In chemistrypH (potential of hydrogen) is a numeric scale used to specify the acidity or basicity of an aqueous solution. It is approximately the negative of the
base 10 logarithm of the molar concentration (-log([H+]), measured in units of moles(the unit of measurement for amount of substance in the International System of Units (SI))
( per liter, of hydrogen ions

More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion. Solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. Distilled water is neutral as you can see on the above image, at pH 7 (25 °C), being neither an acid nor a base. Contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively.
Measurements of pH are important in agronomy, medicine, biology, chemistryagriculture, forestry, food science, environmental science, oceanography, civil engineering, chemical engineering, nutrition, water treatment and water purification, and many other applications.

The pH scale is traceable 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 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 an indicator.

Definition and measurement

### pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution.

${\displaystyle \mathrm {pH} =-\log _{10}(a_{{\textrm {H}}^{+}})=\log _{10}\left({\frac {1}{a_{{\textrm {H}}^{+}}}}\right)}$
For example, a solution with a hydrogen ion activity of 5×10−6 = 1/(2×105) (at that level essentially the number of moles of hydrogen ions per liter of solution) has a pH of log10(2×105) = 5.3. For a commonplace example based on the facts that the masses of a mole of water, a mole of hydrogen ions, and a mole of hydroxide ions are respectively 18 g, 1 g, and 17 g, a quantity of 107 moles of pure (pH 7) water, or 180 tonnes (18×107 g), contains close to 1 g of dissociated hydrogen ions (or rather 19 g of H3O+ hydronium ions) and 17 g of hydroxide ions.

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

This definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. Ideally, electrode potential, E, follows the Nernst equation, which, for the hydrogen ion can be written as
${\displaystyle E=E^{0}+{\frac {RT}{F}}\ln(a_{{\textrm {H}}^{+}})=E^{0}-{\frac {2.303RT}{F}}\mathrm {pH} }$
where E is a measured potential, E0 is the standard electrode potential, R is the gas constant, T is the temperature in kelvins, F is the Faraday constant. For H+ number of electrons transferred is one. It follows that electrode potential is proportional to pH when pH is defined in terms of activity. Precise measurement of pH is presented in International Standard ISO 31-8 as follows:[8] A galvanic cell is set up to measure the electromotive force (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a silver chloride electrode or a calomel electrode. The hydrogen-ion selective electrode is a standard hydrogen electrode.
Reference electrode | concentrated solution of KCl | test solution | H2 |
Firstly, the cell is filled with a solution of known hydrogen ion activity and the emf, ES, is measured. Then the emf, EX, of the same cell containing the solution of unknown pH is measured.
${\displaystyle {\text{pH(X)}}={\text{pH(S)}}+{\frac {E_{\text{S}}-E_{\text{X}}}{z}}}$
The difference between the two measured emf values is proportional to pH. This method of calibration avoids the need to know the standard electrode potential. The proportionality constant, 1/z is ideallyequal to ${\displaystyle {\frac {1}{2.303RT/F}}\ }$ the "Nernstian slope".
To apply this process in practice, a glass electrode is used rather than the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against buffer solutions of known hydrogen ion activity. IUPAC has proposed the use of a set of buffer solutions of known H+ activity.[3] Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To implement this approach to calibration, the electrode is first immersed in a standard solution and the reading on a pH meter is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted, using the "slope" control, to be equal to the pH for that solution. Further details, are given in the IUPAC recommendations.[3] 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.

### p[H]

This was the original definition of Sørensen,[5] which was superseded in favor of pH in 1909. 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 alkaline in the presence of a relatively high concentration of background electrolyte. Since the concentrations of acid and alkaline are known, it is easy to calculate the concentration of hydrogen ions so that the measured potential can be correlated with concentrations. The calibration is usually carried out using a Gran plot.[9] The calibration yields a value for the standard electrode potential, E0, and a slope factor, f, so that the Nernst equation in the form
${\displaystyle E=E^{0}+f{\frac {2.303RT}{F}}\log[{\mbox{H}}^{+}]}$
can be used to derive hydrogen ion concentrations from experimental measurements of E. The slope factor, f, is usually slightly less than one. A slope factor of less than 0.95 indicates that the electrode is not functioning correctly. The presence of background electrolyte ensures that the hydrogen ion activity coefficient is effectively constant during the titration. As it is constant, its value can be set to one by defining the standard state as being the solution containing the background electrolyte. Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration.

The glass electrode (and other ion selective electrodes) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition, as detailed below.

The difference between p[H] and pH is quite small. It has been stated[10] that pH = p[H] + 0.04. It is common practice to use the term "pH" for both types of measurement.

### pH indicators

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

### pOH

Relation between p[OH] and p[H] (red = acidic region, blue = basic region)
pOH is sometimes used as a measure of the concentration of hydroxide ions. OH−. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
${\displaystyle [\mathrm {OH} ^{-}]={\frac {K_{W}}{[\mathrm {H} ^{+}]}}}$
where KW is the self-ionisation constant of water. Taking logarithms
${\displaystyle \mathrm {pOH} =\mathrm {pK_{W}} -\mathrm {pH} }$
So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity.

### Extremes of pH

Measurement of pH below about 2.5 (ca. 0.003 mol dm−3 acid) and above about 10.5 (ca. 0.0003 mol dm−3 alkaline) requires special procedures because, when using the glass electrode, the Nernst law breaks down under those conditions. Various factors contribute to this. It cannot be assumed that liquid junction potentialsare independent of pH.[11] Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by ionic strength variation. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as Na+ and K+ in the solution.[12]Specially constructed electrodes are available which partly overcome these problems.

Runoff from mines or mine tailings can produce some very low pH values.[13]

### Non-aqueous solutions

Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents. pH values based on these measurements belong to a different scale from aqueous pH values, because activities relate to different standard states. Hydrogen ion activity, aH+, can be defined[14][15] as:
${\displaystyle a_{H^{+}}=\exp \left({\frac {\mu _{H^{+}}-\mu _{H^{+}}^{\ominus }}{RT}}\right)}$
where μH+ is the chemical potential of the hydrogen ion, μoH+ is its chemical potential in the chosen standard state, R is the gas constant and T is the thermodynamic temperature. Therefore, pH values on the different scales cannot be compared directly due to different solvated proton ions such as lyonium ions, requiring an intersolvent scale which involves the transfer activity coefficient of hydronium/lyonium ion.

pH is an example of an acidity function. Other acidity functions can be defined. For example, the Hammett acidity function, H0, has been developed in connection with superacids.

The concept of "Unified pH scale" has been developed on the basis of the absolute chemical potential of the proton. This scale applies to liquids, gases and even solids