour, reacting with metals such as calcium, and bases like sodium carbonate. Aqueous acids have a pH of less than 7, where an acid of lower pH is typically stronger, and turn blue litmus paper red...

 is dissolved in water, the pH will be less than 7 (if at 25 °C (77 °F)). When a base
Base (chemistry)
For the term in genetics, see base A base in chemistry is a substance that can accept hydrogen ions or more generally, donate electron pairs. A soluble base is referred to as an alkali if it contains and releases hydroxide ions quantitatively...

, or alkali
Alkali
In chemistry, an alkali is a basic, ionic salt of an alkali metal or alkaline earth metal element. Some authors also define an alkali as a base that dissolves in water. A solution of a soluble base has a pH greater than 7. The adjective alkaline is commonly used in English as a synonym for base,...

, is dissolved in water, the pH will be greater than 7 (if at 25 °C (77 °F)). A solution of a strong acid, such as hydrochloric acid
Hydrochloric acid
Hydrochloric acid is a solution of hydrogen chloride in water, that is a highly corrosive, strong mineral acid with many industrial uses. It is found naturally in gastric acid....

, at concentration 1 mol/L has a pH of 0. A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol/L, has a pH of 14. Thus, measured pH values will lie mostly in the range 0 to 14. Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration.

Because the glass electrode (and other ion selective electrode
Ion selective electrode
An ion-selective electrode , also known as a specific ion electrode , is a transducer that converts the activity of a specific ion dissolved in a solution into an electrical potential, which can be measured by a voltmeter or pH meter. The voltage is theoretically dependent on the logarithm of the...

s) responds to activity, the electrode 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.

An approximate measure of pH may be obtained by using a pH indicator
PH indicator
A pH indicator is a halochromic chemical compound that is added in small amounts to a solution so that the pH of the solution can be determined visually. Hence a pH indicator is a chemical detector for hydronium ions or hydrogen ions in the Arrhenius model. Normally, the indicator causes the...

. A pH indicator is a substance that changes color around a particular pH value. It is a weak acid
Weak acid
A weak acid is an acid that dissociates incompletely. It does not release all of its hydrogens in a solution, donating only a partial amount of its protons to the solution...

 or weak base
Weak base
In chemistry, a weak base is a chemical base that does not ionize fully in an aqueous solution. As Brønsted–Lowry bases are proton acceptors, a weak base may also be defined as a chemical base in which protonation is incomplete. This results in a relatively low pH compared to strong bases...

 and the color change occurs around 1 pH unit either side of its acid dissociation constant
Acid dissociation constant
An acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid-base reactions...

, or pKa, value. For example, the naturally occurring indicator litmus
Litmus test (chemistry)
Litmus is a water-soluble mixture of different dyes extracted from lichens, especially Roccella tinctoria. It is often absorbed onto filter paper to produce one of the oldest forms of pH indicator, used to test materials for acidity. Blue litmus paper turns red under acidic conditions and red...

 is red in acidic solutions (pH<7 at 25 °C (77 °F)) and blue in alkaline (pH>7 at 25 °C (77 °F)) solutions. Universal indicator
Universal indicator
A Universal indicator is a pH indicator composed of a blend of several compounds that exhibits several smooth colour changes over a pH value range from 1-14 to indicate the acidity or basicity of solutions. Although there are a number of commercially available universal pH indicators, most are a...

 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 simple paper that has been impregnated with universal indicator.
Universal indicator components
Indicator Low pH color Transition pH range High pH color
Thymol blue
Thymol blue
Thymol blue is a brownish-green or reddish-brown crystalline powder that is used as a pH indicator. It is insoluble in water but soluble in alcohol and dilute alkali solutions. It transitions from red to yellow at pH 1.2–2.8 and from yellow to blue at pH 8.0–9.6.-Bibliography:* Merck. "Thymol...

 (first transition)
Red 1.2 – 2.8 Yellow
Methyl red
Methyl red
Methyl red, also called C.I. Acid Red 2, is an indicator dye that turns red in acidic solutions. It is an azo dye, and is a dark red crystalline powder....

Red 4.4 – 6.2 Yellow
Bromothymol blue
Bromothymol blue
Bromothymol blue is a chemical indicator for weak acids and bases. The chemical is also used for observing photosynthetic activities or respiratory indicators .Bromothymol blue acts as a weak acid in solution...

Yellow 6.0 – 7.6 Blue
Thymol blue (second transition) Yellow 8.0 – 9.6 Blue
Phenolphthalein
Phenolphthalein
Phenolphthalein is a chemical compound with the formula C20H14O4 and is often written as "HIn" or "phph" in shorthand notation. Often used in titrations, it turns colorless in acidic solutions and pink in basic solutions...

Colorless   8.3 – 10.0 Fuchsia


A solution whose pH is 7 (at 25 °C (77 °F)) is said to be neutral, that is, it is neither acidic nor basic. Water is subject to a self-ionization
Self-ionization of water
The self-ionization of water is the chemical reaction in which a proton is transferred from one water molecule to another, in pure water or an aqueous solution, to create the two ions, hydronium, H3O+ and hydroxide, OH−...

 process.
H2O H+ + OH

The dissociation constant, KW, has a value of about 10−14, so, in neutral solution of a salt, both the hydrogen ion concentration and hydroxide ion concentration are about 10−7 mol dm−3.
The pH of pure water decreases with increasing temperatures. For example, the pH of pure water at 50 °C is 6.55. Note, however, that water that has been exposed to air is mildly acidic. This is because water absorbs carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...

 from the air, which is then slowly converted into carbonic acid
Carbonic acid
Carbonic acid is the inorganic compound with the formula H2CO3 . It is also a name sometimes given to solutions of carbon dioxide in water, because such solutions contain small amounts of H2CO3. Carbonic acid forms two kinds of salts, the carbonates and the bicarbonates...

, which dissociates to liberate hydrogen ions:
CO2 + H2O  H2CO3  HCO3 + H+

Examples

Substance pH
Lead-battery acid 
Vinegar
Vinegar
Vinegar is a liquid substance consisting mainly of acetic acid and water, the acetic acid being produced through the fermentation of ethanol by acetic acid bacteria. Commercial vinegar is produced either by fast or slow fermentation processes. Slow methods generally are used with traditional...

 
2.0
Baking soda
Sodium bicarbonate
Sodium bicarbonate or sodium hydrogen carbonate is the chemical compound with the formula Na HCO3. Sodium bicarbonate is a white solid that is crystalline but often appears as a fine powder. It has a slightly salty, alkaline taste resembling that of washing soda . The natural mineral form is...

 

Strong acids and bases


Strong acid
Strong acid
A strong acid is an acid that ionizes completely in an aqueous solution by losing one proton, according to the equationFor sulfuric acid which is diprotic, the "strong acid" designation refers only to dissociation of the first protonMore precisely, the acid must be stronger in aqueous solution than...

s and bases are those that, for practical purposes, completely dissociate (ionize) in water. Hydrochloric acid
Hydrochloric acid
Hydrochloric acid is a solution of hydrogen chloride in water, that is a highly corrosive, strong mineral acid with many industrial uses. It is found naturally in gastric acid....

 (HCl) is a good example of a strong acid.

A commonly encountered problem is to calculate the pH of a solution of a given concentration of a strong acid. Normally, the concentration of the acid will be very high compared to the baseline concentration of H+ ions in pure water, which is 10−7 molar. Under these conditions, the H+ ion concentration is very nearly that of the acid concentration, and the pH is calculated simply by taking the negative logarithm of that value

For example, for a 0.01M solution of HCl, the H+ concentration can be taken as 0.01M, and the pH is −log10(0.01). That is, pH = 2.

For very weak concentrations, i.e. concentrations around 10−6M or less, the baseline concentration of H+ ions in pure water becomes significant, and must be taken into account. A method of solution is as follows. At equilibrium, any aqueous solution must satisfy the dissociation equilibrium equation for water,


Another constraint is that the nominal concentration of the acid must be preserved. The nominal concentration is designated Ca, and is equivalent to the amount of acid that is initially added to the reaction. This is known as the mass balance equation
Mass balance
A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...

, and can be written,


Where "HA" refers to the protonated form of the acid, and "A" to the conjugate base anion.

Note that for a given reaction, Ca is constant. This equation is merely saying that the molecules of acid can either be protonated or ionized, but that the total number will stay the same.

For a strong acid which is completely dissociated, [A] >> [HA], and the [HA] term can be dropped:


Another relationship that must be satisfied is known as the electroneutrality principle, or the charge balance equation, and is the statement that the total charge of the solution must be zero. So the sum of all the negative ion charges must equal the sum of the positive ion charges. This can be written,


For a strong acid, one can use Ca in place of [A], and eliminate [OH] from this equation by substituting the value derived from the equilibrium equation for water, [OH] = Kw / [H+]. Thus,


Putting this into the form of a quadratic equation
Quadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...

,


Which is readily solved for [H+].

For example, to find the pH of a solution of 5×10−8M of HCl, first note that this concentration is small compared to the baseline concentration of [H+] in water (10−7). So the quadratic equation derived above should be used.



Weak acids and bases


The problem in this case would be to determine the pH of a solution of a specific concentration of an acid, when that acid's pKa or Ka (acid dissociation constant) is given.

In this case, the acid is not completely dissociated, but the degree of dissociation is given by the equilibrium equation for that acid:


The mass balance and charge balance equations can be applied here as well, but in the case of a weak acid, the acid is not completely dissociated, and thus the assumption [A] >> [HA] is not valid. Therefore the mass balance equation is


Unless the acid is very weak, or the concentration is very dilute, it is reasonable to assume that the concentration of [H+] is much greater than the concentration of [OH]. This assumption simplifies the calculation and can be verified after the result is found. Note that this is equivalent to the assumption that the pH value is lower than about 6. With this assumption, the charge balance equation is


There are three equations with three unknowns ([H+], [A], and [HA]), which need to be solved for [H+]. The mass balance equation allows to solve for [HA] in terms of [H+]:


And then plug these into the equilibrium equation for the acid


Rearrange this to put it in the form of a quadratic equation,


The ICE table
ICE table
An ICE table, ICE chart, or ICE box is a tabular system of keeping track of changing concentrations in an equilibrium reaction. ICE stands for "Initial, Change, Equilibrium". It is used in chemistry to keep track of the changes in amount of substance of the reactants and also organize a set of...

—a mnemonic device for implementing the mass balance and charge balance equations for a given reaction, by accounting for the movements of the acid molecules and the charges—can be used to evaluate of the differences in concentrations before and after the reaction. The equation derived by using the ICE table is the same as the quadratic equation given above.

For example, consider a problem of finding the pH of a 0.01M solution of benzoic acid
Benzoic acid
Benzoic acid , C7H6O2 , is a colorless crystalline solid and the simplest aromatic carboxylic acid. The name derived from gum benzoin, which was for a long time the only source for benzoic acid. Its salts are used as a food preservative and benzoic acid is an important precursor for the synthesis...

, given that, for this acid, Ka = 6.5×10−5 (pKa = 4.19).

The equilibrium equation for this reaction is


One can neglect the [OH] concentration, hoping that the final answer will be pH < 6. Then [H+] = [A], and the equilibrium equation becomes


The mass balance equation is


Solving for [HA] yields


and plugging that into the equilbrium equation, results in the quadratic equation



Which gives the answer



Thus the assumption that pH < 6 was valid, and the [OH] concentration might well be ignored.

pH in nature


pH-dependent plant pigments that can be used as pH indicator
PH indicator
A pH indicator is a halochromic chemical compound that is added in small amounts to a solution so that the pH of the solution can be determined visually. Hence a pH indicator is a chemical detector for hydronium ions or hydrogen ions in the Arrhenius model. Normally, the indicator causes the...

s occur in many plants, including hibiscus
Hibiscus
Hibiscus is a genus of flowering plants in the mallow family, Malvaceae. It is quite large, containing several hundred species that are native to warm-temperate, subtropical and tropical regions throughout the world...

, red cabbage
Red Cabbage
The red cabbage is a sort of cabbage, also known as Red Kraut or Blue Kraut after preparation....

 (anthocyanin
Anthocyanin
Anthocyanins are water-soluble vacuolar pigments that may appear red, purple, or blue according to pH...

), and red wine.

Seawater


The pH of seawater
Seawater
Seawater is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% . This means that every kilogram of seawater has approximately of dissolved salts . The average density of seawater at the ocean surface is 1.025 g/ml...

 plays an important role in the ocean's carbon cycle, and there is evidence of ongoing ocean acidification
Ocean acidification
Ocean acidification is the name given to the ongoing decrease in the pH and increase in acidity of the Earth's oceans, caused by the uptake of anthropogenic carbon dioxide from the atmosphere....

 caused by carbon dioxide emissions. However, pH measurement is complicated by the chemical properties
Chemical property
A chemical property is any of a material's properties that becomes evident during a chemical reaction; that is, any quality that can be established only by changing a substance's chemical identity...

 of seawater
Seawater
Seawater is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% . This means that every kilogram of seawater has approximately of dissolved salts . The average density of seawater at the ocean surface is 1.025 g/ml...

, and several distinct pH scales exist in chemical oceanography
Chemical oceanography
Chemical oceanography is the study of ocean chemistry: the behavior of the chemical elements within the Earth's oceans. The ocean is unique in that it contains - in greater or lesser quantities - nearly every element in the periodic table....

.

As part of its operational definition
Operational definition
An operational definition defines something in terms of the specific process or set of validation tests used to determine its presence and quantity. That is, one defines something in terms of the operations that count as measuring it. The term was coined by Percy Williams Bridgman and is a part of...

 of the pH scale, the IUPAC defines a series of buffer solution
Buffer solution
A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a...

s across a range of pH values (often denoted with NBS or NIST
National Institute of Standards and Technology
The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

 designation). These solutions have a relatively low ionic strength
Ionic strength
The ionic strength of a solution is a measure of the concentration of ions in that solution. Ionic compounds, when dissolved in water, dissociate into ions. The total electrolyte concentration in solution will affect important properties such as the dissociation or the solubility of different salts...

 (~0.1) compared to that of seawater (~0.7), and, as a consequence, are not recommended for use in characterising the pH of seawater, since the ionic strength differences cause changes in electrode potential
Standard electrode potential
In electrochemistry, the standard electrode potential, abbreviated E° or E , is the measure of individual potential of a reversible electrode at standard state, which is with solutes at an effective concentration of 1 mol dm−3, and gases at a pressure of 1 atm...

. To resolve this problem, an alternative series of buffers based on artificial seawater
Artificial seawater
Artificial seawater is a mixture of dissolved mineral salts that simulates seawater. Artificial seawater is primarily used in marine biology and marine aquaria, and allows the easy preparation of media appropriate for marine organisms...

 was developed. 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 pHT.

The total scale was defined using a medium containing sulfate
Sulfate
In inorganic chemistry, a sulfate is a salt of sulfuric acid.-Chemical properties:...

 ions. These ions experience protonation
Protonation
In chemistry, protonation is the addition of a proton to an atom, molecule, or ion. Some classic examples include*the protonation of water by sulfuric acid:*the protonation of isobutene in the formation of a carbocation:2C=CH2 + HBF4 → 3C+ + BF4−*the protonation of ammonia in the...

, H+ + SO42− HSO4, such that the total scale includes the effect of both proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

s (free hydrogen ions) and hydrogen sulfate ions:
[H+]T = [H+]F + [HSO4]


An alternative scale, the free scale, often denoted pHF, omits this consideration and focuses solely on [H+]F, in principle making it a simpler representation of hydrogen ion concentration. Only [H+]T can be determined, therefore [H+]F must be estimated using the [SO42−] and the stability constant of HSO4, KS*:
[H+]F = [H+]T − [HSO4] = [H+]T ( 1 + [SO42−] / KS* )−1


However, it is difficult to estimate KS* in seawater, limiting the utility of the otherwise more straightforward free scale.

Another scale, known as the seawater scale, often denoted pHSWS, takes account of a further protonation relationship between hydrogen ions and fluoride
Fluoride
Fluoride is the anion F−, the reduced form of fluorine when as an ion and when bonded to another element. Both organofluorine compounds and inorganic fluorine containing compounds are called fluorides. Fluoride, like other halides, is a monovalent ion . Its compounds often have properties that are...

 ions, H+ + F HF. Resulting in the following expression for [H+]SWS:
[H+]SWS = [H+]F + [HSO4] + [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:
pHF = − log [H+]F
pHT = − log ( [H+]F + [HSO4] ) = − log [H+]T
pHSWS = − log ( [H+]F + [HSO4] + [HF] ) = − log [H+]SWS


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 carbonate system
Total inorganic carbon
The total inorganic carbon or dissolved inorganic carbon is the sum of inorganic carbon species in a solution. The inorganic carbon species include carbon dioxide, carbonic acid, bicarbonate anion, and carbonate. It is customary to express carbon dioxide and carbonic acid simultaneously as CO2*...

. 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

pH in living systems
Compartment pH
Gastric acid
Gastric acid
Gastric acid is a digestive fluid, formed in the stomach. It has a pH of 1 to 2 and is composed of hydrochloric acid , and large quantities of potassium chloride and sodium chloride...

 
1
Lysosomes  4.5
Granules of chromaffin cell
Chromaffin cell
Chromaffin cells are neuroendocrine cells found in the medulla of the adrenal gland and in other ganglia of the sympathetic nervous system. They are modified post-synaptic sympathetic neurons that receive sympathetic input...

s
5.5
Human skin
Human skin
The human skin is the outer covering of the body. In humans, it is the largest organ of the integumentary system. The skin has multiple layers of ectodermal tissue and guards the underlying muscles, bones, ligaments and internal organs. Human skin is similar to that of most other mammals,...

 
5.5
Urine
Urine
Urine is a typically sterile liquid by-product of the body that is secreted by the kidneys through a process called urination and excreted through the urethra. Cellular metabolism generates numerous by-products, many rich in nitrogen, that require elimination from the bloodstream...

 
6.0
Neutral H2O at 37 °C 6.81
Cytosol
Cytosol
The cytosol or intracellular fluid is the liquid found inside cells, that is separated into compartments by membranes. For example, the mitochondrial matrix separates the mitochondrion into compartments....

 
7.2
Cerebrospinal fluid
Cerebrospinal fluid
Cerebrospinal fluid , Liquor cerebrospinalis, is a clear, colorless, bodily fluid, that occupies the subarachnoid space and the ventricular system around and inside the brain and spinal cord...

 (CSF)
7.3
Blood
Blood
Blood is a specialized bodily fluid in animals that delivers necessary substances such as nutrients and oxygen to the cells and transports metabolic waste products away from those same cells....

 
7.34–7.45
Mitochondrial matrix
Mitochondrial matrix
In the mitochondrion, the matrix contains soluble enzymes that catalyze the oxidation of pyruvate and other small organic molecules.The mitochondrial matrix also contains the mitochondria's DNA and ribosomes. The word "matrix" stems from the fact that this space is viscous, compared to the...

 
7.5
Pancreas
Pancreas
The pancreas is a gland organ in the digestive and endocrine system of vertebrates. It is both an endocrine gland producing several important hormones, including insulin, glucagon, and somatostatin, as well as a digestive organ, secreting pancreatic juice containing digestive enzymes that assist...

 secretions
8.1


The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis
Acid-base homeostasis
Acid–base homeostasis is the part of human homeostasis concerning the proper balance between acids and bases, in other words, the pH. The body is very sensitive to its pH level, so strong mechanisms exist to maintain it...

.

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.

Plaque
Dental plaque
Dental plaque is a biofilm, usually a pale yellow, that develops naturally on the teeth. Like any biofilm, dental plaque is formed by colonizing bacteria trying to attach themselves to a smooth surface...

 can create a local acidic environment that can result in tooth decay by demineralisation.

Enzyme
Enzyme
Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

s and other protein
Protein
Proteins are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function. A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of...

s have an optimum pH range and can become inactivated or denatured
Denaturation (biochemistry)
Denaturation is a process in which proteins or nucleic acids lose their tertiary structure and secondary structure by application of some external stress or compound, such as a strong acid or base, a concentrated inorganic salt, an organic solvent , or heat...

 outside this range.

The most common disorder in acid-base homeostasis is acidosis
Acidosis
Acidosis is an increased acidity in the blood and other body tissue . If not further qualified, it usually refers to acidity of the blood plasma....

, which means an acid overload in the body, generally defined by pH falling below 7.35.

In the blood, pH can be estimated from known base excess
Base excess
In human physiology, base excess and base deficit refer to an excess or deficit, respectively, in the amount of base present in the blood. The value is usually reported as a concentration in units of mEq/L, with positive numbers indicating an excess of base and negative a deficit...

 (be) and bicarbonate
Bicarbonate
In inorganic chemistry, bicarbonate is an intermediate form in the deprotonation of carbonic acid...

concentration (HCO3-) by the following equation:


Extremes of pH


pH is normally measured in a range of 0–14. However, due to the way pH is calculated, it's possible to have negative pH and pH above 14. However, it should be noted that reported values outside the range 0–14 are somewhat controversial as measuring pH beyond this range becomes difficult.

Runoff from mines or mine tailings can produce some of the most acidic pHs ever reported; with negative pHs measured and reported in the literature as low as pH −3.6.

External links