1.5 Acids and Bases: The Arrhenius and Lowry-Brønsted Theories

The concepts of acid and base are central to chemistry as a whole. A vast majority of organic reactions are either promoted by acids or bases, or involve the participation of acids or bases at some stage of the reaction pathway. Moreover, the application of acid-base chemistry in organic chemistry is wide-reaching: unlike the other subdisciplines of chemistry, an overwhelming majority of reactions are carried out in media other than water. This means that the concepts of acids and bases must be applied to a much broader range of conditions than those that applied when most of us learned about acids and bases for the first time. However, let us begin by reviewing the definitions of acids and bases in aqueous solution.    Arrhenius acids and bases  

The earliest operational definitions of acids and bases were related to the neutralization of acids by bases given by the relatively simple equation that follows (equation 1.6):    

                                Acid + Base Salt + Water                                 (1.6)

This simple equation defines neutralization: the destruction of an acid by an equivalent amount of base to give a salt. The formation of the water itself comes from the neutralization process, a situation forst recognized by the great Swedish chemist, Svante Arrhenius. As part of his dissociation theory of electrolytes (that when ionic compounds dissolve in water the ions dissociate and become free to move within the solution), Arrhenius looked at electrolytes that were originally non-conductors, and proposed the first definition of an acid:  

An acid is a substance which functions as a source of hydrogen ions in aqueous solution  

Once acids had been defined in this manner, the extension of this definition to bases was relatively straightforward; the Arrhenius definition of a base states:  

A base is a substance which functions as a source of hydroxide ions in aqueous solution  

The strength of an acid is related to the ease with which it functions as a hydrogen ion (or, more accurately, hydronium ion) source in aqueous solution. The functional definitions of strong and weak acids are still based largely upon the Arrhenius definition. Strong acids ionize (dissociate) completely in aqueous solution, and many are familiar to most students in chemistry: sulfuric acid (H2SO4), nitric acid (HNO3), hydrochloric acid (HCl), hydrobromic acid (HBr), hydriodic acid (HI), and perchloric acid (HClO4) are among the more familiar strong acids. All these acids are covalent when pure, but dissolve in water to give a strongly conducting solution containing hydronium (H3O+) ions. The pH of 1 M solutions of these acids is typically quite low — close to zero. Weak acids, on the other hand, do not dissolve to give complete dissociation. Instead, much of a weak acid remains unionized in aqueous solution. Typical weak acids are compounds such as acetic acid (CH3COOH), which ionizes only to the extent of a few percent in a 1 M solution; the pH of a 1 M solution of a weak acid is much more likely to be close to 2 or 3, indicating a hydronium ion concentration only a few percent of that of a strong acid.

In a similar vein, the strength of a base is related to the ease with which it functions as a source of hydroxide ions in aqueous solution: strong bases are good sources of hydroxide ions in aqueous solution and weak bases are not. Most of the strong bases commonly used in aqueous solution are ionic hydroxides that already have the hydroxide ion present, and so need only dissolve to dissociate and liberate their hydroxide ion. The ionic hydroxides of the Group IA and heavier Group IIA metals, especially those of the Group IA metals, dissolve freely in water to give solutions containing high concentrations of hydroxide ions: LiOH, NaOH and KOH are all widely used as strong bases. Ammonia, on the other hand, dissolves extremely well in water, but it does so without extensive ionization. Ammonia solutions, often labeled as "ammonium hydroxide" are actually best described as ammonia molecules dissolved in water, with only a few percent being converted to ammonium and hydroxide ions. Like the aqueous solutions of weak acids, aqueous solutions of weak bases like ammonia are relatively poor electrolytes.

There are two structural features which one can use to predict the probable strength of an acid: the atom to which the acidic hydrogen is bonded, and the number of multiple bonds between the central atom and oxygen in oxyacids. In general, as the electronegativity of the element bonded to the acidic hydrogen atom increases, acid strength increases: O—H hydrogens are more acidic than N—H hydrogens, which are, in turn, more acidic than C—H hyrogens. Acid strength also increases dramatically as the element to which the hydrogen is bonded becomes larger: although hydrogen fluoride is a relatively weak acid (pKa = 2), hydrogen iodide is the strongest binary (two-element) acid known. The effects of multiple bonds between the central atom and oxygen atoms also appears to be cumulative: hypochlorous acid (H

—O—Cl), which has no chlorine-oxygen double bonds, is a very weak acid; perchloric acid (HClO4), which has three oxygen atoms doubly-bonded to the central chlorine atom, is one of the strongest acids known.    

Lowry-Brønsted acids and bases  

Not all chemistry is carried out in aqueous solution, and not all acid-base reactions result in the formation of water. There are, in fact, many cases where an acid-base reaction has obviously occurred, but where no water is formed. For example, hydrogen chloride gas reacts with ammonia gas to form ammonium chloride, a salt. Since hydroxide ion is never involved in this reaction, it does not fit well with the Arrhenius definition of an acid-base reaction. And yet, this reaction clearly leads to the neutralization of the hydrogen chloride, the acid, and the ammonia, the base, leading to the formation of the salt. A more widely applicable definition of acids and bases is that due to Lowry and Brønsted, who extended the Arrhenius definition of acids and bases to cover just such situations. In the Lowry-Brønsted definition,

                    an acid is a hydrogen ion donor; a base is a hydrogen ion acceptor.    

Figure 1.8 The transfer of a proton to a proton acceptor is an acid-base reaction under the Lowry-Brønsted definition. Here, the proton is transferred from a molecule of hydrogen chloride to a molecule of methanol to generate its conjugate

acid, methyloxonium ion.    

A simple example of an acid-base reaction by the Lowry-Brønsted definition is the protonation of the methanol molecule by hydrogen chloride to give the methyloxonium ion. The oxygen atom of the methanol molecule is functioning as the proton acceptor, and is therefore the base. The hydrogen chloride molecule is the proton donor, and is therefore the acid. When a proton is removed from an acid, H—A, the anion formed, A-, is termed the conjugate base of the acid. When a proton is added to a base, the product of the reaction is termed the conjugate acid of the base. Thus, during the course of the reaction in Figure 1.8, the acid (hydrogen chloride) is converted to its conjugate base (chloride ion), while the base (methanol) is converted to its conjugate acid (methyloxonium ion).

Because of the frequency and importance of proton-transfer reactions in organic chemistry, some familiarity with the concepts of acidity constant, Ka, are required. The acidity constant of a Lowry-Brønsted acid was originally defined in terms of its ability to form hydronium ion, H3O+, from water, and is given in equation 1.8:  

                            HA + H2O H3O+ + A-                                 (1.7)    

                                                 (1.8)

However, with the extension of acid-base chemistry into non-aqueous reaction solvents, this definition is rather too narrow, and we are now in a position where equation 1.7 is too limiting. Nevertheless, we have retained the concept of the acidity constant, Ka, and its negative logarithm (base 10), the pKa, as useful measures of the relative acid strength of a species in solution. Many of these values for organic compounds, however, have been measured indirectly, by competition reactions in a non-aqueous , for example.

As the acid (or base) becomes stronger, its conjugate base (or acid) becomes weaker. Thus, for a strong acid such as hydrogen chloride (or hydrochloric acid), the conjugate base (chloride anion) is weak, while for a weak acid such as water, the conjugate base (hydroxide anion) is strong. All acid-base reactions proceed to give the weaker of the two conjugate acids and the weaker of the two conjugate bases as the products of the reaction.

Let us examine the case of a simple proton-transfer reaction between an acid, HA, and a base, B-:

                                HA + B- HB + A-                                 (1.9)

The equilibrium constant for this reaction is given by equation 1.10.

                                             (1.10)By multiplying both the numerator and the denominator of this expression by [H3O+], expression 1.11 is obtained.

                             (1.11)Reorganization of equation 1.11 gives the particularly useful expression 1.12.

                                              (1.12)

What equation 1.12 tells us is that if HA is a stronger acid than HB (i.e. if the Ka of HA is greater than the Ka of HB), then the equilibrium for the reaction of HA with B- will lie to the right, and that the equilibrium constant for the reaction will be given by the ratios of the Ka values for the two acids. The other measure of acidity, the pKa, which was defined earlier as —log10(Ka), is a much more commonly used measure of acid strength. Stronger acids have an algebraically smaller value of the pKa than weaker acids. Using pKa values for the two acids, the expression given as 1.12 can be rewritten as the useful equations 1.13 and 1.14:

                                 (1.13)

                                                                      (1.14)

As pointed out earlier, acid strength of a covalent compound varies with the element to which the acidic hydrogen is bonded. As the elementv to which the acidic hydrogen is bonded becomes larger, the acid strength increases, and as the electronegativity of the element bonded to the acidic hydrogen increases, acid strength increases. This allows us to observe that Se—H bonds are more acidic than S—H bonds and that S—H bonds are, in turn more acidic than O—H bonds, and that O—H bonds are more acidic than N?H bonds, which are, in turn, more acidic than C—H bonds. One consequence of this is that we can expand our view of acids and, morte particularly, bases. Bases such as amide anion, NH2

-, the conjugate base of ammonia (NH3, pKa = 35) and methyllithium, CH3Li, the conjugate base of methane (CH4, pKa = 45-60), are much stronger bases than hydroxide ion, the conjugate base of water. It is worth repeating here that although the pKa scale was originally defined for Lowry-Brønsted acids in aqueous solution, we will use it for a wide variety of acids and bases which are much too strong to exist in aqueous solution without reacting with the water. Some typical pKa ranges are given in Table 1.8.

   

Table 1.8 Typical Ranges of p K a Values for Representative Acids.  

Functional

Acidic

    Conjugate

  pKa

Group Bond Acid Examples

Base Examples

range

alcohol O—H RO—H H2O, (CH3)3C—OH

RO- OH-, (CH3)3C—O-

15-19

carboxylic acid

COO—H

RCOO—H

HCO—OH, CH3CO—OH

RCO—O-

HCO—O-, CH3CO—O-

4-6

amine N—H R2N—H NH3, (CH3)2CH—NH2

R2N- NH2-,

(CH3)2CH—NH-

33-38

amide CON—H

RCONR—H

CH3CO—NH2

RCONR-

CH3CO—NH-

15-17

alkane C—H R—H CH4, (CH2)6

R- CH3-,

[(CH2)5CH]-

45-60

alkyne CC—H

RCC—H CH3—CC—H

RCC- CH3—CC- 25-30

aldehyde, ketone

COC—H

RCOCR2

—HCH3COCH3

RCOCR2

-CH3COCH2-

25-30

 

Let us now examine some examples of acid-base reactions in organic chemistry, and see just how to approasch the problems associated with proton transfer chemistry.    

Example 1. CH3Li + H2O

In this reaction, as in all potential acid-base reactions, we must first identify the acid and the base. While doing so, we must keep in mind that there is one acid and one base on each side of the arrow. In this example, the two species reacting are methyllithium, CH3Li, and water, H2O. The methyllithium is a compound that contains a Group IA metal, lithium, and we are usually safe in considering that such compounds will react as ionic compounds containing Li+ cations. This means that methyllithium also contains the CH3

- anion. This ion is capable of accepting a proton to become the neutral molecule, methane, CH3—H (or CH4); it is the conjugate base of methane. More importantly, it is highly unlikely that CH3

- will readily lose a proton to become CH2

2-. Therefore, the water is almost certain to be the source of protons in this reaction. At this point, we can fill out the table of reacting species:

  Reacting species

Conjugate

Acid H2O OH-

Base CH3-  CH4

 

This now allows us to write the balanced equation for this reaction:

                CH3- +Li + H2O CH4 + Li+ -OH.

From the data in Table 1.8, we find that the pKa of H2O is in the range 15-18, and the pKa of CH4 is in the range 45-60. On substituting these values in Equation 1.14, we obtain:

                 and 

as the minimum and maximum values for the equilibrium constant for this reaction. These are both huge numbers, so we expect that methyllithium will react completely with water to give methane gas and lithium hydroxide. It does — methyllithium is rapidly (explosively) and quantitatively destroyed by water.    

Example 2. LiN(CH3)2 + (CH2)5

Our first step this reaction, also, is to identify the acid and the base. In this example, the two species reacting are lithium dimethylamide, LiN(CH3)2, and cyclopentane, (CH2)5. Again, we may consider that the lithium dimethylamide

will react as an ionic lithium compound, which means that it contains the (CH3)2N- anion. This ion is capable of accepting a proton to become the neutral molecule, dimethylamine, (CH3)2N—H; it is the conjugate base of dimethylamine. Therefore, the cyclopentane, which cannot accept a proton, is forced to be the source of protons in this reaction. At this point, we can fill out the table of reacting species:

  Reacting species

Conjugate

Acid (CH2)5 [(CH2)4CH]-

Base (CH3)2N-  (CH3)2NH

 

This now allows us to write the balanced equation for this reaction:

                    (CH3)2N- +Li + (CH2)5 (CH3)2NH + [(CH2)4CH]- Li+.

From the data in Table 1.8, we find that the pKa of (CH2)5 is in the range 45-60, and the pKa of (CH3)2NH is in the range 33-38. On substituting these values in Equation 1.14, we obtain:

and 

as the maximum and minimum values for the equilibrium constant for this reaction. These are both very small numbers, so we expect that lithium dimethylamide will not react with cyclopentane. In fact, these numbers suggest that the reverse reaction (between cyclopentyllithium and dimethylamine to give cyclopentane and lithium dimethylamide) should be the one that actually occurs, and this is observed.    

Sample Problem 1.16. Complete the following equations using the approximate pKa values given in Table 1.8. If no reaction should occur, write "N/R" and give the reason.    

(a) CH3CH2CH2CH2Li + CH3OH

(b) NaNH2 + HCC—CH2CH3

(c) LiN(CH3)2 + (CH2)5

Answers:

(a) CH3CH2CH2CH2Li + CH3OH CH3CH2CH2CH3 + Li+OCH3-

(b) NaNH2 + HCC—CH2CH3 Na+ -CC—CH2CH3 + NH3

Note that in this reaction, only the hydrogen directly attached to the triple bond is attacked. Its pKa from Table 1.8 is approximately 25-30, making it a stronger acid than ammonia; the approximate pKa values of the other hydrogens are predicted to be in the 45-60 range.

(c) LiN(CH2CH3)2 + (CH3)4C N/R.

The conjugate acid of LiN(CH2CH3)2 is H-N(CH2CH3)2, which is a stronger acid than (CH3)4C. Using equation 1.13 and the pKa values in Table 1.8, we can calculate that the equilibrium constant in favor of products will be less than 10-5, corresponding to no reaction; the equilibrium strongly favors the weaker acid and the weaker base.    

Problem 1.15. Arrange the following compounds in the expected increasing order of their solubility in water. Give your reasoning.    

(a) CH3(CH2)4OHCH3; (CH3CH2)CHOH; CH3CH2C(CH3)2OH.

(b) (CH3)3COH; (CH3)3CCH2CH2OH; (CH3CH2)3COH.

(c) (CH3)3CCH2NH2; (CH3)2CHCH2NHCH3; (CH3)2NCH2CH2CH3.    

Problem 1.16. n-Butyl alcohol (CH3CH2CH2CH2OH) and diethyl ether (CH3CH2OCH2CH3) have the same solubility in water, but the boiling point of diethyl ether is 35°C while the boiling point of n-butyl alcohol is 118°C. Explain these observations.    

Leveling effect    

There is one very important consequence of equations 1.12 and 1.13, and this is known as the leveling effect. Simply stated, the leveling effect states that one cannot use an acid or base in a solvent which has a stronger conjugate base or acid than the acid one is trying to use. In other words, the solvent limits both the strongest acid you can use (the conjugate acid of the solvent) and the strongest base (the conjugate base of the solvent). In water, for example, this means that any attempt to use an acid stronger than hydronium ion, H3O+, is doomed to failure, as is any attempt to use a base stronger than hydroxide ion, OH- because the stronger acid will simply react with the water to give hydronium ion, and the stronger base will, likewise, react with the water to give hydroxide ion. For example, since methane (CH4) has a pKa of 45-60, one cannot use its conjugate base, methyllithium (CH3Li) in any solvent with a pKa less than this. Using the equation of Sample Problem 1.16(a), above, we see that if one tries to use methyllithium in water, the solvent reacts with the base to give lithium hydroxide (the conjugate base of water) and methane. For similar reasons, one cannot use concentrated sulfuric acid (pKa = —7) in aqueous solution, because it reacts with the water to give the conjugate acid of water, hydronium ion, H3O+. It is a frequent and common error committed by learning students to attempt to use H3O+ and OH- in the same solution: of course, these two react to give water; similar errors are frequently made using other incompatible acid-base combinations.