Sección 2: Comparando la acidez y basicidad de los grupos funcionales orgánicos - el constante de acidez

7.2A: Defining  Ka and pKa

You are no doubt aware that some acids are stronger than others.  Sulfuric acid is strong enough to be used as a drain cleaner, as it will rapidly dissolve clogs of hair and other organic material.

Not surprisingly, concentrated sulfuric acid will also cause painful burns if it touches your skin, and permanent damage if it gets in your eyes (there’s a good reason for those safety goggles you wear in chemistry lab!).  Acetic acid (vinegar), will also burn your skin and eyes, but is not nearly strong enough to make an effective drain cleaner.  Water, which we know can act as a proton donor, is obviously not a very strong acid.  Even hydroxide ion could theoretically act as an acid – it has, after all, a proton to donate – but this is not a reaction that we would normally consider to be relevant in anything but the most extreme conditions.

The relative acidity of different compounds or functional groups – in other words, their relative capacity to donate a proton to a common base under identical conditions – is quantified by a number called the dissociation constant, abbreviated Ka. The common base chosen for comparison is water.

We will consider acetic acid as our first example.  When a small amount of acetic acid is added to water, a proton-transfer event (acid-base reaction) occurs to some extent.

Notice the phrase ‘to some extent’ – this reaction does not run to completion, with all of the acetic acid converted to acetate, its conjugate base.  Rather, a dynamic equilibrium is reached, with proton transfer going in both directions (thus the two-way arrows) and finite concentrations of all four species in play.  The nature of this equilibrium situation, as you recall from General Chemistry, is expressed by an equilibrium constant, Keq.

We added a small amount of acetic acid to a large amount of water: water is the solvent for this reaction. Therefore, in the course of the reaction, the concentration of water (approximately 55.6 mol/L) changes very little, and can be treated as constant. The acid dissociation constant, or Ka, for acetic acid is defined as:

$K_a=K_{eq}[H_2O] = \dfrac{[CH_3COO^-][H_3O^+]}{[CH_3COOH]} = 1.75 \times 10^{-5}$

In more general terms, the dissociation constant for a given acid is expressed as:

The first expression applies to a neutral acid such as like HCl or acetic acid, while the second applies to a cationic acid like ammonium (NH4+).

The value of Ka = 1.75 x 10-5 for acetic acid is very small  - this means that very little dissociation actually takes place, and there is much more acetic acid in solution at equilibrium than there is acetate ion. Acetic acid is a relatively weak acid, at least when compared to sulfuric acid (Ka = 109) or hydrochloric acid (Ka = 107), both of which undergo essentially complete dissociation in water.

A number like 1.75 x 10- 5 is not very easy either to say or to remember. Chemists have therefore come up with a more convenient term to express relative acidity: the pKa value.

$pK_a = -\log K_a$

Doing the math, we find that the pKa of acetic acid is 4.8.  The use of pKa values allows us to express the acidity of common  compounds and functional groups on a numerical scale of about –10 (very strong acid) to 50 (not acidic at all). Table 7 at the end of the text lists exact or approximate pKa values for different types of protons that you are likely to encounter in your study of organic and biological chemistry.  Looking at Table 7, you see that the pKa of carboxylic acids are in the 4-5 range, the pKa of sulfuric acid is –10, and the pKa of water is 15.7. Alkenes and alkanes, which are not acidic at all, have pKa values above 30.

Note

The lower the pKa value, the stronger the acid.

It is important to realize that pKa is not at all the same thing as pH: the former is an inherent property of a compound or functional group, while the latter is the measure of the hydronium ion concentration in a particular aqueous solution:

$pH = -\log [H_3O^+]$

Any particular acid will always have the same pKa (assuming that we are talking about an aqueous solution at room temperature) but different aqueous solutions of the acid could have different pH values, depending on how much acid is added to how much water.

Our table of pKa values will also allow us to compare the strengths of different bases by comparing the pKavalues of their conjugate acids.  The key idea to remember is this: the stronger the conjugate acid, the weaker the conjugate base.  Sulfuric acid is the strongest acid on our list with a pKa value of –10, so HSO4- is the weakest conjugate base.  You can see that hydroxide ion is a stronger base than ammonia (NH3), because ammonium (NH4+, pKa = 9.2) is a stronger acid than water (pKa = 15.7).

While Table 7 provides the pKa values of only a limited number of compounds, it can be very useful as a starting point for estimating the acidity or basicity of just about any organic molecule. Here is where your familiarity with organic functional groups will come in very handy.  What, for example, is the pKaof cyclohexanol? It is not on the table, but as it is an alcohol it is probably somewhere near that of ethanol (pKa = 16).  Likewise, we can use Table 7 to predict that para-hydroxyphenyl acetaldehyde, an intermediate compound in the biosynthesis of morphine, has a pKa in the neighborhood of 10, close to that of our reference compound, phenol.

Notice in this example that we need to evaluate the potential acidity at four different locations on the molecule.

Aldehyde and aromatic protons are not at all acidic (pKavalues are above 40 – not on our table). The two protons on the carbon next to the carbonyl are slightly acidic, with pKa values around 19-20 according to the table. The most acidic proton is on the phenol group, so if the compound were to be subjected to a single molar equivalent of strong base, this is the proton that would be donated.

As you continue your study of organic chemistry, it will be a very good idea to commit to memory the approximate pKa ranges of some important functional groups, including water, alcohols, phenols, ammonium, thiols, phosphates, carboxylic acids and carbons next to carbonyl groups (so-called a-carbons). These are the groups that you are most likely to see acting as acids or bases in biological organic reactions.

A word of caution: when using the pKa table, be absolutely sure that you are considering the correct conjugate acid/base pair.  If you are asked to say something about the basicity of ammonia (NH3) compared to that of ethoxide ion (CH3CH2O-), for example, the relevant pKa values to consider are 9.2 (the pKa of ammonium ion) and 16 (the pKa of ethanol). From these numbers, you know that ethoxide is the stronger base. Do not make the mistake of using the pKa value of 38: this is the pKa of ammonia acting as an acid, and tells you how basic the NH2- ion is (very basic!)

Example 7.2

Using the pKa table, estimate pKa values for the most acidic group on the compounds below, and draw the structure of the conjugate base that results when this group donates a proton.

7.2B: Using pKa values to predict reaction equilibria

By definition, the pKa value tells us the extent to which an acid will react with water as the base, but by extension, we can also calculate the equilibrium constant for a reaction between any acid-base pair.  Mathematically, it can be shown that:

Keq (for the acid base reaction in question) = 10ΔpKa

where ΔpKa = pKa of product acid minus pKa of reactant acid.

Consider a reaction between methylamine and acetic acid:

First, we need to identify the acid species on either side of the equation.  On the left side, the acid is of course acetic acid, while on the right side the acid is methyl ammonium. The specific pKa values for these acids are not on our very generalized pKa table, but are given in the figure above. Without performing any calculations, you should be able to see that this equilibrium lies far to the right-hand side: acetic acid has a lower pKa, is a stronger acid, and thus it wants to give up its proton more than methyl ammonium does.  Doing the math, we see that

Keq = 10ΔpKa = 10(10.6 – 4.8) = 105.8 = 6.3 x 105

So Keqis a very large number (much greater than 1) and the equilibrium lies far to the right-hand side of the equation, just as we had predicted.  If you had just wanted to approximate an answer without bothering to look for a calculator, you could have noted that the difference in pKa values is approximately 6, so the equilibrium constant should be somewhere in the order of 106, or one million. Using the pKa table in this way, and making functional group-based pKa approximations for molecules for which we don’t have exact values, we can easily estimate the extent to which a given acid-base reaction will proceed.

Example 7.3

Show the products of the following acid-base reactions, and estimate the value of Keq

7.2C: pKa and pH: the Henderson-Hasselbalch equation

It was mentioned previously that pKa and pH are not the same thing - however, they are related.  Probably the most commonly-used equation relating the two concepts is known as the Henderson-Hasselbalch equation (which is really just a rearrangement of the equation that defines pKa):

If an acid is exactly 50% dissociated in aqueous solution, then the concentration of A- is equal to the concentration of HA, and the fraction term in the Henderson-Hasselbalch equation is equal to 1.  Because log(1) = 0, it follows that pH = pKa at these conditions.  This is very useful: it means that the pKa of an acid is equal to the pH at which it is 50% disassociated (deprotonated).  For example, if a 0.1 M  aqueous solution of acetic acid is brought to pH 4.8 by the addition of sodium hydroxide, we know by the Henderson-Hasselbalch equation that the solution is now 0.05 M in acetic acid and 0.05 M in acetate ion.

The above situation – an aqueous solution that contains equal or nearly equal concentrations of a weak acid and its conjugate base – should sound very familiar to you.  This is a buffer!  As we discuss the organic reactions that occur in living things, it will be very important to always keep in mind that most of these reactions are occurring in an aqueous solution that is buffered to approximately pH 7.3 (the exceptions are reactions occuring in lysosomes and endosomes, specialized organelles in eukaryotic cells that maintain a slightly acidic interior). The buffer in a living cell is not composed of acetic acid/acetate mixture, or course – that would make the pH far too acidic.  Rather, the chemistry of life occurs in a buffer that consists of a mixture of various phosphate and ammonium compounds.

So, what does the side chain of an aspartate amino acid residue look like if it is on the surface of a protein in an aqueous solution buffered to pH 7.0? Is it protonated or deprotonated?  With an approximate pKa of 3.9, the Henderson-Hasselbalch equation tells us that the side chain should be greater than 99% deprotonated:

7.0 = 3.9 + log ([A-] / [HA])

([A-] / [HA]) = 1.3 x 103

. . . so,  [A-] >> [HA]

What about the amino group on a lysine side chain?  With an approximate pKa of 10.8, it should be >99% protonated, in the positively-charged, ammonium form:

7.0 = 10.8 + log ([A] / [HA+])

([A] / [HA+]) = 1.6 x 10-4

. . . so,  [HA+] >> [A]

So, in an aqueous solution buffered at pH 7, carboxylic acid groups can be expected to be essentially 100% deprotonated and negatively charged (ie. in the carboxylate form), and amine groups essentially 100% protonated and positively charged (i.e., in the ammonium form).  Alcohols are fully protonated and neutral at pH 7, as are thiols. The imidizole group on the histidine side chain has a pKa near 7, and thus exists in physiological solutions as mixture of both protonated and deprotonated forms.

Example 7.4

Exercise 7.4:  If an arginine side chain in a protein is exposed to buffer with pH = 8.5, to what extent (expressed as a percentage) is it deprotonated?

Exercise 7.5:  A small amount of acetic acid is dissolved in a buffer of pH = 5.2.  What percent of the acetic acid molecules are charged?