pH

The pH scale is logarithmic and inversely indicates the activity of hydrogen ions in the solution

${\displaystyle {\ce {pH}}=-\log(a_{{\ce {H+}}})\thickapprox -\log([{\ce {H+}}])}$

where [H⁺] is the

In modern chemistry, the p stands for "the negative decimal logarithm of", and is used in the term pK_a for acid dissociation constants,^[10] so pH is "the negative decimal logarithm of H⁺ ion concentration", while pOH is "the negative decimal logarithm of OH- ion concentration".

Bacteriologist

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:

${\displaystyle {\ce {pH}}=-\log _{10}(5\times 10^{-6})=5.3}$

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:

${\displaystyle E=E^{0}+{\frac {RT}{F}}\ln(a_{{\ce {H+}}})=E^{0}-{\frac {2.303RT}{F}}{\ce {pH}}}$

where E is a measured potential, E⁰ is the standard electrode potential, R is the gas constant, T is the temperature in Kelvin, F is the Faraday constant. For H⁺, 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 as follows:^[14] 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, 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.

${\displaystyle {\ce {pH(X)}}={\ce {pH(S)}}+{\frac {E_{{\ce {S}}}-E_{{\ce {X}}}}{z}}}$

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 ${\displaystyle {\frac {1}{2.303RT/F}}\ }$, the "Nernstian slope".

In practice, a

The pH scale is logarithmic and therefore pH is a dimensionless quantity.^[16]

p[H]

This was the original definition of Sørensen in 1909,^[17] which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [H⁺] in modern chemistry. 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.

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.^[18] This procedure makes the activity of hydrogen ions equal to the numerical value of concentration.

The glass electrode (and other

The difference between p[H] and pH is quite small, and it has been stated that pH = p[H] + 0.04.^[19] 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, OH⁻. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by

${\displaystyle [{\ce {OH^-}}]={\frac {K_{{\ce {W}}}}{[{\ce {H^+}}]}}}$

where K_W is the self-ionization constant of water. Taking Logarithms,

${\displaystyle {\ce {pOH}}={\ce {p}}K_{{\ce {W}}}-{\ce {pH}}.}$

So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of

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

where μ_H⁺ is the chemical potential of the hydrogen ion, ${\displaystyle \mu _{{\ce {H+}}}^{\ominus }}$ 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, but there are others that can be defined. For example, the Hammett acidity function, H₀, 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.^[22] 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 such conditions when using a glass electrode. There are several factors that contribute to this problem. Firstly, liquid junction potentials may not be independent of pH.^[23] Secondly, the high ionic strength 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 Na⁺ and K⁺ in the solution.^[24] To overcome these problems, specially constructed electrodes are available.

Runoff from mines or mine tailings can produce some extremely low pH values.^[25]

Applications

Pure water has a pH of 7 at 25°C, meaning it is neutral. When an acid is dissolved in water, the pH will be less than 7, while a base, or alkali, 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, 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.

Neutrality is not exactly 7 at 25°C, but 7 serves as a good approximation in most cases. Neutrality occurs when the concentration of hydrogen ions ([H⁺]) equals the concentration of hydroxide ions ([OH⁻]), or when their activities are equal. Since self-ionization of water holds the product of these concentration [H⁺] × [OH⁻] = K_w, it can be seen that at neutrality [H⁺] = [OH⁻] = √K_w, or pH = pK_w/2. pK_w is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution of NaCl in pure water are both neutral, since 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, so K_w 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).

CO
₂+ H
₂O ⇌ HCO⁻
₃+ H⁺

pH in soil

The United States Department of Agriculture Natural Resources Conservation Service, formerly Soil Conservation Service classifies soil pH ranges as follows:^[26]

In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map^[27] 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 plants

The pH of

An alternative scale, the free scale, often denoted pH_F, 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,[31] therefore [H⁺]_F must be estimated using the [SO²⁻
₄] and the stability constant of HSO⁻
₄, K^*
_S:

[H⁺]_F = [H⁺]_T − [HSO⁻
₄] = [H⁺]_T ( 1 + [SO²⁻
₄] / K^*
_S )⁻¹

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 pH_SWS, 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 summarize the three scales of pH:

pH_F = −log [H⁺]_F

pH_T = −log([H⁺]_F + [HSO⁻
₄]) = −log[H⁺]_T

pH_SWS = −log(H⁺]_F + [HSO⁻
₄] + [HF]) = −log[v]_SWS

pH of various body fluids

pH of various body fluids^[32]

Compartment	pH
Gastric acid	1.5–3.5[33][34]
Lysosomes	4.5[32]
Human skin	4.7[35]
Granules of chromaffin cells	5.5
Urine	6.0
Breast milk	7.0-7.45[36]
Cytosol	7.2
Blood (natural pH)	7.34–7.45[32]
Cerebrospinal fluid (CSF)	7.5
Mitochondrial matrix	7.5
Pancreas secretions	8.1

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 blood 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 and other Proteins 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

Water itself is a weak acid and a weak base, so its dissociation must be taken into account at high pH and low solute concentration (see amphoterism). It dissociates according to the equilibrium

2 H₂O ⇌ H₃O⁺ (aq) + OH⁻ (aq)

with a dissociation constant, K_w defined as

${\displaystyle K_{w}={\ce {[H+][OH^{-}]}}}$

where [H⁺] stands for the concentration of the aqueous

Strong acids and bases

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

For example, what is the pH of a 0.01M solution of benzoic acid, pK_a = 4.19?

• Step 1: ${\displaystyle K_{a}=10^{-4.19}=6.46\times 10^{-5}}$
• Step 2: Set up the quadratic equation. ${\displaystyle [{\ce {H}}]^{2}+6.46\times 10^{-5}[{\ce {H}}]-6.46\times 10^{-7}=0}$
• Step 3: Solve the quadratic equation. ${\displaystyle [{\ce {H+}}]=7.74\times 10^{-4};\quad \mathrm {pH} =3.11}$

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 ${\displaystyle {\frac {K_{w}}{{\ce {[H+]}}}}}$, the resulting equation is:

${\displaystyle C_{\ce {H}}={\frac {[{\ce {H}}]+[{\ce {HA}}]-K_{w}}{\ce {[H]}}}}$

General method

Some systems, such as with

• pH indicator
• Arterial blood gas
• Chemical equilibrium
• pCO₂
• pK_a

References

External links

Scholia has a profile for pH (Q40936).

Wikidata has the property:

• pH value (P9440) (see uses)

• The dictionary definition of ph at Wiktionary
• Media related to pH at Wikimedia Commons
• Learning materials related to PH at Wikiversity