Acid constant

Glasses with different pH values (0-14) and each with an indicator . The different pH values ​​can be caused by acids with the same concentration but different acid constants .

The acid constant K _S is a material constant and provides information about the extent to which a material reacts in an equilibrium reaction with water with protolysis :

${\displaystyle \mathrm {HA+H_{2}O\ \rightleftharpoons \ H_{3}O^{+}+A^{-}} }$.

HA stands for a Brønsted acid (after Johannes Nicolaus Brønsted ), which can give off a proton H ⁺ to a solvent such as water, leaving an anion A ^- behind. More generally, Brønsted's definition also applies to non-aqueous systems, here applies to any protonatable solvent Y :

${\displaystyle \mathrm {HA+Y\ \rightleftharpoons \ HY^{+}+A^{-}} }$.

K _S is the equilibrium constant of this reaction multiplied by [Y] and thus a measure of the strength of an acid . The stronger the acid, the more the reaction is shifted to the right; d. i.e., the higher the concentrations of HY ⁺ and A ^- . The equilibrium constant is usually as their negative decadic logarithm , the p K _S specified value (also p K _a , of Engl. Acid = acid). This means: the smaller the p K _S value, the stronger the acid.

Derivation of the acid constant

The acid constant is derived as the equilibrium constant of a chemical reaction from the Gibbs energy (also free enthalpy ). If this is known, the equilibrium constant of any chemical reaction applies : ${\displaystyle G}$ ${\displaystyle K_{\text{th}}}$

${\displaystyle K_{\text{th}}=e^{-{\frac {\Delta G}{R\cdot T}}}}$,

wherein the universal gas constant , the temperature and the Euler number is. The formula also describes the observable temperature dependence of the acid constant. ${\displaystyle R}$ ${\displaystyle T}$ ${\displaystyle e}$

${\displaystyle K_{\text{th}}}$is defined as the product of the activities and is a dimensionless quantity. If mixing effects are neglected, the following applies . This is possible without major errors in solutions up to 1 mmol / l. Constants can therefore be set up with the activities as well as with the concentrations. However, they have a different numerical value. Due to the historical development of chemistry from a practical science, the concentration-related constants are usually given, as these were found experimentally before the thermodynamic justification. ${\displaystyle a_{i}=c_{i}/c_{i,{\text{ref}}}}$

Acid starch

The property of a certain substance to react as an acid is inextricably linked with its potential ability to transfer a proton (H ⁺ ) to a reaction partner . Such a reaction is called protolysis . The strength of an acid describes the extent of this ability . However, this depends on the ability of a reaction partner to take up the proton. If the acid strength of different acids is to be compared, it makes sense to consider the interaction with a standard reaction partner. This is usually water , which is also the most important compound and solvent in many processes in nature. The reaction equation of an acid HA in and with water can be represented as follows:

${\displaystyle \mathrm {1)\ HA+H_{2}O\ \rightleftharpoons \ H_{3}O^{+}+A^{-}} \,}$

An equilibrium is quickly established in this reaction. In addition to HA, H ₃ O ^{+ also} has the ability to transfer a proton to a reaction partner: They are both acids . H ₂ O and A ^- , on the other hand ^, have the ability to take up a proton, which is why they are both called bases . If you mentally separate the standard reactants water and H ₃ O ⁺ , HA and A ^- remain. Since the concentrations of these components are bound to an equilibrium, the extent to which HA is able to be an acid is coupled to the extent to which A ^{- is able} to be a base. For example, if HA has a great potential to donate a proton and A ^- a small potential to accept a proton, HA is called a strong acid. The balance (1) would be on the right. If the acid HA has a high potential to donate a proton (i.e. a low p K _S value), then its corresponding base A ^{- has} a potential that is low (i.e. a high p K _B value) to accept a proton . For water z. E.g. p K _B + p K _S = p K _W = 14

The acid constant (or the p K _S value) is a measure of the strength of an acid. The acidity is greater, the lower its p K _S value. The p K _S value is numerically equal to the pH value of a solution if HA and A ^- are present in the same concentration according to equilibrium (1).

In aqueous solutions, very strong acids and very strong bases protolyze completely to H ₃ O ⁺ or OH ^- ions. The different acid strengths of hydrogen chloride and perchloric acid in water can no longer be distinguished on the basis of the pH value . Here one speaks of the leveling effect (from French : niveler = equalize) of the water. In order to be able to distinguish even very strong acids with regard to acid strength, equilibrium constants are determined in non-aqueous solutions and these are approximately transferred to the solvent water.

The standard reaction partner water has the special property of being able to react as acid and base:

${\displaystyle \mathrm {2)\ H_{2}O+H_{2}O\ \rightleftharpoons \ H_{3}O^{+}+OH^{-}} }$

This so-called autoprotolysis allows the determination of the extent of the ability of a base to take over a proton from water and is explained in more detail under base constant .

Causes of the different acid strengths

The acidity of a molecule can be estimated based on various factors.

The stronger an acid or the easier it gives off a proton,

• when there is an inductive electron train ( -I effect ).
• the more stable the corresponding base, that is, the weaker the corresponding base.
• if the more electronegative atom carries the dissociable hydrogen atom (for atoms of the same size).
• when the larger atom carries the hydrogen atom (for atoms of different sizes).
• the lower the standard enthalpy of formation is.
• the more unstable the acid molecule is.

Acid-base reaction

Between an acid HA and its Base A ^- is in aqueous solution, the following equilibrium reaction steps:

${\displaystyle \mathrm {HA+H_{2}O\ \rightleftharpoons \ H_{3}O^{+}+A^{-}} }$

Example: acid-base reaction of acetic acid and water.
Red arrows: deprotonation of acetic acid.
Green arrows: protonation of the acetate with the formation of acetic acid.

According to the law of mass action , the position of the equilibrium is described by the equilibrium constant K :

${\displaystyle {\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )\cdot c(\mathrm {H} _{2}\mathrm {O} )}}=K}$

Since the concentration of water ( c (H ₂ O)) in the reaction remains practically constant, can be c (H ₂ O) in the constant  K include. This finally gives the acid constant  K _S with the unit mol / l:

${\displaystyle K_{\text{S}}={\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}=K\cdot c(\mathrm {H_{2}O} )}$

The negative decadic logarithm of K _S , the so-called p K _S value , is often given:

${\displaystyle \mathrm {p} K_{\text{S}}=-\lg \left(K_{\text{S}}\cdot 1\mathrm {\frac {l}{mol}} \right)=-\lg \left({\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}\cdot 1\mathrm {\frac {l}{mol}} \right)}$

The smaller the p K _S value, the stronger the acid. For example, nitric acid (HNO ₃ , degree of dissociation of 96% at a concentration of 1 mol / l) has the p K _S value −1.32, acetic acid (degree of dissociation of 0.4% at a concentration of 1 mol / l) a p K _S of 4.75.

There is accordingly a base constant (p K _B value). The smaller the p K _B value, the stronger the tendency of the base to take up protons. The p K _S value can be converted to the base constant of the corresponding base:

${\displaystyle \mathrm {p} K_{\text{S}}+\mathrm {p} K_{\text{B}}=14\quad \Leftrightarrow \quad \mathrm {p} K_{\text{B}}=14-\mathrm {p} K_{\text{S}}}$.

Acid and base constants are temperature dependent. As a rule, the constants are determined at temperatures in the range from 23 to 25 degrees Celsius. In this range, the ion product of the water is sufficiently accurate

${\displaystyle \mathrm {p} K_{\text{S}}+\mathrm {p} K_{\text{B}}=\mathrm {p} K_{\text{W}}=14}$.

Multi-protonic acids

Hägg diagram of phosphoric acid - H ₃ PO ₄ : black; H ₂ PO ₄ ^- : purple; HPO ₄ ²⁻ : blue; PO ₄ ³⁻ : brown; H ⁺ : dashed; OH ^- : dotted

Hägg diagram of sulfuric acid - H ₂ SO ₄ : black; HSO ₄ ^- : violet; SO ₄ ²⁻ : turquoise; H ⁺ : dashed; OH ^- : dotted

In the case of a multi-protonic acid, protolysis occurs gradually. There is a separate acid constant or p K _S value for each protolysis stage . For the individual protolysis steps, the following generally applies: K _{S 1}  > K _{S 2}  > K _{S 3} (or p K _{S 1}  <p K _{S 2}  <p K _{S 3} ), since the further protolysis is less due to the increasing ionic charge of the residual acid anion formed is energetically favored.

An example applies to phosphoric acid :

${\displaystyle \mathrm {H_{3}PO_{4}+H_{2}O\ \rightleftharpoons \ H_{2}PO_{4}^{-}+H_{3}O^{+}} }$	${\displaystyle K_{\mathrm {s1} }=7{,}4\cdot 10^{-3}}$	${\displaystyle \mathrm {p} K_{\mathrm {s1} }=2{,}13\ }$
${\displaystyle \mathrm {H_{2}PO_{4}^{-}+H_{2}O\ \rightleftharpoons \ HPO_{4}^{2-}+H_{3}O^{+}} }$	${\displaystyle K_{\mathrm {s2} }=6{,}3\cdot 10^{-8}}$	${\displaystyle \mathrm {p} K_{\mathrm {s2} }=7{,}20\ }$
${\displaystyle \mathrm {HPO_{4}^{2-}+H_{2}O\ \rightleftharpoons \ PO_{4}^{3-}+H_{3}O^{+}} }$	${\displaystyle K_{\mathrm {s3} }=4{,}4\cdot 10^{-13}}$	${\displaystyle \mathrm {p} K_{\mathrm {s3} }=12{,}36\ }$

At a pH value of 7.20, the concentrations of dihydrogen and hydrogen phosphate ions are approximately the same; the concentrations of undissociated phosphoric acid and phosphate ions are a million times smaller. These relationships are made use of in phosphate buffers.

Sulfuric acid is five orders of magnitude more acidic than phosphoric acid:

${\displaystyle \mathrm {H_{2}SO_{4}+H_{2}O\ \rightleftharpoons \ HSO_{4}^{-}+H_{3}O^{+}} }$	${\displaystyle K_{\mathrm {s1} }=1{,}0\cdot 10^{+3}}$	${\displaystyle \mathrm {p} K_{\mathrm {s1} }=-3{}\ }$
${\displaystyle \mathrm {HSO_{4}^{-}+H_{2}O\ \rightleftharpoons \ SO_{4}^{2-}+H_{3}O^{+}} }$	${\displaystyle K_{\mathrm {s2} }=1{,}2\cdot 10^{-2}}$	${\displaystyle \mathrm {p} K_{\mathrm {s2} }=1{,}92\ }$

Concentrated sulfuric acid is used as an electrolyte in lead batteries . Free sulfate ions no longer exist under these equilibrium conditions.

There are no more sulfate ions below pH 0

Determination of p K _S values

The p K _S values ​​of acids with values ​​in the range from 4 to about 10 can be determined via acid-base titrations and the determination of the pH value at the half-equivalence point . Here the acid and its corresponding base are present in the same concentration. At this point, it follows from the Henderson-Hasselbalch equation : pH = p K _S .

Acidity of organic acids

In the case of organic acids , three structural properties determine the acid strength:

1. Stabilization of the resulting anion by mesomerism . B. carboxylic acids more acidic than alcohols . Mesomeric effects play a decisive role here: an −M effect (e.g. a nitro group -NO ₂ ) increases the acid strength, a + M effect reduces it.
2. Hybridization of the carbon atom : the strength increases with increasing s content. Thus, ethine (sp hybrid orbital) has a lower p K _S value than ethene (sp ² hybrid orbital) and this has a lower p K _S value than ethane (sp ³ hybrid orbital), so the following applies to the p K _S value: sp <sp ²  <sp ³ ; the values ​​are 25 for ethine, 44 for ethene and 50 for ethane.
3. Inductive effects : the acid strength increases when electron-withdrawing groups are present, e.g. B. Halogens such as fluorine and chlorine or oxygen . For example, trichloroacetic acid is a stronger acid than acetic acid.

Some substituents have both mesomeric and inductive effects, such as the halogens or nitro groups. Halogens have a strong –I- but a weak + M effect; the nitro group has both an electron attracting effect (–I effect) and an –M effect, i. H. both effects work in the same direction.

p K _S and p K _B values ​​of some compounds

The following table lists p K _S and p K _B values ​​of some acids and bases under standard conditions:

Acid starch	p K S	Acid + H 2 O H 3 O + + base ${\displaystyle \ \rightleftharpoons \ }$		p K B	Base strength
very strong	−17	H [SbF 6 ]	[SbF 6 ] -	31
	−10	HClO 4	ClO 4 -	24	very weak
	−10	HI	I -	24
	−8.9	HBr	Br -	22.9
	−6	HCl	Cl -	20th
	−3	H 2 SO 4	HSO 4 -	17th
	−1.32	ENT 3	NO 3 -	15.32
strong	0.00	H 3 O +	H 2 O	14.00	weak
	1.92	HSO 4 -	SO 4 2−	12.08
	2.13	H 3 PO 4	H 2 PO 4 -	11.87
	2.22	[Fe (H 2 O) 6 ] 3+	[Fe (OH) (H 2 O) 5 ] 2+	11.78
	3.14	HF	F -	10.86
	3.75	HCOOH	HCOO -	10.25
medium strength	4.75	CH 3 COOH	CH 3 COO -	9.25	medium strength
	4.85	[Al (H 2 O) 6 ] 3+	[Al (OH) (H 2 O) 5 ] 2+	9.15
	6.52	H 2 CO 3	HCO 3 -	7.48
	6.92	H 2 S	HS -	7.08
	7.20	H 2 PO 4 -	HPO 4 2−	6.80
weak	9.25	NH 4 +	NH 3	4.75	strong
	9.40	HCN	CN -	4.60
	9.8	Trimethyl ammonium	Trimethylamine	4.2
	10.40	HCO 3 -	CO 3 2−	3.60
	10.6	Methyl ammonium	Methylamine	3.4
	10.73	Dimethyl ammonium	Dimethylamine	3.27
	12.36	HPO 4 2−	PO 4 3−	1.64
	13.00	HS -	S 2−	1.00
	14.00	H 2 O	OH -	0.00
very weak	15.90	CH 3 -CH 2 -OH	CH 3 -CH 2 -O -	−1.90	very strong
	23	NH 3	NH 2 -	−9
	48	CH 4	CH 3 -	−34

Web links

Wikibooks: Collection of tables chemistry / pKs / pKb values  - learning and teaching materials

• Bordwell p K _S table in DMSO
• p K _S Data (PDF; 78 kB), Compiled by R. Williams, on chem.wisc.edu.
• Harvard University: Evans Group p K _S table (PDF; 240 kB).
• Entry for Acidity constant . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.A00080 Version: 2.3.1.
• p K _S table CCI ETH
• p K _S table with a large number of substances
• Extensive tables with acids and bases ( MS Excel ; 1.2 MB)
• Interactively sortable, very extensive list with p K _S values ​​of organic and inorganic acids and bases

See also

• Base constant
• Law of mass action
• Dissociation constant
• Hammett acidity function

Individual evidence

1. ↑ ^{a b} Entry on acidity constant . In: IUPAC Compendium of Chemical Terminology (the “Gold Book”) . doi : 10.1351 / goldbook.A00080 Version: 2.3.1.
2. ^ Wissenschaft-Online-Lexika: Entry on acid-base concepts in the Lexikon der Chemie , accessed on April 2, 2008.
3. ↑ Bruice, PY: Organic Chemistry: Study compact . 5th, updated edition Pearson Studium, Munich 2011, ISBN 978-3-86894-102-9 , p. 53-60 .
4. ↑ ^{a b} Alfons Hädener, Heinz Kaufmann: Basics of organic chemistry. 11th revised and expanded edition. Birkhäuser, Basel et al. 2006, ISBN 3-7643-7040-8 .
5. ↑ Michael B. Smith and Jerry March, March's Advanced Organic Chemistry, John Wiley and Sons, 2007, ISBN 0-471-720-91-7
6. ↑ Gerhart Jander , Karl Friedrich year, Gerhard Schulze, Jürgen Simon (eds.): Measure analysis. Theory and practice of titrations with chemical and physical indications. 16th edition. Walter de Gruyter, Berlin et al. 2003, ISBN 3-11-017098-1 , p. 81.
7. ↑ Eberhard Gerdes: Qualitative Inorganic Analysis: A Companion for Theory and Practice . Springer DE, 2000, ISBN 3-540-67875-1 , pp. 154 ( limited preview in Google Book search).
8. ↑ PW Atkins, TL Overton, JP Rourke, MT Weller, FA Armstrong: Shriver & Atkins' inorganic chemistry. 5th edition. Oxford University Press, Oxford New York 2010, ISBN 978-0-19-9236176 , p. 115.
9. ^ AF Holleman , E. Wiberg , N. Wiberg : Textbook of Inorganic Chemistry . 91st – 100th, improved and greatly expanded edition. Walter de Gruyter, Berlin 1985, ISBN 3-11-007511-3 , p. 241.
10. ↑ Jerry March : Advanced Organic Chemistry. Reactions, Mechanisms, and Structure. 3. Edition. Wiley, New York NY et al. 1985, ISBN 0-471-88841-9 , p. 222.