For other uses, see PH (disambiguation).
At 25 °C, 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 this temperature are neutral (e.g. pure water).
The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases.
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.
Measurements of pH are important in chemistry, agronomy, medicine, water treatment, and many other applications.
The concept of pH was first introduced by the Danish chemist Søren Peder Lauritz Sørensen at the Carlsberg Laboratory in 1909 and revised to the modern pH in 1924 to accommodate definitions and measurements in terms of electrochemical cells.
In the first papers, the notation had the H as a subscript to the lowercase p, as so: pH.
The exact meaning of the p in pH is disputed, as Sørensen did not explain why he used it.
He describes a way of measuring it using potential differences, and it represents the negative power of 10 in the concentration of hydrogen ions.
All the words for these start with p in French, German and Danish, all languages Sørensen published in: Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish.
He also used "q" in much the same way elsewhere in the paper.
So the "p" could stand for the French puissance, German Potenz, or Danish potens, meaning "power", or it could mean "potential".
He might also just have labelled the test solution "p" and the reference solution "q" arbitrarily; these letters are often paired.
There is little to support the suggestion that "pH" stands for the Latin terms pondus hydrogenii (quantity of hydrogen) or potentia hydrogenii (power of hydrogen).
Bacteriologist Alice C. Evans, famed for her work's influence on dairying and food safety, credited William Mansfield Clark and colleagues (of whom she was one) 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.
It was in response to local citrus grower Sunkist that wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.
Definition and measurement
For example, for a solution with a hydrogen ion activity of 5×10 (at that level, this is essentially the number of moles of hydrogen ions per litre of solution) there is 1/(5×10) = 2×10, thus such a solution has a pH of log10(2×10) = 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 10 moles of pure (pH 7) water, or 180 tonnes (18×10 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 about 7.47.
At 25 °C it is 7.00, and at 100 °C it is 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
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.
between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution.
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 emf, ES, is measured.
Then the emf, EX, of the same cell containing the solution of unknown pH is measured.
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.
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.
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.
This was the original definition of Sørensen in 1909, which was superseded in favor of pH in 1924.
[H] is the concentration of hydrogen ions, denoted [H] in modern chemistry, which appears to have units of concentration.
More correctly, the thermodynamic activity of H in dilute solution should be replaced by [H]/c0, where the standard state concentration c0 = 1 mol/L.
This ratio is a pure number whose logarithm can be defined.
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.
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 that pH = p[H] + 0.04.
It is common practice to use the term "pH" for both types of measurement.
Main article: pH indicator
|Battery acid||< 1||Acid|
|Gastric acid||1.0 – 1.5|
|Orange juice||3.3 – 4.2|
|Black coffee||5 – 5.03|
|Milk||6.5 – 6.8|
|Sea water||7.5 – 8.4||Base|
|Ammonia||11.0 – 11.5|
|Lye||13.0 – 13.6|
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.
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 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
where KW is the self-ionisation constant of water.
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 acid) and above about 10.5 (ca. 0.0003 mol dm 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 potentials are independent of pH.
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.
Specially constructed electrodes are available which partly overcome these problems.
Runoff from mines or mine tailings can produce some very low pH values.
Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents.
Hydrogen ion activity, aH, can be defined as:
pH is an example of an acidity function.
Other acidity functions can be defined.
Unified absolute pH scale
The concept of "unified pH scale" has been developed on the basis of the absolute chemical potential of the proton.
This model uses the Lewis acid–base definition.
This scale applies to liquids, gases and even solids.
In 2010, a new "unified absolute pH scale" has been proposed that would allow various pH ranges across different solutions to use a common proton reference standard.
Pure water is neutral.
When an acid is dissolved in water, the pH will be less than 7 (25 °C).
A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm has a pH of 0.
A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm, has a pH of 14.
Thus, measured pH values will lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible.
Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration.
The pH of neutrality is not exactly 7 (25 °C), although this is a good approximation in most cases.
Neutrality is defined as the condition where [H] = [OH] (or the activities are equal).
Since self-ionization of water holds the product of these concentration [H]×[OH] = Kw, it can be seen that at neutrality [H] = [OH] = √Kw, or pH = pKw/2.
pKw is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also.
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, so Kw varies with ionic strength.
If pure water is exposed to air it becomes mildly acidic.
pH in soil
Classification of soil pH ranges
|Ultra acidic||< 3.5|
|Very strongly acidic||4.5–5.0|
|Very strongly alkaline||> 9.0|
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
Other carboxylic acids occur in many living systems.
See also: Ocean acidification
The pH of seawater is typically limited to a range between 7.5 and 8.4.
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 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, H + SO 4 ⇌ HSO 4, such that the total scale includes the effect of both protons (free hydrogen ions) and hydrogen sulfate ions:
- [H]T = [H]F + [HSO 4]
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 [SO 4] and the stability constant of HSO 4, K S:
- [H]F = [H]T − [HSO 4] = [H]T ( 1 + [SO 4] / K S )
However, it is difficult to estimate K S 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 + [HSO 4] + [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 + [HSO 4] ) = − log [H]T
- pHSWS = − log ( [H]F + [HSO 4] + [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.
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.
- pH in living systems Compartment pH Gastric acid 1.5-3.5 Lysosomes 4.5 Human skin 4.7 Granules of chromaffin cells 5.5 Urine 6.0 Cytosol 7.2 Blood (natural pH) 7.34–7.45 Cerebrospinal fluid (CSF) 7.5 Mitochondrial matrix 7.5 Pancreas secretions 8.1
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.
Alkalosis is the opposite condition, with blood pH being excessively high.
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.
Calculations of pH
The calculation of the pH of a solution containing acids and/or bases is an example of a chemical speciation calculation, that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution.
The complexity of the procedure depends on the nature of the solution.
For strong acids and bases no calculations are necessary except in extreme situations.
The pH of a solution containing a weak acid requires the solution of a quadratic equation.
The pH of a solution containing a weak base may require the solution of a cubic equation.
A complicating factor is that water itself is a weak acid and a weak base (see amphoterism).
It dissociates according to the equilibrium
with a dissociation constant, Kw defined as
This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
Strong acids and bases
Under normal circumstances this means that the concentration of hydrogen ions in acidic solution can be taken to be equal to the concentration of the acid.
The pH is then equal to minus the logarithm of the concentration value.
Hydrochloric acid (HCl) is an example of a strong acid.
The pH of a 0.01M solution of HCl is equal to −log10(0.01), that is, pH = 2.
Sodium hydroxide, NaOH, is an example of a strong base.
The p[OH] value of a 0.01M solution of NaOH is equal to −log10(0.01), that is, p[OH] = 2.
From the definition of p[OH] above, this means that the pH is equal to about 12.
For solutions of sodium hydroxide at higher concentrations the self-ionization equilibrium must be taken into account.
Self-ionization must also be considered when concentrations are extremely low.
Consider, for example, a solution of hydrochloric acid at a concentration of 5×10M.
The simple procedure given above would suggest that it has a pH of 7.3.
This is clearly wrong as an acid solution should have a pH of less than 7.
Treating the system as a mixture of hydrochloric acid and the amphoteric substance water, a pH of 6.89 results.
Weak acids and bases
A weak acid or the conjugate acid of a weak base can be treated using the same formalism.
First, an acid dissociation constant is defined as follows.
Electrical charges are omitted from subsequent equations for the sake of generality
and its value is assumed to have been determined by experiment.
This being so, there are three unknown concentrations, [HA], [H] and [A] 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 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 [A] = [H].
After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
Solution of this quadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH.
This procedure is illustrated in an ICE table 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?
In this case the resulting equation in [H] is a cubic equation.
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.
Next, write down the mass-balance equations for each reagent:
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.
Because the equations are non-linear, and because 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 formalism, is a key element in the determination of equilibrium constants by potentiometric titration.
Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/PH.