pH

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

Acids and bases:

• Acid-base extraction
• Acid-base reaction
• Acid-base physiology
• Acid-base homeostasis
• Dissociation constant
• Acidity function
• Buffer solutions
• pH
• Proton affinity
• Self-ionization of water
• Acids:
  • Lewis acids
  • Mineral acids
  • Organic acids
  • Strong acids
  • Superacids
  • Weak acids
• Bases:
  • Lewis bases
  • Organic bases
  • Strong bases
  • Superbases
  • Non-nucleophilic bases
  • Weak bases

Overview

pH is a measure of the acidity or alkalinity of a solution. Aqueous solutions at 25°C with a pH less than seven are considered acidic, while those with a pH greater than seven are considered basic (alkaline). When a pH level is 7.0, it is defined as 'neutral' at 25°C because at this pH the concentration of H₃O⁺ equals the concentration of OH⁻ in pure water. pH is formally dependent upon the activity of hydronium ions (H₃O⁺), but for very dilute solutions, the molarity of H₃O⁺ may be used as a substitute with little loss of accuracy. (H⁺ is often used as a synonym for H₃O⁺.) Because pH is dependent on ionic activity, a property which cannot be measured easily or fully predicted theoretically, it is difficult to determine an accurate value for the pH of a solution. The pH reading of a solution is usually obtained by comparing unknown solutions to those of known pH, and there are several ways to do so.

The concept of pH was first introduced by Danish chemist S. P. L. Sørensen at the Carlsberg Laboratory in 1909. The name, pH, has claimed to have come from any of several sources including: pondus hydrogenii, potentia hydrogenii (Latin), potentiel hydrogène (French), and potential of hydrogen (English).

Definition

pH (potential of hydrogen) is defined operationally as follows. For a solution X, first measure the electromotive force E_X of the galvanic cell

<math>\text{pH(X)} = \text{pH(S)} + \frac{(E_{\text{S}} - E_{\text{X}})F}{RT \ln 10}</math>

where

F is the Faraday constant;

R is the molar gas constant;

T is the thermodynamic temperature.

Defined this way, pH is a dimensionless quantity. Values pH(S) for a range of standard solutions S, along with further details, are given in the relevant IUPAC recommendation.

pH has no fundamental meaning as a unit; its official definition is a practical one. However in the restricted range of dilute aqueous solutions having an amount-of-dissolved-substance concentrations less than 0.1 mol/L, and being neither strongly alkaline nor strongly acidic (2 < pH < 12), the definition is such that

<math>\text{pH} = -\log_{10}\left[\frac{\gamma_1 [\text{H}^+]) }{ \text{1 mol L}^{-1} } \right] \pm 0.02</math>

where [H⁺] denotes the amount-of-substance concentration of hydrogen ion H⁺ and γ₁ denotes the activity coefficient of a typical univalent electrolyte in the solution.

Explanation

Visual representation of the pH scale.

Another visual representation of the pH scale.

In simpler terms, the number arises from a measure of the activity of hydrogen ions (or their equivalent) in the solution. The pH scale is an inverse logarithmic representation of hydrogen proton (H⁺) concentration. Unlike linear scales which have a constant relations between the item being measured (H⁺ concentration in this case) and the value reported, each individual pH unit is a factor of 10 different than the next higher or lower unit. For example, a change in pH from 2 to 3 represents a 10-fold decrease in H⁺ concentration, and a shift from 2 to 4 represents a one-hundred (10 × 10)-fold decrease in H⁺ concentration. The formula for calculating pH is:

<math>\mbox{pH} = -\log_{10} \alpha_{\mathrm{H}^+}</math>

Where α_H⁺ denotes the activity of H⁺ ions, and is dimensionless. In solutions containing other ions, activity and concentration will not generally be the same. Activity is a measure of the effective concentration of hydrogen ions, rather than the actual concentration; it includes the fact that other ions surrounding hydrogen ions will shield them and affect their ability to participate in chemical reactions. These other ions change the effective amount of hydrogen ion concentration in any process that involves H⁺.

In dilute solutions (such as tap water), activity is approximately equal to the numeric value of the concentration of the H⁺ ion, denoted as [H⁺] (or more accurately written, [H₃O⁺]), measured in moles per litre (also known as molarity). Therefore, it is often convenient to define pH as:

<math>\mbox{pH} \approx -\log_{10}{\frac{[\mathrm{H^+}]}{1~\mathrm{mol/L}}} </math>

For both definitions, log₁₀ denotes the base-10 logarithm, therefore pH defines a logarithmic scale of acidity. For example, if one makes a lemonade with a H⁺ concentration of 0.0050 moles per litre, its pH would be:

<math>\mbox{pH}_{\mathrm{lemonade}} \approx -\log_{10}{(0.0050)} \approx 2.3</math>

A solution of pH = 8.2 will have an [H⁺] concentration of 10^−8.2 mol/L, or about 6.31 × 10⁻⁹ mol/L. Thus, its hydrogen activity α_H⁺ is around 6.31 × 10⁻⁹. A solution with an [H⁺] concentration of 4.5 × 10⁻⁴ mol/L will have a pH value of 3.35.

In solution at 25 °C, a pH of 7 indicates neutrality (i.e. the pH of pure water) because water naturally dissociates into H⁺ and OH⁻ ions with equal concentrations of 1×10⁻⁷ mol/L. A lower pH value (for example pH 3) indicates increasing strength of acidity, and a higher pH value (for example pH 11) indicates increasing strength of basicity. Note, however, that pure water, when exposed to the atmosphere, will take in carbon dioxide, some of which reacts with water to form carbonic acid and H⁺, thereby lowering the pH to about 5.7.

Neutral pH at 25 °C is not exactly 7. pH is an experimental value, so it has an associated error. Since the dissociation constant of water is (1.011 ± 0.005) × 10⁻¹⁴, pH of water at 25 °C would be 6.998 ± 0.001. The value is consistent, however, with neutral pH being 7.00 to two significant figures, which is near enough for most people to assume that it is exactly 7. The pH of water gets smaller with higher temperatures. For example, at 50 °C, pH of water is 6.55 ± 0.01. This means that a diluted solution is neutral at 50 °C when its pH is around 6.55 and that a pH of 7.00 is basic.

Most substances have a pH in the range 0 to 14, although extremely acidic or extremely basic substances may have pH less than 0 or greater than 14. An example is acid mine runoff, with a pH = –3.6. Note that this does not translate to a molar concentration of 3981 M; such high activity values are the result of the extremely high value of the activity coefficient while concentrations are within a "reasonable" range . E.g. a 7.622 molal H₂SO₄ solution has a pH = -3.13, hydrogen activity α_H⁺ around 1350 and activity coefficient γ_H⁺ = 165.4 when using the MacInnes convention for scaling Pitzer single ion activity coefficient .

Arbitrarily, the pH is <math>-\log_{10}{([\mbox{H}^+])}</math>. Therefore,

<math>\mbox{pH} = -\log_{10}{[{\mbox{H}^+}]}</math>

or, by substitution,

<math>\mbox{pH} = \frac{\epsilon}{0.059}</math>.

The "pH" of any other substance may also be found (e.g. the potential of silver ions, or pAg⁺) by deriving a similar equation using the same process. These other equations for potentials will not be the same, however, as the number of moles of electrons transferred (n) will differ for the different reactions.

Calculation of pH for weak and strong acids

Values of pH for weak and strong acids can be approximated using certain assumptions.

Under the Brønsted-Lowry theory, stronger or weaker acids are a relative concept. But here we define a strong acid as a species which is a much stronger acid than the hydronium (H₃O⁺) ion. In that case the dissociation reaction (strictly HX+H₂O↔H₃O⁺+X⁻ but simplified as HX↔H⁺+X⁻) goes to completion, i.e. no unreacted acid remains in solution. Dissolving the strong acid HCl in water can therefore be expressed:

HCl(aq) → H⁺ + Cl⁻

This means that in a 0.01 mol/L solution of HCl it is approximated that there is a concentration of 0.01 mol/L dissolved hydrogen ions. From above, the pH is: pH = −log₁₀ [H⁺]:

pH = −log (0.01)

which equals 2.

For weak acids, the dissociation reaction does not go to completion. An equilibrium is reached between the hydrogen ions and the conjugate base. The following shows the equilibrium reaction between methanoic acid and its ions:

HCOOH(aq) ↔ H⁺ + HCOO⁻

It is necessary to know the value of the equilibrium constant of the reaction for each acid in order to calculate its pH. In the context of pH, this is termed the acidity constant of the acid but is worked out in the same way (see chemical equilibrium):

K_a = [hydrogen ions][acid ions] / [acid]

For HCOOH, K_a = 1.6 × 10⁻⁴

When calculating the pH of a weak acid, it is usually assumed that the water does not provide any hydrogen ions. This simplifies the calculation, and the concentration provided by water, 1×10⁻⁷ mol/L, is usually insignificant.

With a 0.1 mol/L solution of methanoic acid (HCOOH), the acidity constant is equal to:

K_a = [H⁺][HCOO⁻] / [HCOOH]

Given that an unknown amount of the acid has dissociated, [HCOOH] will be reduced by this amount, while [H⁺] and [HCOO⁻] will each be increased by this amount. Therefore, [HCOOH] may be replaced by 0.1 − x, and [H⁺] and [HCOO⁻] may each be replaced by x, giving us the following equation:

<math>1.6\times 10^{-4} = \frac{x^2}{0.1-x}.</math>

Solving this for x yields 3.9×10⁻³, which is the concentration of hydrogen ions after dissociation. Therefore the pH is −log(3.9×10⁻³), or about 2.4.

Measurement

Representative pH values

Substance	pH
Hydrochloric acid, 10M	-1.0
Lead-acid battery	0.5
Gastric acid	1.5 – 2.0
Lemon juice	2.4
Cola	2.5
Vinegar	2.9
Orange or apple juice	3.5
Tomato Juice	4.0
Beer	4.5
Acid Rain	<5.0
Coffee	5.0
Tea or healthy skin	5.5
Urine	6.0
Milk	6.5
Pure Water	7.0
Healthy human saliva	6.5 – 7.4
Blood	7.34 – 7.45
Seawater	7.7 – 8.3
Hand soap	9.0 – 10.0
Household ammonia	11.5
Bleach	12.5
Household lye	13.5

pH can be measured:

• by addition of a pH indicator into the solution under study. The indicator color varies depending on the pH of the solution. Using indicators, qualitative determinations can be made with universal indicators that have broad color variability over a wide pH range and quantitative determinations can be made using indicators that have strong color variability over a small pH range. Precise measurements can be made over a wide pH range using indicators that have multiple equilibriums in conjunction with spectrophotometric methods to determine the relative abundance of each pH-dependent component that make up the color of solution, or
• by using a pH meter together with pH-selective electrodes (pH glass electrode, hydrogen electrode, quinhydrone electrode, ion sensitive field effect transistor and others).
• by using pH paper, indicator paper that turns color corresponding to a pH on a color key. pH paper is usually small strips of paper (or a continuous tape that can be torn) that has been soaked in an indicator solution, and is used for approximations.

The lowest and highest ends of the pH scale do not oxidize. The middle of the scale is what oxidizes, such as water and blood.

As the pH scale is logarithmic, it does not start at zero. Thus the most acidic of liquids encountered can have a pH as low as −5. The most alkaline typically has pH of 14. Measurement of extremely low pH values has various complications. Calibration of the electrode in such cases can be done with standard solutions of concentrated sulphuric acid whose pH values can be calculated with the Pitzer model.

As an example of home application, the measurement of pH value can be used to quantify the amount of acid in a swimming pool.

pOH

There is also pOH, in a sense the opposite of pH, which measures the concentration of OH⁻ ions, or the basicity. Since water self ionizes, and notating [OH⁻] as the concentration of hydroxide ions, we have

<math> K_w = a_{{\rm{H}}^ * } a_{{\rm{OH}}^ - }= 10^{ - 14}</math> (*)

where K_w is the ionization constant of water.

Now, since

<math>\log _{10} K_w = \log _{10} a_{{\rm{H}}^ + } + \log _{10} a_{{\rm{OH}}^ - }</math>

by logarithmic identities, we then have the relationship:

<math>- 14 = {\rm{log}}_{{\rm{10}}} \,a_{{\rm{H}}^{\rm{ + }} } + \log _{10} \,a_{{\rm{OH}}^ - } </math>

and thus

<math>{\rm{pOH}} = - \log _{10} \,a_{{\rm{OH}}^ - } = 14 + \log _{10} \,a_{{\rm{H}}^ + } = 14 - {\rm{pH}} </math>

This formula is valid exactly for temperature = 298.15 K (25 °C) only, but is acceptable for most lab calculations.

Indicators

The Hydrangea macrophylla blossoms in pink or blue, depending on soil pH. In acidic soils, the flowers are blue; in alkaline soils, the flowers are pink.

An indicator is used to measure the pH of a substance. Common indicators are litmus paper, phenolphthalein, methyl orange, phenol red, bromothymol blue, bromocresol green and bromocresol purple. To demonstrate the principle with common household materials, red cabbage, which contains the dye anthocyanin, is used.

Seawater

In chemical oceanography pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist.

As part of its operational definition of the pH scale, the IUPAC define 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 consequently 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. 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 pH_T.

The total scale was defined using a medium containing sulphate ions. These ions experience protonation, H⁺ + SO₄²⁻ Template:Unicode HSO₄⁻, such that the total scale includes the effect of both protons ("free" hydrogen ions) and hydrogen sulphate ions:

[H⁺]_T = [H⁺]_F + [HSO₄⁻]

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. Analytically, only [H⁺]_T can be determined, so [H⁺]_F must be estimated using the [SO₄²⁻] and the stability constant of HSO₄⁻, K_S^*:

[H⁺]_F = [H⁺]_T − [HSO₄⁻] = [H⁺]_T ( 1 + [SO₄²⁻] / 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⁻ Template:Unicode 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, sulphate ions occur at much greater concentrations (> 400 times) than those of fluoride. Consequently, 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:

pH_F = − log [H⁺]_F

pH_T = − log ( [H⁺]_F + [HSO₄⁻] ) = − log [H⁺]_T

pH_SWS = − 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 (particularly in relation to the ocean's carbonate system). Since it omits consideration of sulphate 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.

See also

• Acidosis
• Alkalosis

External links

• Some Ka values
• Definition of pH by the Gold Book
• pH calculation spreadsheet
• The Measurement of pH - Definition, Standards and Procedures – Report of the Working Party on pH, IUPAC Provisional Recommendation (a proposal to revise the current IUPAC 1985 and ISO 31-8 definition of pH described above)
• CO2SYS is a program for calculating the state of the carbonate system in seawater (including pH). CO2SYS is also available in a version for Microsoft Excel/VBA.
• pH value software provides the color of universal indicator corresponding to a given pH value