Definitions

PH

pH is the measure of the acidity or alkalinity of a solution. It is formally a measure of the activity of dissolved hydrogen ions (H+), but for very dilute solutions, the molarity (molar concentration) of H+ may be used as a substitute with little loss of accuracy. In solution, hydrogen ions occur as a number of cations including hydronium ions (H3O+).

In pure water at 25 °C, the concentration of H+ equals the concentration of hydroxide ions (OH-). This is defined as "neutral" and corresponds to a pH level of 7.0. Solutions in which the concentration of H+ exceeds that of OH- have a pH value lower than 7.0 and are known as acids. Solutions in which OH- exceeds H+ have a pH value greater than 7.0 and are known as bases. 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. Sørensen suggested the notation "PH" for convenience, standing for "power of hydrogen", using the negative logarithm of the concentration of hydrogen ions in solution.

Definition

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 EX of the galvanic cell
reference electrode | concentrated solution of KCl || solution X | H2 | Pt
and then also measure the electromotive force ES 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
$text\left\{pH\left(X\right)\right\} = text\left\{pH\left(S\right)\right\} + frac\left\{\left(E_\left\{text\left\{S\right\}\right\} - E_\left\{text\left\{X\right\}\right\}\right)F\right\}\left\{RT ln 10\right\}$
where
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

$text\left\{pH\right\} = -log_\left\{10\right\}left\left[frac\left\{gamma_1 \left[text\left\{H\right\}^+\right] \right\}\left\{ text\left\{1 mol L\right\}^\left\{-1\right\} \right\} right\right] pm 0.02$

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.Simplified definition pH is a measurement of the concentration of hydrogen ions in a solution. Because of its mathematical formulation, low pH values are associated with solutions with high concentrations of hydrogen ions, while high pH values occur for solutions with low concentrations of hydrogen ions. Pure water has a pH of 7.0, and other solutions are usually described with reference to this value. Acids are defined as those solutions that have a pH less than 7 (i.e. more hydrogen ions than water); while bases are defined as those solutions that have a pH greater than 7 (i.e. less hydrogen ions than water).

pH is a logarithmic scale, that is, the integer part expresses the order of magnitude, e.g. pH 5 has an acidity ten times weaker than pH 4. The fractional part is also logarithmic; pH 4.3 is approximately two times weaker, and pH 4.5 three times.

The definitions of weak and strong acids, and weak and strong bases do not refer to pH, but instead describe whether an acid or base ionizes in solution.

Explanation

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 ion (H+) concentration. Since it is a logarithmic scale, and not a linear scale, 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:

$mbox\left\{pH\right\} = -log_\left\{10\right\} alpha_\left\{mathrm\left\{H\right\}^+\right\}$

Where αH+ 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+] ([H3O+]), measured in moles per litre (also known as molarity). Therefore, it is often convenient to define pH as:

$mbox\left\{pH\right\} approx -log_\left\{10\right\}\left\{frac\left\{\left[mathrm\left\{H^+\right\}\right]\right\}\left\{1~mathrm\left\{mol/L\right\}\right\}\right\}$

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:

$mbox\left\{pH\right\}_\left\{mathrm\left\{lemonade\right\}\right\} approx -log_\left\{10\right\}\left\{\left(0.0050\right)\right\} approx 2.3$

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 αH+ 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 when its pH at 50 °C is around 6.55, and also that a pH of 7.00 is very slightly 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 αH+ around 1350 and activity coefficient γH+ = 165.4 when using the MacInnes convention for scaling Pitzer single ion activity coefficient.

Arbitrarily, the pH is $-log_\left\{10\right\}\left\{\left(\left[mbox\left\{H\right\}^+\right]\right)\right\}$. Therefore,

$mbox\left\{pH\right\} = -log_\left\{10\right\}\left\{\left[\left\{mbox\left\{H\right\}^+\right\}\right]\right\}$

or, by substitution,

$mbox\left\{pH\right\} = frac\left\{epsilon\right\}\left\{0.059\right\}$.

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 weak and strong acids can be approximated using certain theories and 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):

Ka = [hydrogen ions][acid ions] / [acid]

For HCOOH, Ka = 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:

Ka = [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:

$1.6times 10^\left\{-4\right\} = frac\left\{x^2\right\}\left\{0.1-x\right\}.$

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.

It can be further shown with this same reasoning that for a weak acid the fraction which dissociates is a minute part of the original concentration. Therefore, the concentration of acid in the equilibrium remains Co, the original concentration, and thus:

pH = 1/2 (pKa - log Co)

For HCOOH, pKa = 3.8, and if Co = 0.1M then log Co = -1 and therefore:

pH = 1/2 (3.8 - (-1)) = 1/2(4.8) = 2.4

This remains essentially true as long as the pKa of the acid in question is higher than about 2.0

Burrows' weak acid pH equation

A quick way to calculate the pH of a weak acid given the concentration and knowing the Ka (acidity constant) of the said acid is to use Burrows' weak acid pH equation. $pH = -log_\left\{10\right\}\left(sqrt\left\{\left(K_atimes \left[acid\right]\right)\right\}\right)$

If we use this equation with the methanoic acid mentioned above at 0.1M with a Ka = 1.6 × 10−4 we get:

$pH = -log_\left\{10\right\}\left(sqrt\left\{\left(1.6times 10^\left\{-4\right\}times 0.1\right)\right\} \right)$
$\left\{color\left\{White\right\}pH\right\}= 2.39794$

Measurement

Representative pH values
Substance pH
Hydrochloric acid, 10M
−1.0
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
5.0
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 colour varies depending on the pH of the solution. Using indicators, qualitative determinations can be made with universal indicators that have broad colour variability over a wide pH range and quantitative determinations can be made using indicators that have strong colour 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 colour 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 colour corresponding to a pH on a colour key. pH paper is usually strips of paper that has been soaked in an indicator solution, and is used for approximations.

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 sulfuric 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

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

$K_w = a_^ * \right\} a_^ - \right\}= 10^\left\{ - 14\right\}$ (*)
where Kw is the ionization constant of water.

Now, since

$log _\left\{10\right\} K_w = log _\left\{10\right\} a_^ + \right\} + log _\left\{10\right\} a_^ - \right\}$
by logarithmic identities, we then have the relationship:
$- 14 = \left\{rm\left\{log\right\}\right\}_\right\} ,a_^\left\{rm\left\{ + \right\}\right\} \right\} + log _\left\{10\right\} ,a_^ - \right\}$

and thus

$\left\{rm\left\{pOH\right\}\right\} = - log _\left\{10\right\} ,a_^ - \right\} = 14 + log _\left\{10\right\} ,a_^ + \right\} = 14 - \left\{rm\left\{pH\right\}\right\}$

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

Indicators

An indicator is used to measure the pH of a substance. Common indicators are congo red, 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.

In addition to red cabbage, some flower petals (such as hibiscus and marigold) impart a bluish stain when crushed onto white paper, and may be used as 'homemade indicators'. Addition of acidic substances will turn the paper red, after which alkaline substances will return it to blue.

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 pHT.

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

[H+]T = [H+]F + [HSO4]

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. Analytically, only [H+]T can be determined, therefore, [H+]F must be estimated using the [SO42−] and the stability constant of HSO4, KS*:

[H+]F = [H+]T − [HSO4] = [H+]T (1 + [SO42−] / KS* )−1

However, it is difficult to estimate KS* 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 + [HSO4] + [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. 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:

pHF = − log [H+]F
pHT = − log ([H+]F + [HSO4] ) = − log [H+]T
pHSWS = − 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 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.

Body fluids

pH in body fluids
Fluid pH
gastric acid 0.7
lysosome 5.5
granule of chromaffin cell 5.5
Neutral H2O at 37°C 6.81
cytosol 7.2
CSF 7.3
arterial blood plasma 7.4
mitochondrial matrix 7.5
exocrine secretions of pancreas 8.1

The pH of different body fluids, including urine, saliva, and blood, varies with function and other factors. They are mostly tightly regulated systems to keep the acid-base homeostasis. A notable acidic substance in the body is plaque. Plaque's pH is low and will dissolve teeth if not removed. The pH of blood is known to be slightly basic, at a value of 7.4. pH is vital in maintaining the functioning of cells. For example, enzymes are heavily affected by changes in pH, and have an optimum pH at which they operate. Outside a small range they can denature and cease to catalyse vital reactions.