Mito

Definition of the pH

In 1909, S.P.L. Sørensen defined the acidity of a solution as being the decimal cologarithme of the concentration in Ion S hydrogen: pH = - log “. In this notation, p is the abbreviation of the German word potenz (potential) and H is the symbol of the Hydrogène.
The introduction of the concept of activity required to redefine the pH as being the decimal Cologarithme of the activity of the ions hydrogen:

pH = - log has (H⁺) or pH = - log a_H
where
has (H⁺) (or a_H) is the activity of the Ion S H⁺ solvates, without unit. The value of the activity depends on all the ions present in the solution, it does not have there a simple formula.
For concentrations lower than 0,1mol. L^-1, the relation pH= - log perhaps used, by considering that the activity is then equal to the concentration of the ions hydrogen expressed in moles by Liter.

These two definitions are interchangeable in the case of diluted aqueous solutions.
By considering the molality, the equation becomes:

pH = - log m_Hy_H/m⁰ ,
where
m_H is the concentration in hydrogen ion, y_H is its coefficient of activity and m⁰ = 1 mol/kg.

In aqueous solution, the H⁺ writing is equivalent to H₃O⁺ (ion Oxonium or Hydronium), by admitting that the Proton joins only one molecule Eau; actually, several water molecules can take part in the solvation of the proton.

Acids and bases

Bronsted and Lowry gave a simple definition of the concepts of Acide and of as being respectively bases a donor and an acceptor of Proton. Other designs of acidity are used in mediums nonprotic (mediums where the exchangeable species is not the proton), the such theory of Lewis:

Examples:

NaOH is a base of Arrhenius, Bronsted and Lewis;
NH₃ is a base of Bronsted and Lewis, but not of Arrhenius;
BF₃ is a base of Lewis, but neither of Arrhenius, nor of Bronsted.

Autoprotolyse

The pH varies in the interval defined thanks to the constant of car-protolysis of solvent.

In aqueous solution, to standard temperature and pressure (TPN), a pH of 7,0 indicates neutrality because water, amphoteric, dissociates naturally in ions H⁺ and OH^- with the concentrations from 1,0 × 10^-7mol/L; This dissociation is called autoprotolyse water:

water is an acid: H₂O (L) = H⁺ (aq) + OH^- (aq)
water is a base: H₂O (L) + H⁺ (aq) = H₃O⁺ (aq)
from where reaction: 2:00 ₂O (L) = H₃O⁺ (aq) + OH^- (aq)

Under the normal conditions of temperature and pressure (TPN), the ionic product of water ([OH^-]) is worth 1,0116 × 10^-14, from where pK_e = 13,995. One can also define the pOH (- log a_OH-), so that pH + pOH = pK_e.

The pH must be redefined - starting from the equation of Nernst - in the event of change of conditions of temperature, pressure or solvent.

Influence pressure and temperature

The ionic product of water ([OH^-]) varies with the pressure and the temperature: under 1013 hPa and to 298 K (TPN), the ionic product is worth 1,0116 × 10^-14, from where pK_e = 13,995; under 10¹⁰ Pa and to 1073 K, pK_e is only of 7,68: the pH of a neutral water is then of 3,84! Under an atmosphere of 1013 hPa (steam pressure of saturating water), one a:

with 0°C: pK_e = 14,938, from where pH of neutrality = 7,4690;
with 25 °C: pK_e = 13,995, from where pH of neutrality = 6,9975;
with 100 °C: pK_e = 12,265, from where pH of neutrality = 6,1325.

The ionic product of water varies according to the following equation (Marshall and Franck, 1981):

log K_e^* = -4,098 - 3245,2/T + 2,2362 × 10⁵/T² - 3,984 × 10⁷/T³ + (13,957+1262,3/T + 8,5641 × 10⁵/T²) log d_e^*

in which K_e^* = K_e/(mol.kg^-1) and d_e^*=d_e/(g.cm^-3) (steam pressure)

Influence solvent

In other solvents that water, the pH is not function of the dissociation of water. For example, the pH of neutrality of the Acétonitrile is of 27 (TPN) and not of 7,0.

The pH is defined in nonaqueous solution compared to the concentration in protons solvates and not compared to the concentration in dissociated protons. Indeed, in certain solvents little solvatants, the pH of a strong acid and concentrated is not necessarily weak. In addition, according to the properties of solvent, the scale of pH is shifted compared to water. Thus, in water the sulphuric acid is a strong acid, while in the ethanol, it is a weak acid. To work in nonaqueous medium returns the calculation of the very complicated pH.

Acidity and alkalinity

A pH less low than that of neutrality (for example 5 for an aqueous solution) indicates an increase in the acidity, and a higher pH (for example 9 for an aqueous solution) indicates an increase in alkalinity, i.e. of the alkalinity.

An acid will decrease the pH of a neutral or basic solution; a base will increase the pH of an acid or neutral solution. When the pH of a solution is not very sensitive to the acids and the bases, it is said that it is about a buffer solution (of pH); it is the case of blood, of the milk or the sea water, which contain acido-basic couples likely to deaden the fluctuations of the pH, such carbon dioxide/hydrogénocarbonate/carbonate, acid phosphoric/hydrogénophosphate/phosphate, acid boric/borate.

The pH of a solution known as physiological is of 7,41.

Activity and concentration

For important ionic concentrations, the activity cannot be comparable any more with the concentration and one must take account of the ionic force, for example thanks to the theory of Debye-Hückel. The pH of a solution décamolaire of strong acid is thus not equal to -1 as the pH of a solution basic décamolaire strong is not equal to 15. The aggressiveness of such solutions and their important ionic force returns the measurement of the delicate pH with the usual electrodes of glass. One thus has recourse to other methods being pressed on the indicators (spectroscopy UV or RMN). For high concentrations of H⁺, one can define by analogy other scales of measurement of acidity, the such scale of Hammett H₀.

Measure and Indicators

The activity of an ion not being directly measurable, one measures the electromotive force generated by a difference in pH, from where the use of a reference. This relation follows the law of Nernst:

\ rm {pH} \ left (X \ right) = \ rm {pH} \ left (S \ right) + \ ln \ left (10 \ right). R.T.F^ {- 1} \ left E (S) - E (X) \ right

in which X is the solution whose pH is unknown and S, the reference solution; with ln (10). R.T.F^-1 = 59,159 mV to 298 K (R is the constant of perfect gases, T, the temperature and F, the constant of Faraday).

Generally, the pH is measured by electrochemistry with a PH-mètre, apparatus comprising a special, said electrode combined electrode of glass, or two electrodes separate. The electrode of reference is in general with saturated calomel ( ECS ).

There exists in many ways to measure acidity, one frequently uses indicating of pH.

Formulas of approximate computation of the pH for aqueous solutions

Case of a Strong acid

$\ rm {pH} = - \ rm {log} (C_a) \ \ \,$ where $C_a$ is the concentration in acid in mol/L

This relation is not valid for concentrations lower than 10^-7 mol. L^-1 and should apply only with concentrations higher than 10^-5 mol. L^-1. Its application to a diluted solution with 10^-8 gives indeed pH = 8, which is absurd since the solution is acid and nonalkaline (the pH of such a solution is of 6,98);

In the case of a monoacide, the pH is calculated by solving the cubic equation following: (H⁺) ³ + K_a (H⁺) ² - (H⁺) + K_a C - K_a.K_e = 0;

In the borderline case $K_a \ to + \ infty$ , the preceding equation becomes $then (\ textrm {H} ^+) ^2 - C_a \ textrm {H} ^+ - K_e = 0$ from where it is deduced that $\ textrm {H} ^+ = \ frac {C_a + \ sqrt {C_a^2 + 4K_e}} {2}$ . When $C_a \ gg 2 \ sqrt {K_e} \ approx 2 \ cdot 10^ {- 7}$ , one has $\ textrm {pH} = - \ log_ {10} \ textrm {H} ^+ \ approx - \ log_ {10} C_a$ .

Case of a strong Base

$\ rm {pH} = 14 + \ log (C_b) ~$ where $C_b$ is the concentration bases some in mol. L^-1

This relation is subjected to the same remarks as in the case of a strong acid.

Case of a Weak acid

$\ rm {pH} = \ frac {1} {2} (pK_a - \ log (C_a)) ~$ where the $pK_a$ is that of the acid.

Case of a weak Base

$\ rm {pH} = 7 + \ frac {1} {2} (pK_a + \ log (C_b)) ~$ where the $pK_a$ is that of the base

Case of a mixture of known solutions of pH

$\ rm {pH} = - \ rm {log} \ left (\ frac {10^ {- \ rm {pH} _1.V_1} +10^ {- \ rm {pH} _2.V_2}} {V_1+V_2} \ right)$

This formula is very approximate, in particular if the acids or bases used are weak.

negative pH

Consequently formulas the preceding one, when the concentration is very important, with a molarity higher than 1; what does not have anything impossible , the pH becomes negative.

In solutions rather little concentrated (one says " aqueous "), acidity is measured by the concentration in ions Hydronium or, because the H⁺ ions join, which could limit the pH to 0 (all the water molecules received an ion H⁺), but nothing empèche the existence ion H⁺ in solution in water higher concentrations.

For example, the laboratories can get a commercial concentrated acid chlorydric (37% in mass) which provides a pH of approximately -1,1; in the same way, a solution saturated with NaOH has a pH of 15.0.

The products more acid than the sulphuric acid with 100%, are described as Superacide S. The superacide most extremely known currently is the fluoroantimonic Acide with a pH of -25.

Obviously, acidities lower than 0 or 1 or the alkalinities higher than 14 are very seldom met, even in laboratory, without speaking about the superacides which are curiosities.

pH of a ground

The pH of a ground has an influence on the assimilation of the Nutriments and Oligoélément S by a Plante.

See too

Articles

Indicating PH-meter
of universal pH
Indicating
Superacide

External bonds

Influence of the pH of a ground on the assimilation of the nutritive elements for a plant

Simple: PH Zh-min-nan: PH

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