Arrhenius Acids

The Arrhenius concept is the easiest one retained by majority of peelers, because most of peelings acids are ionic compounds, acting as a source of H₃O⁺ when dissolved in water.

The Swedish chemist Svante Arrhenius attributed the properties of acidity to hydrogen in 1884. An Arrhenius acid is a substance that increases the concentration of the hydronium ion, H₃O⁺, when dissolved in water. This definition stems from the equilibrium dissociation of water into hydronium and hydroxide (OH⁻) ions:

In pure water the majority of molecules exist as H₂O, but a small number of molecules are constantly dissociating and reassociating. Pure water is neutral with respect to acidity or basicity because the concentration of hydroxide ions is always equal to the concentration of hydronium ions. An Arrhenius base is a molecule which increases the concentration of the hydroxide ion when dissolved in water. Note that chemists often write H⁺(aq) and refer to the hydrogen ion when describing acid-base reactions but the free hydrogen nucleus, a proton, does not exist alone in water, it exists as the hydronium ion, H₃O⁺.

Brønsted Acids

While the Arrhenius concept is useful for describing many reactions, it is also quite limited in its scope. Brønsted acids act by donating a proton to water and at the difference of Arrhenius acids, can also be used to describe molecular compounds, whereas Arrhenius acids must be ionic compounds.

In 1923 chemists Johannes Nicolaus Brønsted and Thomas Martin Lowry independently recognized that acid–base reactions involve the transfer of a proton. A Brønsted–Lowry acid (or simply Brønsted acid) is a species that donates a proton to a Brønsted–Lowry base. Brønsted–Lowry acid–base theory has several advantages over Arrhenius theory. Consider the following reactions of acetic acid (CH₃COOH), (used as chemical peel for the décolleté by some great peelers like L. Wiest) the organic acid that gives vinegar its characteristic taste:

Both theories easily describe the first reaction: CH₃COOH acts as an Arrhenius acid because it acts as a source of H₃O⁺ when dissolved in water, and it acts as a Brønsted acid by donating a proton to water. In the second example CH₃COOH undergoes the same transformation, donating a proton to ammonia (NH3), but cannot be described using the Arrhenius definition of an acid because the reaction does not produce hydronium.

As with the acetic acid reactions, both definitions work for the first example, where water is the solvent and hydronium ion is formed. The next reaction does not involve the formation of ions but can still be viewed as proton transfer reaction.

Lewis Acids

The Brønsted–Lowry definition is the most widely used definition; unless otherwise specified acid–base reactions are assumed to involve the transfer of a proton (H⁺) from an acid to a base.

A third concept was proposed by Gilbert N. Lewis which includes reactions with acid-base characteristics that do not involve a proton transfer. A Lewis acid is a species that accepts a pair of electrons from another species; in other words, it is an electron pair acceptor. Brønsted acid–base reactions are proton transfer reactions while Lewis acid–base reactions are electron pair transfers. All Brønsted acids are also Lewis acids, but not all Lewis acids are Brønsted acids. Contrast the following reactions which could be described in terms of acid-base chemistry:

In the first reaction a fluoride ion, F⁻, gives up an electron pair to boron trifluoride to form the product tetrafluoroborate. Fluoride ‘loses’ a pair of valence electrons because the electrons shared in the B—F bond are located in the region of space between the two atomic nuclei and are therefore more distant from the fluoride nucleus than they are in the lone fluoride ion. BF3 is a Lewis acid because it accepts the electron pair from fluoride. This reaction cannot be described in terms of Brønsted theory because there is no proton transfer. The second reaction can be described using either theory. A proton is transferred from an unspecified Brønsted acid to ammonia, a Brønsted base; alternatively, ammonia acts as a Lewis base and transfers a lone pair of electrons to form a bond with a hydrogen ion. The species that gains the electron pair is the Lewis acid; for example, the oxygen atom in H₃O⁺ gains a pair of electrons when one of the H—O bonds is broken and the electrons shared in the bond become localized on oxygen. Depending on the context, Lewis acids may also be described as a reducing agent or an electrophile.

Dissociation and Equilibrium

Reactions of acids are often generalized in the form HA  H⁺ + A⁻, where HA represents the acid and A⁻ is the conjugate base. Acid–base conjugate pairs differ by one proton, and can be interconverted by the addition or removal of a proton (protonation and deprotonation, respectively). Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA  H⁺ + A. In solution there exists an equilibrium between the acid and its conjugate base. The equilibrium constant K is an expression of the equilibrium concentrations of the molecules or the ions in solution. Brackets indicate concentration, such that [H₂O] means the concentration of H₂O. The acid dissociation constant K_a is generally used in the context of acid-base reactions. The numerical value of K_a is equal to the concentration of the products divided by the concentration of the reactants, where the reactant is the acid (HA) and the products are the conjugate base and H⁺.

The stronger of two acids will have a higher K_a than the weaker acid; the ratio of hydrogen ions to acid will be higher for the stronger acid as the stronger acid has a greater tendency to lose its proton. Because the range of possible values for K_a spans many orders of magnitude, a more manageable constant, pK_a is more frequently used, where pK_a = −log₁₀K_a. Stronger acids have a smaller pK_a than weaker acids. Experimentally determined pK_a at 25°C in aqueous solution are often quoted in textbooks and reference material.

Acid Strength

For peelers, this notion is very important because stronger acids have a higher K_a and a lower pK_a than weaker acids.

For our classification, two parameters have to be taken in consideration for peelers:

For chemists, the strength of an acid refers to its ability or tendency to lose a proton. A strong acid is one that completely dissociates in water; in other words, one mole of a strong acid HA dissolves in water yielding one mole of H⁺ and one mole of the conjugate base, A⁻, and none of the protonated acid HA. In contrast a weak acid only partially dissociates and at equilibrium both the acid and the conjugate base are in solution. In water each of these essentially ionizes 100%. The stronger an acid is, the more easily it loses a proton, H⁺. Two key factors that contribute to the ease of deprotonation are the polarity of the H—A bond and the size of atom A, which determines the strength of the H—A bond. Acid strengths are also often discussed in terms of the stability of the conjugate base.

According to the classification of A. Tenenbaum, which is described later in this chapter, peelers should be careful with the dangerous distinction between so called ‘cosmetic’, peelings for acids with pK_a > 3 and ‘medical’, peelings for acids with pK_a < 3, because some acids like salicylic acid with a pK_a near 3, as the phenol, toxic substance with a pK_a > 3 need to be exclusively used by trained physicians.

Monoprotic Acids

Monoprotic acids are those acids that are able to donate one proton per molecule during the process of dissociation (sometimes called ionization) as shown below (symbolized by HA):

Common examples of monoprotic acids in organic acids indicate the presence of one carboxyl group and mostly these acids are known as monocarboxylic acid. Examples in organic acids include acetic acid (CH₃COOH), glycolic acid and lactic acid.

Polyprotic Acids

Polyprotic acids are able to donate more than one proton per acid molecule, in contrast to monoprotic acids that only donate one proton per molecule. Specific types of polyprotic acids have more specific names, such as diprotic acid (two potential protons to donate) and triprotic acid (three potential protons to donate).

A diprotic acid (here symbolized by H₂A) can undergo one or two dissociations depending on the pH. Each dissociation has its own dissociation constant, K_a1 and K_a2.

The first dissociation constant is typically greater than the second; i.e., K_a1 > K_a2. For example, the weak unstable carbonic acid (H₂CO₃) can lose one proton to form bicarbonate anion (HCO₃⁻) and lose a second to form carbonate anion (CO₃²⁻). Both Ka values are small, but K_a1 > K_a2.

Diprotic acids used for peelings are malic, tartaric and azelaic acids.

Two dissociations depending on the pH mean that such acids can generate two peelings with the second one less acidic than the first one, in case we consider one peeling reaction per one dissociation.

A triprotic acid (H₃A) can undergo one, two, or three dissociations and has three dissociation constants, where K_a1 > K_a2 > K_a3.

An organic example of a triprotic acid is citric acid, which can successively lose three protons to finally form the citrate ion. Even though the positions of the protons on the original molecule may be equivalent, the successive K_a values will differ since it is energetically less favorable to lose a proton if the conjugate base is more negatively charged.

Weak Acid/Weak Base Equilibria

In order to lose a proton, it is necessary that the pH of the system rise above the pK_a of the protonated acid. The decreased concentration of H⁺ in that basic solution shifts the equilibrium towards the conjugate base form (the deprotonated form of the acid). In lower-pH (more acidic) solutions, there is a high enough H⁺ concentration in the solution to cause the acid to remain in its protonated form, or to protonate its conjugate base (the deprotonated form).

Solutions of weak acids and salts of their conjugate bases form buffer solutions.

Le Chatelier’s Principle

In a solution there is an equilibrium between a weak acid, HA, and its conjugate base, A⁻:

Thus, in both cases, some of the added reagent is consumed in shifting the equilibrium in accordance with Le Chatelier’s principle and the pH changes by less than it would if the solution were not buffered.

Henderson–Hasselbach Equation

The acid dissociation constant for a weak acid, HA, is defined as:

Simple manipulation with logarithms gives the Henderson–Hasselbach equation, which describes pH in terms of pK_a:

In this equation [A⁻] is the concentration of the conjugate base and [HA] is the concentration of the acid. It follows that when the concentrations of acid and conjugate base are equal, often described as half-neutralization, pH = pK_a. In general, the pH of a buffer solution may be easily calculated, knowing the composition of the mixture, by means of an ICE table.

One should remember that the calculated pH may be different from measured pH.

Buffer Capacity

Figure 1.1 Buffer capacity for pK_a = 7 as percentage of maximum

Buffer capacity is a quantitative measure of the resistance of a buffer solution to pH change on addition of hydroxide ions. It can be defined as follows:

where dn is an infinitesimal amount of added base and d(pH) is the resulting infinitesimal change in pH. With this definition the buffer capacity can be expressed as:

where K_w is the self-ionization constant of water and C_A is the analytical concentration of the acid, equal to [HA]+[A⁻]. The term K_w/[H⁺] becomes significant at pH greater than about 11.5 and the second term becomes significant at pH less than about 2. Both these terms are properties of water and are independent of the weak acid. Considering the third term, it follows that:

Useful Buffer Mixtures

Neutralization

There is among physicians a big confusion between a buffered peel (see above) and a neutralized peel. In chemistry, neutralization is a chemical reaction whereby an acid and a base react to form water and a salt.