# pH

pH

In chemistry, pH is a measure of the acidity or basicity of an aqueous solution.[1] 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 or alkaline. pH measurements are important in medicine, biology, chemistry, agriculture, forestry, food science, environmental science, oceanography, civil engineering and many other applications.

In a solution pH approximates but is not equal to p[H], the negative logarithm (base 10) of the molar concentration of dissolved hydronium ions (H3O+); 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 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+.[2] The pH scale has no upper or lower limit and can therefore be lower than 0 or higher than 14.[3] For an aqueous solution 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 (H3O+) or higher species (e.g., H9O4+) to account for solvation, 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;[4] 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. 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. As a result, pH can be affected by the ionic strength of a solution—for example, the pH of a 0.05 M potassium hydrogen phthalate solution can vary by as much as 0.5 pH units as a function of added potassium chloride, even though the added salt is neither acidic nor basic.[5]

Hydrogen ion activity coefficients 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.[6] 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 Søren Peder Lauritz Sørensen at the Carlsberg Laboratory in 1909[7][8] 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.[5] In the first papers, the notation had the "H" as a subscript to the lowercase "p", like so: pH.[9]

It is unknown what the exact definition of "p" in "pH" is. Some references suggest the "p" stands for "power",[10]others refer to the German Potenz (meaning "power"),[11] others refer to French 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".[10] 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";[12] "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).[13]

## Definitions

### Mathematical definition

pH is defined as a negative decimal logarithm of the hydrogen ion activity in a solution.[14]

$\mathrm{pH} = - \log_{10}(a_{\textrm{H}^+}) = \log_{10}\left(\frac{1}{a_{\textrm{H}^+}}\right)$

where aH+ is the activity of hydrogen ions 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, to hydrogen ion activity. pH is commonly measured by means of a glass electrode connected to a milli-voltmeter with very high input impedance, which measures the potential difference, or electromotive force, E, between an electrode sensitive to the hydrogen ion activity and a reference electrode, such as a calomel electrode or a silver chloride electrode. 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:

$E = E^0 + \frac{RT}{nF} \ln(a_{\textrm{H}^+}); \qquad \mathrm{pH} = \frac{E^0-E}{2.303 RT/F}$

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, T is the temperature in kelvins, 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 and an activity coefficient. To get proper results, the electrode must be calibrated using standard solutions of known activity.

The operational definition of pH is officially defined by International Standard ISO 31-8 as follows:[15] For a solution X, first measure the electromotive force EX of the galvanic 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

$\text{pH(X)} - \text{pH(S)} = \frac{E_\text{S} - E_\text{X} }{2.303RT/F}$

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 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.[16] 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,[17] 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.[18]

pH is an example of an acidity function. 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. Superacids are a class of non-aqueous acids for which the Hammett acidity function, H0, has been developed.

pH in its usual meaning is a measure of acidity of (dilute) aqueous solutions only.[1] Recently the concept of "Unified pH scale"[19] 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,[10] 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.[20] The calibration yieds a value for the standard electrode potential, E0, and a slope factor, f, so that the Nernst equation in the form

$E = E^0 + f\frac{RT}{nF} \ln[\mbox{H}^+]$

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 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[21] 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. 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 logarithms

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.

## Applications

Some typical pH values

Pure (neutral) water has a pH around 7 at 25 °C (77 °F); this value varies with temperature. When an acid is dissolved in water, the pH will be less than 7 (if at 25 °C (77 °F)). When a base, or alkali, 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, 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 electrodes) 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. A pH indicator is a substance that changes color around a particular pH value. It is a weak acid or weak base and the color change occurs around 1 pH unit either side of its acid dissociation constant, or pKa, value. For example, the naturally occurring indicator litmus 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 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 (first transition) Red 1.2 – 2.8 Yellow
Methyl red Red 4.4 – 6.2 Yellow
Bromothymol blue Yellow 6.0 – 7.6 Blue
Thymol blue (second transition) Yellow 8.0 – 9.6 Blue
Phenolphthalein 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 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 from the air, which is then slowly converted into carbonic acid, which dissociates to liberate hydrogen ions:

CO2 + H2 H2CO3  HCO3 + H+

## Examples

Substance pH
Vinegar[23] 2.0
Baking soda[23] 9.0

## Calculations of pH

### Strong acids and bases

Strong acids and bases are those that, for practical purposes, completely dissociate (ionize) in water. Hydrochloric 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[24]

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.[25] A method of solution is as follows. At equilibrium, any aqueous solution must satisfy the dissociation equilibrium equation for water,

[H + ][OH ] = Kw = 10 − 14

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, and can be written,

Ca = [HA] + [A ]

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:

Ca = [A ]

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,

[H + ] = [A ] + [OH ]

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,

$[H^+] = C_a + \frac{K_w}{[H^+]}$

Putting this into the form of a quadratic equation,

[H + ]2Ca[H + ] − Kw = 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.

$[H^+]^2 - 5 \times 10^{-8} [H^+] - 10^{-14} = 0$
$[H^+] = 1.28 \times 10^{-7}$
pH = 6.89

### 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:

$K_a = \frac{[H^+] [A^-]}{[HA]}$

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

Ca = [HA] + [A ]

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

[H + ] = [A ]

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+]:

[HA] = Ca − [A ] = Ca − [H + ]

And then plug these into the equilibrium equation for the acid

$K_a = \frac{[H^+]^2}{C_a - [H^+]}$

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

[H + ]2 + Ka[H + ] − KaCa = 0

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

The equilibrium equation for this reaction is

$6.5 \times 10^{-5} = \frac{[H^+] [A^-]}{[HA]}$

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

$6.5 \times 10^{-5} = \frac{[H^+]^2}{[HA]}$

The mass balance equation is

0.01M = [HA] + [A ] = [HA] + [H + ]

Solving for [HA] yields

[HA] = 0.01M − [H + ]

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

$6.5 \times 10^{-5} = \frac{[H^+]^2}{0.01 - [H^+]}$
$[H^+]^2 + 6.5 \times 10^{-5}[H^+] - 6.5 \times 10^{-5} \times 0.01 = 0$

$[H^+] = 7.74 \times 10^{-4}$
pH = − log[H + ] = 3.11

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

## pH in nature

Hydrangea macrophylla blossoms vary from pink to blue, according to a pH-dependent mobilization and uptake of soil aluminium into the plants.

pH-dependent plant pigments that can be used as pH indicators occur in many plants, including hibiscus, red cabbage (anthocyanin),[26] and red wine.

### Seawater

The pH of seawater plays an important role in the ocean's carbon cycle, and there is evidence of ongoing ocean acidification caused by carbon dioxide emissions.[27] However, pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist in chemical oceanography.[28]

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 NBS or NIST designation). These solutions have a relatively low ionic strength (~0.1) compared to that of seawater (~0.7), and, as a consequence, are not recommended for use in characterising 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.[29] 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, H+ + SO42− HSO4, such that the total scale includes the effect of both protons (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,[30] 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 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.[28] 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[31]
Compartment pH
Gastric acid 1
Lysosomes 4.5
Granules of chromaffin cells 5.5
Human skin 5.5
Urine 6.0
Neutral H2O at 37 °C 6.81
Cytosol 7.2
Cerebrospinal fluid (CSF) 7.3
Blood 7.34–7.45
Mitochondrial matrix 7.5
Pancreas secretions 8.1
General symptoms of acidosis,[32] [33] resulting from decrease in body pH.

The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis.

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

Enzymes and other proteins have an optimum pH range and can become inactivated or denatured outside this range.

The most common disorder in acid-base homeostasis is acidosis, which means an acid overload in the body, generally defined by pH falling below 7.35.[citation needed]

In the blood, pH can be estimated from known base excess (be) and bicarbonate concentration (HCO3-) by the following equation:[34]

$\mathrm{pH} = \frac{be - 0.93\mathrm{HCO_3} + 124}{13.77}$

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