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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, pH (), also referred to as ''acidity'', historically denotes "potential of hydrogen" (or "power of hydrogen"). It is a scale used to specify the acidity or basicity of an
aqueous solution An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be re ...
. Acidic solutions (solutions with higher concentrations of hydrogen ( ) ions) are measured to have lower pH values than basic or
alkaline In chemistry, an alkali (; from ar, القلوي, al-qaly, lit=ashes of the saltwort) is a base (chemistry), basic, ionic compound, ionic salt (chemistry), salt of an alkali metal or an alkaline earth metal. An alkali can also be defined as ...
solutions. The pH scale is
logarithmic Logarithmic can refer to: * Logarithm, a transcendental function in mathematics * Logarithmic scale, the use of the logarithmic function to describe measurements * Logarithmic spiral, * Logarithmic growth * Logarithmic distribution, a discrete pr ...
and inversely indicates the activity of hydrogen ions ( in the solution.Bates, Roger G. ''Determination of pH: theory and practice''. Wiley, 1973. : \ce = - \log(a_\ce) \thickapprox -\log( ce where +is the equilibrium molar concentration (mol/L) of H+ in the solution. At 25  °C (77
°F The Fahrenheit scale () is a temperature scale based on one proposed in 1724 by the physicist Daniel Gabriel Fahrenheit (1686–1736). It uses the degree Fahrenheit (symbol: °F) as the unit. Several accounts of how he originally defined his ...
), solutions with a pH less than 7 are acidic, and solutions with a pH greater than 7 are basic. Solutions with a pH of 7 at 25  °C are neutral (i.e. have the same concentration of H+ ions as OH ions, i.e. the same as pure water). The neutral value of the pH depends on the temperature and is lower than 7 if the temperature increases above 25 °C. The pH value can be less than 0 for very concentrated strong acids or greater than 14 for very concentrated strong bases. The pH scale is
traceable Traceability is the capability to trace something. In some cases, it is interpreted as the ability to verify the history, location, or application of an item by means of documented recorded identification. Other common definitions include the capab ...
to a set of standard solutions whose pH is established by international agreement. Primary pH standard values are determined using a concentration cell with transference by measuring the potential difference between a
hydrogen electrode The standard hydrogen electrode (abbreviated SHE), is a redox electrode which forms the basis of the Table of standard electrode potentials, thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be ...
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 indicator. Measurements of pH are important in
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
,
agronomy Agronomy is the science and technology of producing and using plants by agriculture for food, fuel, fiber, chemicals, recreation, or land conservation. Agronomy has come to include research of plant genetics, plant physiology, meteorology, and ...
, medicine, water treatment, and many other applications.


History

In 1909, the Danish chemist Søren Peter Lauritz Sørensen introduced the concept of pH at the Carlsberg Laboratory Two other publications appeared in 1909, one in French and one in Danish., originally using the notation "pH•", with H• as a subscript to the lowercase p. The concept was later revised in 1924 to the modern pH to accommodate definitions and measurements in terms of electrochemical cells.
For the sign ''p'', I propose the name 'hydrogen ion exponent' and the symbol pH•. Then, for the hydrogen ion exponent (pH•) of a solution, the negative value of the
Briggsian logarithm In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered i ...
of the related hydrogen ion normality factor is to be understood.
Sørensen did not explain why he used the letter p, and the exact meaning of the letter is still disputed. Sørensen described a way of measuring pH using ''potential'' differences, and it represents the negative ''power'' of 10 in the concentration of hydrogen ions. The letter ''p'' could stand for the French ''puissance,'' German ''Potenz,'' or Danish ''potens'', all meaning "power", or it could mean "potential". All of these words start with the letter ''p'' in
French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...
, German, and Danish, which where the languages Sørensen published in (Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish). He also used the letter ''q'' in much the same way elsewhere in the paper, and he might have arbitrarily labelled the test solution "p" and the reference solution "q"; these letters are often paired. Some literature sources suggest that "pH" stands for the Latin term ''pondus hydrogenii'' (quantity of hydrogen) or ''potentia hydrogenii'' (power of hydrogen), although this is not supported by Sørensen's writings. In modern
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, the p stands for "the negative decimal logarithm of", and is used in the term p''K''a for acid dissociation constants, so pH is "the negative decimal logarithm of H+ ion concentration", while pOH is "the negative decimal logarithm of OH- ion concentration". Bacteriologist
Alice Catherine Evans Alice Catherine Evans (January 29, 1881 – September 5, 1975) was an American microbiologist. She became a researcher at the U.S. Department of Agriculture. There she investigated bacteriology in milk and cheese. She later demonstrated that '' ...
, who influenced dairying and
food safety Food safety (or food hygiene) is used as a scientific method/discipline describing handling, preparation, and storage of food in ways that prevent food-borne illness. The occurrence of two or more cases of a similar illness resulting from t ...
, credited William Mansfield Clark and colleagues, including herself, 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. She said:
In these studies
f bacterial metabolism F, or f, is the sixth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ef'' (pronounced ), and the plural is ''efs''. Hist ...
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 the 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.
The first electronic method for measuring pH was invented by Arnold Orville Beckman, a professor at the California Institute of Technology in 1934. It was in response to a request from the local citrus grower Sunkist, which wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.


Definition


pH

The pH of a solution is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, ''a''H+. Mathematically, pH is expressed as: : \ce = - \log_(a_\ce) = \log_\left(\frac 1 \right) For example, for a solution with a hydrogen ion activity of 5×10−6 (i.e., the concentration of hydrogen ions in moles per litre), the pH of the solution can be calculated as follows: \ce = - \log_(5*10^-6) = 5.3 The concept of pH was developed because ion-selective electrodes, which are used to measure pH, respond to activity. The electrode potential, ''E'', follows the Nernst equation for the hydrogen ion, which can be expressed as: : E = E^0 + \frac \ln(a_\ce)=E^0 - \frac \ce where ''E'' is a measured potential, ''E''0 is the standard electrode potential, ''R'' is the gas constant, ''T'' is the temperature in kelvins, ''F'' is the Faraday constant. For , the number of electrons transferred is one. The electrode potential is proportional to pH when pH is defined in terms of activity. The precise measurement of pH is presented in International Standard
ISO 31-8 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 In the tables of quantities and their units, the ...
as follows: A galvanic cell is set up to measure the
electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...
(e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a silver chloride electrode or a calomel electrode, and the hydrogen-ion selective electrode is a standard hydrogen electrode. : Reference electrode , concentrated solution of KCl , , test solution , H2 , Pt Firstly, the cell is filled with a solution of known hydrogen ion activity and the electromotive force, ''E''S, is measured. Then the electromotive force, ''E''X, of the same cell containing the solution of unknown pH is measured. : \ce = \ce+\frac The difference between the two measured electromotive force values is proportional to pH. This method of calibration avoids the need to know the standard electrode potential. The proportionality constant, 1/''z'', is ideally equal to \frac\ , the "Nernstian slope". In practice, a glass electrode is used instead of the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against buffer solutions of known hydrogen ion () activity proposed by the International Union of Pure and Applied Chemistry ( IUPAC). Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To calibrate the electrode, it is first immersed in a standard solution, and the reading on a pH meter is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted using the "slope" control to be equal to the pH for that solution. Further details, are given in the IUPAC recommendations. 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 °C and a correction factor to be applied for other temperatures. The pH scale is logarithmic and therefore pH is a
dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
. The pH scale ranges from 0 to 14, with a pH of 7 indicating neutrality, values less than 7 indicating acidity, and values greater than 7 indicating basicity. The pH scale is based on the hydrogen ion concentration, with each pH value representing a tenfold difference in hydrogen ion concentration.


p

This was the original definition of Sørensen in 1909, which was superseded in favor of pH in 1924. is the concentration of hydrogen ions, denoted [] in modern chemistry. More correctly, the thermodynamic activity of in dilute solution should be replaced by []/c0, where the standard state concentration c0 = 1 mol/L. This ratio is a pure number whose logarithm can be defined. It is possible to measure the concentration of hydrogen ions directly using an electrode calibrated in terms of hydrogen ion concentrations. One common method is to titrate a solution of known concentration of a strong acid with a solution of known concentration of strong base in the presence of a relatively high concentration of background electrolyte. By knowing the concentrations of the acid and base, the concentration of hydrogen ions can be calculated and the measured potential can be correlated with concentrations. The calibration is usually carried out using a Gran plot. This procedure makes the activity of hydrogen ions equal to the numerical value of concentration. The glass electrode (and other
ion selective electrodes An ion-selective electrode (ISE), also known as a specific ion electrode (SIE), is a transducer (or sensor) that converts the activity of a specific ion dissolved in a solution into an electrical potential. The voltage is theoretically dependent o ...
) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition. The difference between p and pH is quite small, and it has been stated that pH = p + 0.04. However, 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, . pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by : ce= \frac where ''K''W is the self-ionization constant of water. Taking logarithms : \ce = \ceK_\ce - \ce So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity.


Measurement


pH Indicators

pH can be measured using indicators, which change color depending on the pH of the solution they are in. By comparing the color of a test solution to a standard color chart, the pH can be estimated to the nearest whole number. For more precise measurements, the color can be measured using a colorimeter or spectrophotometer. Universal indicator is a mixture of several indicators that can provide a continuous color change over a range of pH values, typically from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. An alternative method of measuring pH is using an electronic pH meter, which directly measures the voltage difference between a pH-sensitive electrode and a reference electrode.


Non-aqueous solutions

pH values can be measured in non-aqueous solutions, but they are based on a different scale from aqueous pH values, because the
standard states Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object t ...
used for calculating hydrogen ion concentrations ( activities) are different. The hydrogen ion activity, ''aH+'', is defined as: : a_\ce = \exp\left (\frac\right ) where ''μ''H+ is the chemical potential of the hydrogen ion, \mu^_\ce 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 because of differences in the solvated proton ions, such as lyonium ions, which require an intersolvent scale which involves the transfer activity coefficient of hydronium/lyonium ion. pH is an example of an
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 (or accept protons from) a solute ( Brønsted acidity). The pH scale is by far the most commonly used ac ...
, but there are others that can be defined. For example, the
Hammett acidity function The Hammett acidity function (''H''0) 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 fu ...
, ''H''0, has been developed in connection with superacids.


Unified absolute pH scale

In 2010, a new approach to measuring pH was proposed, called the "unified absolute pH scale". This approach allows for a common reference standard to be used across different solutions, regardless of their pH range. The unified absolute pH scale is based on the absolute chemical potential of the proton, as defined by the Lewis acid–base theory. This scale is applicable to liquids, gases, and even solids. The advantages of the unified absolute pH scale include consistency, accuracy, and applicability to a wide range of sample types. It is precise and versatile because it serves as a common reference standard for pH measurements. However, implementation efforts, compatibility with existing data, complexity, and potential costs are some challenges.


Extremes of pH measurements

The measurement of pH can become difficult at extremely acidic or alkaline conditions, such as below pH 2.5 (ca. 0.003  mol/dm3 acid) or above pH 10.5 (above ca. 0.0003 mol/dm3 alkaline). This is due to the breakdown of the Nernst equation in this conditions when using a glass electrode. There are several factors contribute to this problem. Firstly, liquid junction potentials may not be independent of pH. Secondly, the high
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 ...
of concentrated solutions can affect the electrode potentials. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as and in the solution. To overcome these problems, specially constructed electrodes are available. Runoff from mines or mine tailings can produce some extremely low pH values.


Applications

The pH scale ranges from 0 to 14, with 7 being neutral. Pure water has a pH of 7 at 25°C, meaning it is neutral. When an
acid In computer science, ACID ( atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity despite errors, power failures, and other mishaps. In the context of databases, a sequ ...
is dissolved in water, the pH will be less than 7, while a base, or
alkali In chemistry, an alkali (; from ar, القلوي, al-qaly, lit=ashes of the saltwort) is a basic, ionic salt of an alkali metal or an alkaline earth metal. An alkali can also be defined as a base that dissolves in water. A solution of a ...
, will have a pH greater than 7. A strong acid, such as hydrochloric acid, at concentration 1 mol dm−3 has a pH of 0, while a strong alkali like
sodium hydroxide Sodium hydroxide, also known as lye and caustic soda, is an inorganic compound with the formula NaOH. It is a white solid ionic compound consisting of sodium cations and hydroxide anions . Sodium hydroxide is a highly caustic base and alkali ...
, at the same concentration, has a pH of 14. Since pH is a logarithmic scale, a difference of one in pH is equivalent to a tenfold difference in hydrogen ion concentration. It's important to note that neutrality isn't exactly 7 at 25°C, although it's a good approximation in most cases. Neutrality occurs when the concentration of hydrogen ions ([]) equals the concentration of hydroxide ions ([]), or when their activities are equal. Since self-ionization of water holds the product of these concentration [] × [] = Kw, it can be seen that at neutrality [] = [] = , or pH = pKw/2. pKw 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 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 ...
, so Kw varies with ionic strength. When 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). :


pH in Soil


Classification of soil pH ranges

The United States Department of Agriculture
Natural Resources Conservation Service Natural Resources Conservation Service (NRCS), formerly known as the Soil Conservation Service (SCS), is an agency of the United States Department of Agriculture (USDA) that provides technical assistance to farmers and other private landowners an ...
, formerly Soil Conservation Service classifies
soil pH Soil pH is a measure of the acidity or basicity (alkalinity) of a soil. Soil pH is a key characteristic that can be used to make informative analysis both qualitative and quantitatively regarding soil characteristics. pH is defined as the neg ...
ranges as follows: In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map 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

Plants contain pH-dependent pigments that can be used as pH indicators, such as those found in hibiscus, red cabbage (
anthocyanin Anthocyanins (), also called anthocyans, are water-soluble vacuolar pigments that, depending on their pH, may appear red, purple, blue, or black. In 1835, the German pharmacist Ludwig Clamor Marquart gave the name Anthokyan to a chemical compo ...
), and grapes (
red wine Red wine is a type of wine made from dark-colored grape varieties. The color of the wine can range from intense violet, typical of young wines, through to brick red for mature wines and brown for older red wines. The juice from most purple grap ...
). Citrus fruits have acidic jiuice primarily due to the presence of citric acid, while other
carboxylic acids In organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is or , with R referring to the alkyl, alkenyl, aryl, or other group. Carboxylic ...
can be found in various living systems. For instance,
muscle Skeletal muscles (commonly referred to as muscles) are organs of the vertebrate muscular system and typically are attached by tendons to bones of a skeleton. The muscle cells of skeletal muscles are much longer than in the other types of muscl ...
activity results in the production of lactic acid. The protonation state of phosphate derivatives, including
ATP ATP may refer to: Companies and organizations * Association of Tennis Professionals, men's professional tennis governing body * American Technical Publishers, employee-owned publishing company * ', a Danish pension * Armenia Tree Project, non ...
, is pH-dependent. Hemoglobin, an oxygen-transport enzyme, is also affected by pH in a phenomenon known as the Root effect.


pH in Seawater

The pH of seawater is typically limited to a range between 7.4 and 8.5. It plays an important role in the ocean's carbon cycle, and there is evidence of ongoing ocean acidification caused by carbon dioxide emissions. However, pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist in chemical oceanography.Zeebe, R. E. and Wolf-Gladrow, D. (2001) ''CO2 in seawater: equilibrium, kinetics, isotopes'', Elsevier Science B.V., Amsterdam, Netherlands As part of its operational definition of the pH scale, the IUPAC defines a series of buffer solutions 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 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 ...
(≈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 electrode potential. To resolve this problem, an alternative series of buffers based on artificial seawater 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 ions. These ions experience protonation, + , such that the total scale includes the effect of both protons (free hydrogen ions) and hydrogen sulfate ions: : []T = []F + [] An alternative scale, the 'free scale', often denoted 'pHF', omits this consideration and focuses solely on []F, in principle making it a simpler representation of hydrogen ion concentration. Only []T can be determined, therefore []F must be estimated using the [] and the stability constant of , : : []F = []T − [] = []T ( 1 + [] / K )−1 However, it is difficult to estimate K 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 (). According to this source, is a possible pronunciation in British English. is an inorganic, monatomic anion of fluorine, with the chemical formula (also written ), whose salts are typically white or colorless. Fluoride salts typ ...
ions, + ⇌ HF. Resulting in the following expression for []SWS: : []SWS = []F + [] + [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 summarize the three scales of pH: : pHF = −log []F : pHT = −log([]F + []) = −log[]T : pHSWS = −log(]F + [] + [HF]) = −log[v]SWS In practical terms, the three seawater pH scales differ in their pH values up to 0.10, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean's carbonate system. 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

: In living organisms, the pH of various body fluids, cellular compartments, and organs is tightly regulated to maintain a state of acid-base balance known as acid–base homeostasis. Acidosis, defined by a pH below 7.35, is the most common disorder of acid–base homeostasis and occurs when there is an excess of acid in the body. In contrast, alkalosis is characterized by excessively high blood pH. Blood pH is usually slightly basic, with a pH of 7.365, referred to as physiological pH in biology and medicine. Plaque formation in teeth can create a local acidic environment that results in tooth decay through demineralization.
Enzymes Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrate (chemistry), substrates, and the enzyme converts the substrates into different molecule ...
and other
proteins Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
have an optimal pH range for function and can become inactivated or denatured outside this range.


pH Calculations

When calculating the pH of a solution containing acids and/or bases, a chemical speciation calculation is used to determine the concentration of all chemical species present in the solution. The complexity of the procedure depends on the nature of the solution. Strong acids and bases are compounds that are almost completely dissociated in water, which simplifies the calculation. However, for weak acids, a quadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set of
non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
simultaneous equations must be solved. Water itself is a weak acid and a weak base, so its dissociation must be takent into account at high pH and low solute concentration (see
amphoterism In chemistry, an amphoteric compound () is a molecule or ion that can react both as an acid and as a base. What exactly this can mean depends on which definitions of acids and bases are being used. One type of amphoteric species are amphiproti ...
). It dissociates according to the equilibrium : with a
dissociation constant In chemistry, biochemistry, and pharmacology, a dissociation constant (K_D) is a specific type of equilibrium constant that measures the propensity of a larger object to separate (dissociate) reversibly into smaller components, as when a complex fa ...
, ' defined as : K_w = \ce where +stands for the concentration of the aqueous hydronium ion and Hrepresents the concentration of the
hydroxide ion Hydroxide is a diatomic anion with chemical formula OH−. It consists of an oxygen and hydrogen atom held together by a single covalent bond, and carries a negative electric charge. It is an important but usually minor constituent of water. It ...
. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.


Strong acids and bases

Strong acids and bases are compounds that are essentially fully dissociated in water. This means that in an acidic solution, the concentration of hydrogen ions (H+) can be considered equal to the concentration of the acid. Similarly, in a basic solution, the concentration of hydroxide ions (OH-) can be considered equal to the concentration of the base. The pH of a solution is defined as the negative logarithm of the concentration of H+, and the pOH is defined as the negative logarithm of the concentration of OH-. For example, the pH of a 0.01M solution of hydrochloric acid (HCl) is equal to 2 (pH = −log10(0.01)), while the pOH of a 0.01M solution of sodium hydroxide (NaOH) is equal to 2 (pOH = −log10(0.01)), which corresponds to a pH of about 12. However, self-ionization of water must also be considered when concentrations of a strong acid or base is very low or high. For instance, a 5×10−8M solution of HCl would be expected to have a pH of 7.3 based on the above procedure, which is incorrect as it is acidic and should have a pH of less than 7. In such cases, the system can be treated as a mixture of the acid or base and water, which is an amphoteric substance. By accounting for the self-ionization of water, the true pH of the solution can be calculated. For example, a 5×10−8M solution of HCl would have a pH of 6.89 when treated as a mixture of HCl and water. The self-ionization equilibrium of solutions of sodium hydroxide at higher concentrations must also be considered.


Weak acids and bases

A weak acid or the conjugate acid of a weak base can be treated using the same formalism. * Acid HA: * Base A: First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality : K_a = \frac \ce\ce and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, A +and 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. : C_\ce = \ce + \ce : C_\ce = \ce + \ce 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 Ka, there are now three equations in three unknowns. When an acid is dissolved in water CA = CH = Ca, the concentration of the acid, so = After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained. : ce H2 + K_a ce H- K_a C_a = 0 Solution of this quadratic equation gives the hydrogen ion concentration and hence p or, more loosely, pH. This procedure is illustrated in an
ICE table An ICE table or RICE box or RICE chart 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 su ...
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 CA ≠ CH. For example, what is the pH of a 0.01M solution of benzoic acid, pKa = 4.19? * Step 1: K_a = 10^ = 6.46\times10^ * Step 2: Set up the quadratic equation. ce2 + 6.46\times 10^ ce- 6.46\times 10^ = 0 * Step 3: Solve the quadratic equation. ce= 7.74\times 10^;\quad \mathrm = 3.11 For alkaline solutions, an additional term is added to the mass-balance equation for hydrogen. Since the addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to \frac\ce, the resulting equation is: : C_\ce = \frac\ce


General method

Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations. With three or more reagents or when many complexes are formed with general formulae such as ApBqHr, 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. : ce_p\ce_q\ce_r=\beta_ ce A ce B ce H Next, write down the mass-balance equations for each reagent: : \begin C_\ce &= ce A+ \Sigma p \beta_ ce Ap ce Bq ce H \\ C_\ce &= ce B+ \Sigma q \beta_ ce Ap ce Bq ce Hr \\ C_\ce &= ce H+ \Sigma r \beta_ ce Ap ce Bq ce Hr - K_w ce H \end 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 three
non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
simultaneous equations in the three unknowns, and Because the equations are non-linear and their 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 approach, is a key element in the determination of equilibrium constants by potentiometric titration.


See also

* pH indicator * Arterial blood gas * Chemical equilibrium * p * p''K''a


References


External links

{{DEFAULTSORT:pH Acid–base chemistry Equilibrium chemistry Units of measurement Water quality indicators Logarithmic scales of measurement General chemistry