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For other uses, see PH (disambiguation). PH_sentence_0

In chemistry, pH (/piːˈeɪtʃ/, denoting 'potential of hydrogen' or 'power of hydrogen') is a scale used to specify the acidity or basicity of an aqueous solution. PH_sentence_1

Acidic solutions (solutions with higher concentrations of H ions) are measured to have lower pH values than basic or alkaline solutions. PH_sentence_2

The pH scale is logarithmic and inversely indicates the concentration of hydrogen ions in the solution. PH_sentence_3

This is because the formula used to calculate pH approximates the negative of the base 10 logarithm of the molar concentration of hydrogen ions in the solution. PH_sentence_4

More precisely, pH is the negative of the base 10 logarithm of the activity of the H ion. PH_sentence_5

At 25 °C, solutions with a pH less than 7 are acidic, and solutions with a pH greater than 7 are basic. PH_sentence_6

Solutions with a pH of 7 at this temperature are neutral (e.g. pure water). PH_sentence_7

The neutral value of the pH depends on the temperature, being lower than 7 if the temperature increases. PH_sentence_8

The pH value can be less than 0 for very strong acids, or greater than 14 for very strong bases. PH_sentence_9

The pH scale is traceable to a set of standard solutions whose pH is established by international agreement. PH_sentence_10

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. PH_sentence_11

The pH of aqueous solutions can be measured with a glass electrode and a pH meter, or a color-changing indicator. PH_sentence_12

Measurements of pH are important in chemistry, agronomy, medicine, water treatment, and many other applications. PH_sentence_13

History PH_section_0

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. PH_sentence_14

In the first papers, the notation had the H as a subscript to the lowercase p, as so: pH. PH_sentence_15

The exact meaning of the p in pH is disputed, as Sørensen did not explain why he used it. PH_sentence_16

He describes a way of measuring it using potential differences, and it represents the negative power of 10 in the concentration of hydrogen ions. PH_sentence_17

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. PH_sentence_18

He also used "q" in much the same way elsewhere in the paper. PH_sentence_19

So the "p" could stand for the French puissance, German Potenz, or Danish potens, meaning "power", or it could mean "potential". PH_sentence_20

He might also just have labelled the test solution "p" and the reference solution "q" arbitrarily; these letters are often paired. PH_sentence_21

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). PH_sentence_22

Currently in chemistry, the p stands for "decimal cologarithm of", and is also used in the term pKa, used for acid dissociation constants and pOH, the equivalent for hydroxide ions. PH_sentence_23

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. PH_sentence_24

In her memoir, she does not mention how much, or how little, Clark and colleagues knew about Sørensen's work a few years prior. PH_sentence_25

She said: PH_sentence_26

The first electronic method for measuring pH was invented by Arnold Orville Beckman, a professor at California Institute of Technology in 1934. PH_sentence_27

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. PH_sentence_28

Definition and measurement PH_section_1

pH PH_section_2

pH is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity, aH+, in a solution. PH_sentence_29

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. PH_sentence_30

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. PH_sentence_31

Note that pH depends on temperature. PH_sentence_32

For instance at 0 °C the pH of pure water is about 7.47. PH_sentence_33

At 25 °C it is 7.00, and at 100 °C it is 6.14. PH_sentence_34

This definition was adopted because ion-selective electrodes, which are used to measure pH, respond to activity. PH_sentence_35

Ideally, electrode potential, E, follows the Nernst equation, which, for the hydrogen ion can be written as PH_sentence_36

where E is a measured potential, E is the standard electrode potential, R is the gas constant, T is the temperature in kelvins, F is the Faraday constant. PH_sentence_37

For H number of electrons transferred is one. PH_sentence_38

It follows that electrode potential is proportional to pH when pH is defined in terms of activity. PH_sentence_39

Precise measurement of pH is presented in International Standard ISO 31-8 as follows: A galvanic cell is set up to measure the electromotive force (e.m.f.) PH_sentence_40

between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. PH_sentence_41

The reference electrode may be a silver chloride electrode or a calomel electrode. PH_sentence_42

The hydrogen-ion selective electrode is a standard hydrogen electrode. PH_sentence_43


  • Reference electrode | concentrated solution of KCl || test solution | H2 | PtPH_item_0_0

Firstly, the cell is filled with a solution of known hydrogen ion activity and the emf, ES, is measured. PH_sentence_44

Then the emf, EX, of the same cell containing the solution of unknown pH is measured. PH_sentence_45

To apply this process in practice, a glass electrode is used rather than the cumbersome hydrogen electrode. PH_sentence_46

A combined glass electrode has an in-built reference electrode. PH_sentence_47

It is calibrated against buffer solutions of known hydrogen ion activity. PH_sentence_48

IUPAC has proposed the use of a set of buffer solutions of known H activity. PH_sentence_49

Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. PH_sentence_50

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. PH_sentence_51

The reading from a second standard buffer solution is then adjusted, using the "slope" control, to be equal to the pH for that solution. PH_sentence_52

Further details, are given in the IUPAC recommendations. PH_sentence_53

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. PH_sentence_54

Commercial standard buffer solutions usually come with information on the value at 25 °C and a correction factor to be applied for other temperatures. PH_sentence_55

The pH scale is logarithmic and therefore pH is a dimensionless quantity. PH_sentence_56

p[H] PH_section_3

This was the original definition of Sørensen in 1909, which was superseded in favor of pH in 1924. PH_sentence_57

[H] is the concentration of hydrogen ions, denoted [H] in modern chemistry, which appears to have units of concentration. PH_sentence_58

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. PH_sentence_59

This ratio is a pure number whose logarithm can be defined. PH_sentence_60

However, it is possible to measure the concentration of hydrogen ions directly, if the electrode is calibrated in terms of hydrogen ion concentrations. PH_sentence_61

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. PH_sentence_62

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. PH_sentence_63

The calibration is usually carried out using a Gran plot. PH_sentence_64

Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration. PH_sentence_65

The glass electrode (and other ion selective electrodes) should be calibrated in a medium similar to the one being investigated. PH_sentence_66

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. PH_sentence_67

The difference between p[H] and pH is quite small. PH_sentence_68

It has been stated that pH = p[H] + 0.04. PH_sentence_69

It is common practice to use the term "pH" for both types of measurement. PH_sentence_70

pH indicators PH_section_4

Main article: pH indicator PH_sentence_71


Average pH of common solutionsPH_table_caption_0
SubstancePH_header_cell_0_0_0 pH rangePH_header_cell_0_0_1 TypePH_header_cell_0_0_2
Battery acidPH_cell_0_1_0 < 1PH_cell_0_1_1 AcidPH_cell_0_1_2
Gastric acidPH_cell_0_2_0 1.0 – 1.5PH_cell_0_2_1
VinegarPH_cell_0_3_0 2.5PH_cell_0_3_1
Orange juicePH_cell_0_4_0 3.3 – 4.2PH_cell_0_4_1
Black coffeePH_cell_0_5_0 5 – 5.03PH_cell_0_5_1
MilkPH_cell_0_6_0 6.5 – 6.8PH_cell_0_6_1
Pure waterPH_cell_0_7_0 7PH_cell_0_7_1 NeutralPH_cell_0_7_2
Sea waterPH_cell_0_8_0 7.5 – 8.4PH_cell_0_8_1 BasePH_cell_0_8_2
AmmoniaPH_cell_0_9_0 11.0 – 11.5PH_cell_0_9_1
BleachPH_cell_0_10_0 12.5PH_cell_0_10_1
LyePH_cell_0_11_0 13.0 – 13.6PH_cell_0_11_1

Indicators may be used to measure pH, by making use of the fact that their color changes with pH. PH_sentence_72

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. PH_sentence_73

More precise measurements are possible if the color is measured spectrophotometrically, using a colorimeter or spectrophotometer. PH_sentence_74

Universal indicator consists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. PH_sentence_75

Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. PH_sentence_76

Another method of measuring pH is using an electronic pH meter. PH_sentence_77

pOH PH_section_5

pOH is sometimes used as a measure of the concentration of hydroxide ions, OH. PH_sentence_78

pOH values are derived from pH measurements. PH_sentence_79

The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by PH_sentence_80

where KW is the self-ionisation constant of water. PH_sentence_81

Taking logarithms PH_sentence_82

So, at room temperature, pOH ≈ 14 − pH. PH_sentence_83

However this relationship is not strictly valid in other circumstances, such as in measurements of soil alkalinity. PH_sentence_84

Extremes of pH PH_section_6

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. PH_sentence_85

Various factors contribute to this. PH_sentence_86

It cannot be assumed that liquid junction potentials are independent of pH. PH_sentence_87

Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by ionic strength variation. PH_sentence_88

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. PH_sentence_89

Specially constructed electrodes are available which partly overcome these problems. PH_sentence_90

Runoff from mines or mine tailings can produce some very low pH values. PH_sentence_91

Non-aqueous solutions PH_section_7

Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents. PH_sentence_92

pH values based on these measurements belong to a different scale from aqueous pH values, because activities relate to different standard states. PH_sentence_93

Hydrogen ion activity, aH, can be defined as: PH_sentence_94

pH is an example of an acidity function. PH_sentence_95

Other acidity functions can be defined. PH_sentence_96

For example, the Hammett acidity function, H0, has been developed in connection with superacids. PH_sentence_97

Unified absolute pH scale PH_section_8

The concept of "unified pH scale" has been developed on the basis of the absolute chemical potential of the proton. PH_sentence_98

This model uses the Lewis acid–base definition. PH_sentence_99

This scale applies to liquids, gases and even solids. PH_sentence_100

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. PH_sentence_101

Applications PH_section_9

Pure water is neutral. PH_sentence_102

When an acid is dissolved in water, the pH will be less than 7 (25 °C). PH_sentence_103

When a base, or alkali, is dissolved in water, the pH will be greater than 7. PH_sentence_104

A solution of a strong acid, such as hydrochloric acid, at concentration 1 mol dm has a pH of 0. PH_sentence_105

A solution of a strong alkali, such as sodium hydroxide, at concentration 1 mol dm, has a pH of 14. PH_sentence_106

Thus, measured pH values will lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible. PH_sentence_107

Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration. PH_sentence_108

The pH of neutrality is not exactly 7 (25 °C), although this is a good approximation in most cases. PH_sentence_109

Neutrality is defined as the condition where [H] = [OH] (or the activities are equal). PH_sentence_110

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. PH_sentence_111

pKw is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. PH_sentence_112

Pure water and a solution of NaCl in pure water are both neutral, since dissociation of water produces equal numbers of both ions. PH_sentence_113

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. PH_sentence_114

If pure water is exposed to air it becomes mildly acidic. PH_sentence_115

This is because water absorbs carbon dioxide from the air, which is then slowly converted into bicarbonate and hydrogen ions (essentially creating carbonic acid). PH_sentence_116

pH in soil PH_section_10

Classification of soil pH ranges PH_section_11

The United States Department of Agriculture Natural Resources Conservation Service, formerly Soil Conservation Service classifies soil pH ranges as follows: PH_sentence_117


DenominationPH_header_cell_1_0_0 pH rangePH_header_cell_1_0_1
Ultra acidicPH_cell_1_1_0 < 3.5PH_cell_1_1_1
Extremely acidicPH_cell_1_2_0 3.5–4.4PH_cell_1_2_1
Very strongly acidicPH_cell_1_3_0 4.5–5.0PH_cell_1_3_1
Strongly acidicPH_cell_1_4_0 5.1–5.5PH_cell_1_4_1
Moderately acidicPH_cell_1_5_0 5.6–6.0PH_cell_1_5_1
Slightly acidicPH_cell_1_6_0 6.1–6.5PH_cell_1_6_1
NeutralPH_cell_1_7_0 6.6–7.3PH_cell_1_7_1
Slightly alkalinePH_cell_1_8_0 7.4–7.8PH_cell_1_8_1
Moderately alkalinePH_cell_1_9_0 7.9–8.4PH_cell_1_9_1
Strongly alkalinePH_cell_1_10_0 8.5–9.0PH_cell_1_10_1
Very strongly alkalinePH_cell_1_11_0 > 9.0PH_cell_1_11_1

In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. PH_sentence_118

A recent map of topsoil pH in Europe shows the alkaline soils in Mediterranean, Hungary, East Romania, North France. PH_sentence_119

Scandinavian countries, Portugal, Poland and North Germany have more acid soils. PH_sentence_120

pH in nature PH_section_12

pH-dependent plant pigments that can be used as pH indicators occur in many plants, including hibiscus, red cabbage (anthocyanin), and grapes (red wine). PH_sentence_121

The juice of citrus fruits is acidic mainly because it contains citric acid. PH_sentence_122

Other carboxylic acids occur in many living systems. PH_sentence_123

For example, lactic acid is produced by muscle activity. PH_sentence_124

The state of protonation of phosphate derivatives, such as ATP, is pH-dependent. PH_sentence_125

The functioning of the oxygen-transport enzyme hemoglobin is affected by pH in a process known as the Root effect. PH_sentence_126

Seawater PH_section_13

See also: Ocean acidification PH_sentence_127

The pH of seawater is typically limited to a range between 7.5 and 8.4. PH_sentence_128

It plays an important role in the ocean's carbon cycle, and there is evidence of ongoing ocean acidification caused by carbon dioxide emissions. PH_sentence_129

However, pH measurement is complicated by the chemical properties of seawater, and several distinct pH scales exist in chemical oceanography. PH_sentence_130

As part of its operational definition of the pH scale, the IUPAC defines a series of buffer solutions across a range of pH values (often denoted with NBS or NIST designation). PH_sentence_131

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. PH_sentence_132

To resolve this problem, an alternative series of buffers based on artificial seawater was developed. PH_sentence_133

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. PH_sentence_134

The total scale was defined using a medium containing sulfate ions. PH_sentence_135

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: PH_sentence_136


  • [H]T = [H]F + [HSO 4]PH_item_1_1

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. PH_sentence_137

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: PH_sentence_138


  • [H]F = [H]T − [HSO 4] = [H]T ( 1 + [SO 4] / K S )PH_item_2_2

However, it is difficult to estimate K S in seawater, limiting the utility of the otherwise more straightforward free scale. PH_sentence_139

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. PH_sentence_140

Resulting in the following expression for [H]SWS: PH_sentence_141


  • [H]SWS = [H]F + [HSO 4] + [HF]PH_item_3_3

However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. PH_sentence_142

In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. PH_sentence_143

As a consequence, for most practical purposes, the difference between the total and seawater scales is very small. PH_sentence_144

The following three equations summarise the three scales of pH: PH_sentence_145


  • pHF = − log [H]FPH_item_4_4
  • pHT = − log ( [H]F + [HSO 4] ) = − log [H]TPH_item_4_5
  • pHSWS = − log ( [H]F + [HSO 4] + [HF] ) = − log [H]SWSPH_item_4_6

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. PH_sentence_146

Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. PH_sentence_147

Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly. PH_sentence_148

Living systems PH_section_14


The pH of different cellular compartments, body fluids, and organs is usually tightly regulated in a process called acid-base homeostasis. PH_sentence_149

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. PH_sentence_150

Alkalosis is the opposite condition, with blood pH being excessively high. PH_sentence_151

The pH of blood is usually slightly basic with a value of pH 7.365. PH_sentence_152

This value is often referred to as physiological pH in biology and medicine. PH_sentence_153

Plaque can create a local acidic environment that can result in tooth decay by demineralization. PH_sentence_154

Enzymes and other proteins have an optimum pH range and can become inactivated or denatured outside this range. PH_sentence_155

Calculations of pH PH_section_15

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. PH_sentence_156

The complexity of the procedure depends on the nature of the solution. PH_sentence_157

For strong acids and bases no calculations are necessary except in extreme situations. PH_sentence_158

The pH of a solution containing a weak acid requires the solution of a quadratic equation. PH_sentence_159

The pH of a solution containing a weak base may require the solution of a cubic equation. PH_sentence_160

The general case requires the solution of a set of non-linear simultaneous equations. PH_sentence_161

A complicating factor is that water itself is a weak acid and a weak base (see amphoterism). PH_sentence_162

It dissociates according to the equilibrium PH_sentence_163

with a dissociation constant, Kw defined as PH_sentence_164

where [H] stands for the concentration of the aqueous hydronium ion and [OH] represents the concentration of the hydroxide ion. PH_sentence_165

This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low. PH_sentence_166

Strong acids and bases PH_section_16

Strong acids and bases are compounds that, for practical purposes, are completely dissociated in water. PH_sentence_167

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. PH_sentence_168

The pH is then equal to minus the logarithm of the concentration value. PH_sentence_169

Hydrochloric acid (HCl) is an example of a strong acid. PH_sentence_170

The pH of a 0.01M solution of HCl is equal to −log10(0.01), that is, pH = 2. PH_sentence_171

Sodium hydroxide, NaOH, is an example of a strong base. PH_sentence_172

The p[OH] value of a 0.01M solution of NaOH is equal to −log10(0.01), that is, p[OH] = 2. PH_sentence_173

From the definition of p[OH] above, this means that the pH is equal to about 12. PH_sentence_174

For solutions of sodium hydroxide at higher concentrations the self-ionization equilibrium must be taken into account. PH_sentence_175

Self-ionization must also be considered when concentrations are extremely low. PH_sentence_176

Consider, for example, a solution of hydrochloric acid at a concentration of 5×10M. PH_sentence_177

The simple procedure given above would suggest that it has a pH of 7.3. PH_sentence_178

This is clearly wrong as an acid solution should have a pH of less than 7. PH_sentence_179

Treating the system as a mixture of hydrochloric acid and the amphoteric substance water, a pH of 6.89 results. PH_sentence_180

Weak acids and bases PH_section_17

A weak acid or the conjugate acid of a weak base can be treated using the same formalism. PH_sentence_181

First, an acid dissociation constant is defined as follows. PH_sentence_182

Electrical charges are omitted from subsequent equations for the sake of generality PH_sentence_183

and its value is assumed to have been determined by experiment. PH_sentence_184

This being so, there are three unknown concentrations, [HA], [H] and [A] to determine by calculation. PH_sentence_185

Two additional equations are needed. PH_sentence_186

One way to provide them is to apply the law of mass conservation in terms of the two "reagents" H and A. PH_sentence_187

C stands for analytical concentration. PH_sentence_188

In some texts, one mass balance equation is replaced by an equation of charge balance. PH_sentence_189

This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. PH_sentence_190

Together with the equation defining Ka, there are now three equations in three unknowns. PH_sentence_191

When an acid is dissolved in water CA = CH = Ca, the concentration of the acid, so [A] = [H]. PH_sentence_192

After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained. PH_sentence_193

Solution of this quadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. PH_sentence_194

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. PH_sentence_195

For example, what is the pH of a 0.01M solution of benzoic acid, pKa = 4.19? PH_sentence_196

In this case the resulting equation in [H] is a cubic equation. PH_sentence_197

General method PH_section_18

Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations. PH_sentence_198

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. PH_sentence_199

For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β. PH_sentence_200

Next, write down the mass-balance equations for each reagent: PH_sentence_201

Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. PH_sentence_202

Much more complicated expressions are required if activities are to be used. PH_sentence_203

There are 3 non-linear simultaneous equations in the three unknowns, [A], [B] and [H]. PH_sentence_204

Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. PH_sentence_205

However, many computer programs are available which can be used to perform these calculations. PH_sentence_206

There may be more than three reagents. PH_sentence_207

The calculation of hydrogen ion concentrations, using this formalism, is a key element in the determination of equilibrium constants by potentiometric titration. PH_sentence_208

See also PH_section_19


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