pH

For other uses, see PH (disambiguation).

pH is a measure of the acidity or basicity of a solution. It is defined as the cologarithm of the activity of dissolved hydrogen ions (H⁺). Hydrogen ion activity coefficients cannot be measured experimentally, so they are based on theoretical calculations. The pH scale is not an absolute scale; it is relative to a set of standard solutions whose pH is established by international agreement.

The concept of pH was first introduced by Danish chemist Søren Peder Lauritz Sørensen at the Carlsberg Laboratory in 1909. It is unknown what the exact definition of p is. Some references suggest the p stands for “Power”, others refer to the German word “Potenz” (meaning power in German), still others refer to “potential”. Jens Norby published a paper in 2000 arguing that p is a constant and stands for “negative logarithm”; which has also been used in other works. H stands for Hydrogen. Sørensen suggested the notation "PH" for convenience, standing for "power of hydrogen", using the cologarithm of the concentration of hydrogen ions in solution, p[H] Although this definition has been superseded p[H] can be measured if an electrode is calibrated with solution of known hydrogen ion concentration.

Pure water is said to be neutral. The pH for pure water at 25 °C (77 °F) is close to 7.0. Solutions with a pH less than 7 are said to be acidic and solutions with a pH greater than 7 are said to be basic or alkaline. pH measurements are important in medicine, biology, chemistry, food science, environmental science, oceanography and many other applications.

Definitions

pH

pH is defined as minus the decimal logarithm of the hydrogen ion activity in an aqueous solution. By virtue of its logarithmic nature, pH is a dimensionless quantity.

$\mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})=\log _{10}({\frac {1}{a_{{\textrm {H}}^{+}}}})$

where a_H is the (dimensionless) activity of hydrogen ions. The reason for this definition is that a_H is a property of a single ion, which can only be measured experimentally by means of an ion-selective electrode which responds, according to the Nernst equation, to hydrogen ion activity. pH is commonly measured by means of a combined glass electrode, 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. The combined glass electrode ideally follows the Nernst equation:

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

where E is a measured potential , E⁰ is the standard electrode potential, that is, the electode potential for the standard state in which the activity is one. R is the gas constant, T is the temperature in Kelvin, F is the Faraday constant and n is the number of electrons transferred, 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. The single-ion activity coefficient of the hydrogen ion is a quantity which cannot be measured experimentally. To get around this difficulty, the electrode is calibrated in terms of solutions of known activity.

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

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

and then also measure the electromotive force E_S 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. 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. 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.

p[H]

This was the original definition of Sørensen, which was superseded in favour of pH. 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

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

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 that pH = p[H] + 0.04. Unfortunately 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⁻] = K_W /[H⁺]

where K_W is the self-ionisation constant of water. Taking cologarithms

pOH = pK_W − 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 water has a pH around 7; the exact values depends on the temperature. When an acid is dissolved in water the pH will be less than 7 and when a base, or alkali is dissolved in water the pH will be greater than 7. A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm⁻³ has a pH of 0. A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm⁻³ has a pH of 14. Thus, measured pH values will mostly lie in the range 0 to 14. Since pH is a logarithmic scale a difference of one pH unit is equivalent to a ten-fold 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 colour around a particular pH value. It is a weak acid or weak base and the colour change occurs around 1 pH unit either side of its acid dissociation constant, or pK_a, value. For example, the naturally occurring indicator litmus is red in acidic solutions (pH<7) and blue in alkaline (pH>7) solutions. Universal indicator consists of a mixture of indicators such that there is a continuous colour 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	orange
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	purple

A solution whose pH is 7 is said to be neutral, that is, it is neither acidic nor basic. Water is subject to a self-ionisation process.

H₂O ⇌ H⁺ + OH⁻

The dissociation constant, K_W, 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 + H₂O ⇌ H₂CO₃ ⇌ HCO₃⁻ + H⁺

Calculation of pH for weak and strong acids

In the case of a strong acid, there is complete dissociation, so the pH is simply equal to minus the logarithm of the acid concentration. For example, a 0.01 molar solution of hydrochloric acid has a pH of −log(0.01), that is, pH = 2.

The pH of a solution of a weak acid may be calculated by means of an ICE table. For acids with a pK_a value greater than about 2,

pH = ½ ( pK_a − log c₀),

where c₀ is the concentration of the acid. This is equivalent to Burrows' weak acid pH equation

${\text{pH}}=-\log _{10}\left({\sqrt {K_{a}c_{0}}}\right)\,$

A more general method is as follows. Consider the case of dissolving a weak acid, HA, in water. First write down the equilibrium expression.

HA $\rightleftharpoons$ A⁻ + H⁺

The equilibrium constant for this reaction is specified by

$K_{\text{a}}=\mathrm {\frac {[A^{-}][H^{+}]}{[HA]}}$

where [] indicates a concentration. The analytical concentration of the two reagents, C_A for [A⁻] and C_H for [H⁺] must be equal to the sum of concentrations of those species that contain the reagents. C_H is the concentration of added mineral acid.

C_A = [A⁻] + K_a[A⁻][H⁺]

C_H = [H⁺] + K_a[A⁻][H⁺]

From the first equation

$\mathrm {[A^{-}]={\frac {{\mathit {C}}_{A}}{1+{\mathit {K}}_{a}[H^{+}]}}}$

Substitution of this expression into the second equation gives

$\mathrm {{\mathit {C}}_{H}=[H^{+}]+{\frac {{\mathit {K}}_{a}{\mathit {C}}_{A}[H^{+}]}{1+{\mathit {K}}_{a}[H^{+}]}}}$

This simplifies to a quadratic equation in the hydrogen ion concentration

$\mathrm {{\mathit {K}}_{a}[H^{+}]^{2}+{\bigg (}1+({\mathit {C}}_{A}-{\mathit {C}}_{H}){\mathit {K}}_{a}{\bigg )}[H^{+}]-{\mathit {C}}_{H}=0}$

Solution of this equation gives [H⁺] and hence pH.

This method can also be used for polyprotic acids. For example, for the diprotic acid oxalic acid, writing A²⁻ for the oxalate ion,

C_A = [A²⁻] + β₁[A²⁻][H⁺] + β₂[A²⁻][H⁺]²

C_H = [H⁺] + β₁[A²⁻][H⁺] + 2β₂[A²⁻][H⁺]²

where β₁ and β₂ are cumulative protonation constants. Following the same procedure of substituting from the first equation into the second, a cubic equation in [H⁺] results. In general, the degree of the equation is one more than the number of ionisable protons. The solution of these equations can be obtained relatively easily with the aid of a spreadsheet such as EXCEL or Origin.

pH in nature

Hydrangea macrophylla blossoms are either pink or blue, depending on 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, marigold, red cabbage (anthocyanin), and red wine.

Seawater

The pH of seawater is very important and there is evidence for ocean acidification. Distinct pH scales exist depending on the method of determination.

1. NBS Scale, denoted pH_NBS. This scale is useful for pH determinations by galvanic cells calibrated with NIST standards. Unfortunately, the ionic strength of the standard buffer solutions are much lower(~0.1 M) than that of seawater (~0.7 M). Consequently, a strong liquid junction potential perturbation leaves the pH_NBS scale not recommended for use with seawater pH determinations.
2. The total scale, denoted pH_T. A set of buffers based on artificial seawater was developed. This pH scale is referred to as the total scale, denoted by pH_T. The total scale was defined using a medium containing sulfate ions, which are subject to the proton absorbing equilibrium H⁺ + SO₄²⁻ ⇌ HSO₄⁻.
3. The free scale, denoted pH_F. This scale omits the effect of sulfate ions and focuses solely on [H⁺]_F, in principle making it a simpler representation of hydrogen ion concentration. Analytically, only [H⁺]_T can be determined, therefore, [H⁺]_F must be estimated using the [SO₄²⁻] and the dissociation constant constant of HSO₄⁻. The utility of this scale is limited by the complexity of the calculations. pH values measured on the free scale differ by up to 0.12 pH units from both the total and seawater scales.
4. The seawater scale, denoted pH_SWS . Lastly, the seawater scale takes into account of the fact that hydrogen fluoride is a weak acid, H⁺ + F⁻ ⇌ HF. However, the concentration of sulfate ions is about 400 times larger than the concentration of fluoride, so the difference between the total and seawater scales is very small.

Living systems

pH in living systems

Compartment	pH
Gastric acid	0.7
Lysosomes	4.5
Granules of chromaffin cells	5.5
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, 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 7.4. 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.

In the body, pH can be estimated from known base excess (be) and bicarbonate concentration (HCO₃) by the following equation:

$\mathrm {pH} ={\frac {be-0.93\mathrm {HCO_{3}} +124}{13.77}}$

See also

• Acidosis
• Alkalosis
• pH meter
• pH indicator

External links

• Online pH Calculator