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DISSOCIATION CONSTANTS: STRENGTH OF ACIDS AND BASES

DISSOCIATION CONSTANTS: STRENGTH OF ACIDS AND BASES

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2. LAW OF MASS ACTION



199



2.1. Ionic Product of Water

When the above concepts are applied to the reaction in which water is ionized, the

following can be expressed:

H2 O ỵ H2 O % OH ỵ H3 Oỵ

acid1 base2



base1



acid2



This chemical equation is produced because water is amphoteric; that is, it can act as an

acid or a base. The equilibrium constant for this reaction is expressed as:

Kw ẳ









H3 Oỵ $ OH

ẵH2 O2



ẳ KH2 O ¼ constant



Kw is the constant of the product of the molar concentration of the protons and hydroxyl

ions produced in the self-ionization of water. At 25 C it has a value of 10À14 when the concentrations are expressed in moles per liter.

[H2O], the concentration of water, is considered to be constant as the proportion of water

that dissociates is very small compared to the proportion that does not. It can therefore be

stated that:

Kw ẳ 1014 ẳ ẵH3 Oỵ ẵOH

Although the self-ionization of water is an equilibrium reaction that contributes Hỵ and

OHÀ ions to a solution, the concentration of these ions is negligible compared to the Hỵ

ions produced by an acid or the OHÀ ions produced by a base in their dissociation reactions

(unless of course the acids or bases are very weak).



2.2. pH

Natural solutions and liquids tend to contain very low concentrations of Hỵ ions. Pure

water, for example, has [Hỵ] ẳ 10À7mol/L. To avoid the use of decimals or exponents to

express the concentration of protons in aqueous solutions, Soărensen introduced the concept

of pH:

pH ẳ logẵH3 Oỵ / pH ẳ logẵHỵ Š

Accordingly, pOH was defined as Àlog[OHÀ].

The equilibrium constant pK can also be expressed as logK.

For water: pKw ẳ pH ỵ pOH / pH ỵ pOH ẳ 14

For pure water: pH ẳ log ẵHỵ ẳ log ẵ107 ẳ 7

pOH ¼ 14 À 7 ¼ 7



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13. ACID-BASE EQUILIBRIA IN WINE



TABLE 13.1



pH Values of Natural Liquids



Liquid



pH



Pure water



7



Water



5À8



Beer



4À5



Wine



3e4



Vinegar



2.5 e 3.5



Sodas and other carbonated drinks



1.8 e 3.0



An acid solution has a higher concentration of Hỵ ions than pure water, and accordingly,

will have a pH of less than 7. A neutral solution, in turn, has the same concentration

of Hỵ ions as pure water and will therefore have a pH of 7. Finally, a basic solution

will have a pH of more than 7 as it has a lower concentration of Hỵ ions than pure

water.

The contribution from the self-ionization of water in aqueous solutions is only taken into

account for very weak acids or bases; that is, substances that have a concentration of H3Oỵ or

OH ions less than 10À6 M.



3. DISSOCIATION CONSTANTS: STRENGTH

OF ACIDS AND BASES

The relative strength of acids and bases is indicated by the value of their dissociation

constant (Ka and Kb). Both Ka and Kb are equilibrium constants. Therefore, the higher their

value, the more the equilibrium is shifted to the right and the greater their tendency to

produce Hỵ or OH ions.





AcO $ H ỵ

AcOH $ AcO ỵ Hỵ ; Ka ẳ

ẵAcOH

The strength scale is used only for weak acids and bases as the equilibrium of strong acids

and bases is always displaced completely to the right. In such cases, the value of Ka or Kb is

N, as the molecular species does not exist in solution.

Example for a strong acid:













HCl / Cl ỵ H ;







H ỵ $ Cl

ẳ N; as ẵHCl / 0

K ¼

½HClŠ



Examples of strong acids are HClO4, HCl, HNO3 and H2SO4, and strong bases are NaOH

and KOH.



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201



3. DISSOCIATION CONSTANTS: STRENGTH OF ACIDS AND BASES



TABLE 13.2



Dissociation Constants and pKa of a Range of Acids

Ka (25 C)



Acid

HSO4À

ClCH2-COOH

HF

HCOOH

CH3-COOH

CO2

À



1.2 Â 10



À2



1.4 Â 10



À3



6.8 Â 10



À4



1.8 Â 10



À4



1.8 Â 10



À5



4.2 Â 10



À7



pKa

1.92

2.85

3.17

3.74

4.74

6.38



À14



10



HS



14



According to the values in the above table, the higher the equilibrium constant (Ka), the

lower the pKa will be. Therefore, acids with a higher Ka (and a lower pKa) will be stronger.

The same occurs with bases (higher Kb and lower pKb).



3.1. Degree of Dissociation

The degree of dissociation (a) for weak acids and bases is defined as the fraction of 1 mole

that dissociates at equilibrium.

AcOH $ AcO ỵ Hỵ

Initial point :



1 mole



0



0



Equilibrium :



1a



a



a



Ka ẳ

If there are c moles :



c2 a2

ca2



c1 aị

1a

c1 aị



ca



ca



By definition, a is a unit factor but it is often also expressed as a percentage.

If absolute concentrations are used instead of the degree of dissociation, the equilibrium

constant is expressed as follows:

AcOH $ AcO ỵ Hỵ

Initial point :



c



x2

cx

Equilibrium : c x



0



0



x



x



Ka ¼



On comparing the expressions at equilibrium, it is seen that:

x

ca ¼ x; 0a ¼

c



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13. ACID-BASE EQUILIBRIA IN WINE



Two methods can be used to solve the Ka equation: the first involves resolving the seconddegree equation and the second involves performing successive approximations. In the

second method, the following approximation is performed:

cÀx z c, which gives the following equation:

Ka ¼



pffiffiffiffiffiffiffiffiffiffi

x2

; from which / x ¼ Ka $c

c



The value obtained for x is used to calculate a value for cÀx, which, in turn, is used to

calculate a new value for x. The method ends when there is practically no difference between

two successive approximations.

Example

Let us consider a solution of acetic acid: [AcOH] ¼ 10À3 M; Ka (AcOH) ẳ 1.8 105

AcOH $ AcO ỵ Hỵ

103 x



x



x



Second-degree equation method:

Ka ẳ



x2

;

3

10 x



Ka ặ



x ẳ ẵHỵ ẳ



p

Ka2 ỵ 4Ka C0

ẳ 1:27 104 M; 0 pH ¼ 3:90

2



Successive approximation method:

x2

;

10À3

pffiffiffiffiffiffiffiffiffiffiffiffiffi

x ¼ 10À3 K ¼ 1:36 Â 10À4 ;



Ka ¼



Ka ¼

Ka ¼



x2

;

10À3 À 1:36 Â 10À4



x ¼



pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

8:64 Â 10À4 Ka ¼ 1:26 Â 10À4



x2

;

À 1:26 Â 10À4



x ¼



pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

8:74 Â 10À4 Ka ¼ 1:27 Â 10À4



10À3



The successive approximation method is particularly useful when dealing with third- or

fourth-degree equations.

Other useful relationships can also be established using Ka equations. Therefore, for

a generic weak acid, HA:

HA $ Hỵ ỵ A

ỵ 2

H

x2



;

Ka ẳ

ẵHA

C0 x



C0 x



x



x



Ka C0 Ka x ẳ x2 ;



ENOLOGICAL CHEMISTRY



x2 ỵ Ka x Ka C0 ¼ 0



4. ACTIVITY AND THERMODYNAMIC CONSTANT



The resolved equation yields:









x ẳ H











Ka ặ



203



p

Ka2 ỵ 4Ka C0

2



If a series of conditions are fulfilled, the above expression can be simplified.

When Ka<
ẵHỵ ẳ



Ka p

ặ Ka C0

2



If the above condition is fulfilled and Ka << C0, then:

p

ẵHỵ z Ka C0

Therefore, to be able to ignore the concentration of a dissociated acid with respect to the

starting concentration of an undissociated acid, the acid must be very weak (low Ka) and

rather concentrated (high C0).



4. ACTIVITY AND THERMODYNAMIC CONSTANT

Acids in wine exist partly as free acids and partly as neutralized acids, forming salts.

The relative proportions depend on pH (which tends to be between 3 and 4 for wine)

and on the Ka of the acids. In winemaking, it is always interesting to know the pH of

a particular wine. Thankfully, this can be determined easily by potentiometry. It is not

so easy to determine the ratio of free acid to dissociated acid for a given acid, particularly

tartaric acid.

The percentage of dissociated acid and undissociated molecular acid depends on the

dissociation constant and on the pH according to the following expression:



H $ A





HA $ A ỵ H ; Ka ẳ

ẵHA





ẵHA

ẵHA

H ẳ Ka $ / log Hỵ ẳ log Ka log

ẵA

ẵA



A

ẵHA

pH ẳ pKa log or pH ẳ pKa ỵ log

ẵHA

ẵA

The expression of the acid dissociation constant, Ka, refers to the molar concentrations of

the different species that participate in the equilibrium. The validity of this expression

depends on the mobility of the ions and species in the solution, and this mobility, in turn,

depends on the total number of charged species in the solution.

In the next section, we are going to further explore the concept of the dissociation constant

to study the relationship between pH, pKa, and the amount of free and dissociated acid in

real solutions.



ENOLOGICAL CHEMISTRY



204



13. ACID-BASE EQUILIBRIA IN WINE



The law of mass action as a function of molar concentrations, or in our particular case, the

acid dissociation constant, provides an approximation to reality, as it is only valid when

activities rather than concentrations are considered. In such cases, the equilibrium constant

depends exclusively on temperature and type of solvent.

Kt ẳ



H ỵ ịA ị

;

HAị



Kt ẳ thermodynamic constant, ( ) ẳ activity

Activity is related to molar concentration through what is known as the activity

coefficient:

A ị ẳ fA ẵA ; HAị ẳ fHA ½HAŠ

To help to understand the concept of activity, the next section will look at the DebyeHuăckel theory regarding the conductivity of electrolytes, which is based on an extremely

simple concept.



4.1. Debye-Huăckel Theory

It should be considered that ions with different charges are in constant motion due to the

forces of attraction and repulsion. The mobility of ions depends on three factors: size, charge,

and concentration.

Debye and Huăckel imagined that a cation in solution would be surrounded by anions and

cations, but because ions with the same charge repel each other, they believed that this cation



FIGURE 13.2



electric field.



Central ion surrounded by a cloud of ions with spherical symmetry, in the absence of an



ENOLOGICAL CHEMISTRY



4. ACTIVITY AND THERMODYNAMIC CONSTANT



205



would be mainly surrounded by anions. Likewise, they held that an anion would be surrounded mainly by cations. For simplicity, it can be considered that an ion, whatever its

charge, will be surrounded by a cloud of oppositely charged ions. The stronger the electrostatic interaction between any pair of ions, the lower the effective concentration of the ions

will be.

The forces of electrostatic interaction (attraction or repulsion) are the main forces responsible for the formation of aggregates and, thus, for the reduction in the mobility of ions.

Logically, these forces depend on the size and charge of the ions and their concentration

in the medium. Accordingly, they can be considered to be non-existent in infinitely dilute

solutions.

Onsager studied the effects of asymmetry and electrophoresis by extending the DebyeHuăckel theory. In this model, it is considered that in the presence of an electric field, an

ion and its cloud of oppositely charged ions will be facing opposite directions. The effect

will be an asymmetric ion cloud, which in the absence of an electric field, will have spherical

symmetry.

With respect to the electrophoretic effect, it is considered that the resulting separation of

charges reduces the mobility of ions. A positively charged ion moving towards the negative

pole will have reduced mobility because its surrounding cloud of ions will be oriented

towards the opposite pole, and because it will also be affected by the motion of negatively

charged ions, together with their cloud, towards the positive pole. The mobility of ions is

also reduced by the fact that these are surrounded by solvent molecules moving towards

them.



- pole



FIGURE 13.3 Effect of asymmetry in

the presence of an electric field.



+ pole



Central ion



Equilibrium



Ion cloud



Electric field



+ pole



- pole



























FIGURE 13.4







Electrophoretic effect or drag force.



ENOLOGICAL CHEMISTRY



206



13. ACID-BASE EQUILIBRIA IN WINE



4.2. Calculating Activity

The effective concentration or activity of an ion in an aqueous solution at 25 C can be

calculated using the following expression:

p

log f ẳ 0:509:ẵZỵ Z : I

I ẳ



ẳn

1 iX

M Z2

2 i¼1 i i



a ¼ f:c



Z ¼ charge of the cation and anion

I ¼ ionic strength

a ¼ activity

i ¼ any cation or anion in the solution

f ¼ activity coefficient

c ¼ molar concentration

Mi ¼ molar concentration of ion i

In the case of electrolytes such as NaCl and HCl, which give rise to ions in equal concentrations and with a like charge, the ionic strength is equal to the molar concentration.

Example: Consider a 0.5 M solution of NaCl in water:

ẵNaCl / Naỵ ỵ Cl

0:5

0:5

1

I ẳ 0:5 1ị2 ỵ 0:5 1ị2 ị ẳ 0:5

2

p

Z2 A I

p

log f ẳ

1ỵB I

For solutions in solvents other than pure water, the activity coefficient in the DebyeHuăckel expression takes account of the influence of temperature and the dielectric constant

of the medium. A and B are dependent on both temperature and the dielectric constant of the

medium, and Z is the charge of the ion.

Usseglio-Tomasset and Bosia have proposed the following values for the Debye-Huăckel

constants A and B as a function of ethanol content:

A ẳ 0:5047 ỵ 0:0042 %EtOHị ỵ 5 105 %EtOHị2

B ẳ 1:6384 þ 0:004597 Â ð%EtOHÞ þ 3:5 Â 10À5 Â ð%EtOHÞ2

Sample Problem

Calculate the activity of Naỵ in a 0.5 M solution of NaCl and 15% EtOH



ENOLOGICAL CHEMISTRY



5. MIXED AND THERMODYNAMIC DISSOCIATION CONSTANTS



207



NaCl / Naỵ ỵ Cl

0:5



0:5



1X

1

Mi Z2i ẳ 0:5 1ị2 ỵ 0:5 ỵ1ị2 ị ẳ 0:5

2

2

p



Z2 A I

p

log fi ẳ

1ỵB I



I ẳ



A ẳ 0:5047 ỵ 0:0042 15ị ỵ 5 105 15ị2 ẳ 0:57895

B ẳ 1:6384 þ 0:004597 Â ð15Þ þ 3:5 Â 10À5 Â ð15Þ2 ẳ 1:71523

p

12 0:57895 0:5

p ẳ 0:185;

log fNaỵ ẳ

fNaỵ ẳ fCl ẳ 100:185 ẳ 0:653

1 ỵ 1:71523 0:5





Naỵ ị ẳ Naỵ fNaỵ ẳ 0:5 0:653 ẳ 0:326





Cl ị ¼ ClÀ Â fClÀ Â 0:653 ¼ 0:326:



5. MIXED AND THERMODYNAMIC DISSOCIATION CONSTANTS

We have seen the following acid dissociation constants so far:

ẵH ỵ $ẵA

Ka ẳ

Acidity constant as a function of concentration

ẵHA

H ỵ ịA ị

Acidity constant as a function of activity

Kt ẳ

HAị

In practice, the following mixed dissociation constant is used:

Km





H ỵ ị$ A



ẵHA



This constant is calculated as a function of the activity of the Hỵ ion and the molar concentration of AÀ and HA. This is because the hydrogen ion concentration of a solution is determined by potentiometry using a pH meter, which measures the activity of this ion. It is

therefore possible to establish a relationship between Km and Kt.

Kt ẳ

Km ẳ



H ỵ ịA ị

;

HAị



H ỵ ị$ A

;

ẵHA



Hỵ ị ẳ Kt



HAị

A ị



Hỵ ị ẳ Km



ENOLOGICAL CHEMISTRY



ẵHA

ẵA



208



13. ACID-BASE EQUILIBRIA IN WINE



Bearing in mind that: A ị ẳ fA ẵA ; HAị ẳ fHA ẵHA

Km



ẵHA

ẵHAfHA

ẳ Kt

;

ẵA fA

ẵA



pKm ¼ pKt À log



Km ¼ Kt



fHA

f AÀ



fHA

f AÀ



The above expression shows the relationship between the thermodynamic constant and

the mixed constant as a function of the activity coefficients of the dissociated and undissociated forms of the acid. Presuming that a second dissociation takes place, that is, that the Hỵ

ions originate from an ion, the following can be written:

AZA / BZB ỵ Hỵ

pKm ẳ pKt log



fA

fB



Relationship between charges: ZA ẳ ZB þ 1

The relationship between the thermodynamic constant and the mixed constant as a function of the ionic strength of the medium is more interesting.

pffiffi

Z2 A I

pffiffi

We know that log f ẳ

1ỵB I

The activity coefficient f depends on the ionic strength I of the medium; therefore, for

each ion:

pffiffi

Z2A A I

pffiffi

log fA ẳ

1ỵB I

and

p

Z2B A I

f

p; log A ẳ log fA log fB

log fB ẳ

fB

1ỵ B I

p

p

p

Z2A A I

Z2B A I

A I

2

2

p ẳ ZB ZA ị

p ỵ

p

log fA log fB ẳ

1ỵB I 1ỵB I

1ỵB I

Bearing in mind that ZB ¼ ZA À 1, the following is obtained:

Z2B Z2A ị ẳ ZA 1ị2 ZA2 ẳ ZA2 2ZA ỵ 1 ZA 2 ¼ 1 À 2ZA

The value of the mixed dissociation constant can be calculated when the values of the thermodynamic constant, the ionic strength of the medium, and the constants A and B are

known.



ENOLOGICAL CHEMISTRY



5. MIXED AND THERMODYNAMIC DISSOCIATION CONSTANTS



TABLE 13.3



Relationship Between Thermodynamic Dissociation Constant and Ethanol

Content



Acid



Equation



Acetic acid



pKt ẳ 4.755 ỵ 7.96 103(%EtOH) ỵ 2.88104(%EtOH)2



Lactic acid



pKt ẳ 3.889 ỵ 1.208 102(%EtOH) ỵ 1.50104(%EtOH)2



Gluconic acid



pKt ẳ 3.815 ỵ 1.48 102(%EtOH) ỵ 1.7105(%EtOH)2



Tartaric acid



pKt1 ẳ 3.075 ỵ 1.097 102(%EtOH) þ 1.64 Â 10À4(%EtOH)2

pKt2 ¼ 4.387 þ 1.47 Â 10À2(%EtOH) þ 1.61 Â 10À4(%EtOH)2



Malic acid



pKt1 ¼ 3.474 þ 1.187 Â 102(%EtOH) ỵ 1.53 104(%EtOH)2

pKt2 ẳ 5.099 ỵ 1.701 102(%EtOH) ỵ 1.09 104(%EtOH)2



p 9

>

fA

A I >

>

p >

log

ẳ 1 2ZA ị

>

=

fB

1ỵB I>

pKm ẳ pKt log



fA

fB



>

>

>

>

>

>

;



pKm ẳ pKt 1 2ZA ị



p

A I

p

1ỵB I



pKm ẳ pKt ỵ 2ZA 1ị



p

A I

p

1ỵB I



Sample Calculation for the Mixed Dissociation Constant

Ethanol: 13%

pH ¼ 3.23 / 10À3.23 ¼ jH+j ;

Ammoniacal nitrogen (NH4OH):



h 0.59 meq/L

0.43 meq/L



h



19.05 meq/L



h



745 mg/L



Sodium:



0.87 meq/L



h



20 mg/L



Calcium:



4.70 meq/L



h



94 mg/L



Magnesium:



9.21 meq/L



h



112 mg/L



Potassium:



S Cations:



6 mgN/L



34.85 meq/L



Alkalinity of ash:



23.2 meq/L



Titratable acidity:



100.9 meq/L



Volatile acidity:



13.0 meq/L



Tartaric acid:



19.67 mmol/L



Malic acid:

Lactic acid:

Sulfates:



Trace levels

26.1 mmol/L

3.87 mmoles/L h 7.74 meq/L



Chlorides:



1.61 meq/L

3.02 meq/L



Phosphates (H2PỒ

4 ):



+ ClÀ + H2PỒ

SAnions ¼ alkalinity of ash + SO2À

4

4 ¼ 35.57 meq/L.



ENOLOGICAL CHEMISTRY



209



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