Box 45 Dissociation

Dissociation and dissociation constants (Kd and Ka)

Many chemical components can be described as 'ionizable' meaning they can dissociate to form charged species (ions). In order to describe the degree to which compounds are susceptible to ionization, dissociation constants (Kd) are derived at equilibrium. These dissociation constants are a ratio of dissociated species to undissociated species. Thus, the larger the value of Kd the greater the proportion of dissociated species at equilibrium. Where protons are generated the term Kd can be replaced with the Ka (the acid dissociation constant, see Box 3.3). Thus, Ka provides an indication of a given acid's strength. In general:

where cHA is the concentration of the undissociated species, cA- is the concentration of the dissociated base and cH+ is the concentration of dissociated protons.

For example, phenol dissociates to form phenate ions and a proton:

Phenol

Phenate

For this equilibrium the dissociation constant is derived using the expression:

cPhenol

In the case of phenol the value of Ka = 1.1 x 10-10. This very small value shows that phenol is a weak acid as there is a far greater proportion of undissociated phenol than there is of phenate ions and protons. It is more common to convert Ka values to a negative log scale (pKa), similar to that for pH (see Box 3.5), i.e.:

Proton eqn. 2

eqn.3

Dissociation of a hydroxyl functional group is dependent upon the nature of the rest of the molecule to which it is attached.

Figure 1 indicates how pKa values vary for phenols containing different additional functional groups (see Section 2.7.1). In the case of o-nitrophenol the presence of the nitro functional group (-NO2) increases the pKa value, making it more acidic than phenol. In the case of o-cresol the presence of the methyl functional group (-CH3) decreases the pKa value, making it less acidic than phenol.

These differences are due to the electron-withdrawing or electron-donating nature of the functional groups. The electron-withdrawing/donating nature of a functional group is governed by the electronegativity (Box 4.2) of the atoms comprising the function group, or more specifically by the polarity of the bonds between these atoms. The different pKa values in Fig. 1 are related to the stability of the phenate ion that forms as a product of dissociation (Fig. 2). In o-cresol the negative charge can not be delocalized (see Section 2.7) onto the methyl functional group (as it is electron-donating). Thus, delocalization of the negative charge is only possible over the aromatic ring. In o-nitrophenol the negative charge of the phenate ion can be drawn over a greater number of atoms as a result of the nitro functional group being electron-withdrawing. Thus, the negative charge can be delocalized over both the aromatic ring and the nitro functional group. It is this greater delocalization of the negative charge in o-nitrophenol that increases the stability of the phenate ion. As a consequence of this greater stability the dissociation of the OH-group on o-nitrophenol is energetically more favourable then the dissociation of the OH-group on o-cresol, making o-nitrophenol more acidic than o-cresol.

(continued on p. 82)

phenol pKa = 9.96

o-nitrophenol pKa = 7.22

phenol pKa = 9.96

o-nitrophenol pKa = 7.22

Increasing acidity

Fig. 1 Variation in pKa values for phenols containing different additional functional groups. (a)

Fig. 1 Variation in pKa values for phenols containing different additional functional groups. (a)

nitro-group

Fig. 2 Delocalization of negative charge in the phenate ion where (a) methyl and (b) nitro functional groups are present.

Dissociation and pH

As dissociation is an equilibrium process it is logical that where parameters influence equilibrium the degree of dissociation will also alter. Thus, pH has a huge bearing on the extent to which ionizable species dissociate since pH is a measure of free proton concentrations (or more correctly the free proton activity) (see Section 2.6). Re-arranging equation 1:

Taking the log of this equation yields:

multiplying this equation by -1 yields:

and thus:

(continued)

This is the Henderson-Hasselbalch equation; it indicates the relationship between pH and pKa. Notice that where the concentration of undissociated acid cHA and the concentration of its dissociated base cA- are equal then pH = pKa. Thus, the pKa value is the pH at which there is an equal proportion of dissociated and undissociated acid.

The relationship between extent of dissociation and pH is important because pH can vary sizeably in natural environments. For example, variability in soil pH is marked, suggesting that the behaviour of ionizable species within soils will be different also.

where R denotes aliphatic or aromatic hydrocarbon groups (see Section 2.7). The acidity generated by organic matter decomposition is used to break down most silicate minerals by the process of acid hydrolysis.

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