# 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

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.

## 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

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