Objectives After completing this section, you should be able to write the expression for the K a of any given weak acid, HA. convert a given K a value into a p K a value, and vice versa . arrange a series of acids in order of increasing or decreasing strength, given their K a or p K a values. arrange a series of bases in order of increasing or decreasing strength, given the K a or p K a values of their conjugate acids. Key Terms Make certain that you can define, and use in context, the key terms below. acidity constant, K a equilibrium constant, K eq Study Notes Calculations and expressions involving K a and p K a were covered in detail in your first-year general chemistry course. Note that acidity constant is also known as the acid dissociation constant. 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 K a . 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, K eq . \[ K_{eq} = \dfrac{[CH_3COO^-][H_3O^+]}{[CH_3COOH][H_2O]}\] 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 K a , 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: \[ K_a = \dfrac{[A^-][H_3O^+]}{[HA]} \label{First}\] or \[ K_a = \dfrac{[A][H_3O^+]}{[HA^+]} \label{Second}\] Equation \(\ref{First}\) applies to a neutral acid such as like HCl or acetic acid, while Equation \(\ref{Second}\) applies to a cationic acid like ammonium (NH 4 + ). The value of K a = 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 (K a = 10 9 ) or hydrochloric acid (K a = 10 7 ), 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 pK a value. \[pK_a = -\log K_a\] Doing the math, we find that the pK a of acetic acid is 4.8. The use of pK a 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 2.8.1 at the end of the text lists exact or approximate pK a values for different types of protons that you are likely to encounter in your study of organic and biological chemistry. Looking at Table \(\PageIndex{1}\), you see that the pK a of carboxylic acids are in the 4-5 range, the pK a of sulfuric acid is –10, and the pK a of water is 15.7. Alkenes and alkanes, which are not acidic at all, have pK a values above 30. The lower the pK a value, the stronger the acid. Table \(\PageIndex{1}\): Representative acid constants It is important to realize that pK a 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 pK a (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 pK a values will also allow us to compare the strengths of different bases by comparing the pK a values 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 pK a value of –10, so HSO 4 - is the weakest conjugate base. You can see that hydroxide ion is a stronger base than ammonia (NH 3 ), because ammonium (NH 4 + , pK a = 9.2) is a stronger acid than water (pK a = 15.7). The stronger the conjugate acid, the weaker the conjugate base. While Table \(\PageIndex{1}\) provides the pK a 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 pK a of cyclohexanol? It is not on the table, but as it is an alcohol it is probably somewhere near that of ethanol (pK a = 16). Likewise, we can use Table \(\PageIndex{1}\) to predict that para-hydroxyphenyl acetaldehyde, an intermediate compound in the biosynthesis of morphine, has a pK a 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 (pK a values are above 40 – not on our table). The two protons on the carbon next to the carbonyl are slightly acidic, with pK a 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 pK a 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 pK a 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 (NH 3 ) compared to that of ethoxide ion (CH 3 CH 2 O - ), for example, the relevant pK a values to consider are 9.2 (the pK a of ammonium ion) and 16 (the pK a of ethanol). From these numbers, you know that ethoxide is the stronger base. Do not make the mistake of using the pK a value of 38: this is the pK a of ammonia acting as an acid , and tells you how basic the NH 2 - ion is (very basic!) Example 2.8.1 Using the pK a table, estimate pK a 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. Use the pKa table above and/or from the Reference Tables. Answer a. The most acidic group is the protonated amine, pKa ~ 5-9 b. Alpha proton by the C=O group, pKa ~ 18-20 c. Thiol, pKa ~ 10 d. Carboxylic acid, pKa ~ 5 e. Carboxylic acid, pKa ~ 5 Exercises Write down an expression for the acidity constant of acetic acid, CH 3 COOH. The p K a of acetic acid is 4.72; calculate its K a . The K a of benzoic acid is 6.5 × 10 −5 ; determine its p K a . From your answers to the questions above, determine whether acetic acid or benzoic acid is stronger. Answers: K a = [ CH 3 CO 2 − ] [ H + ] [CH 3 CO 2 H] or K a = [ CH 3 CO 2 − ] [ H 3 O + ] [CH 3 CO 2 H] p K a = − log 10 K a = 4.74 Thus, log 10 K a = − 4.72 and K a = anti-log ( − 4.72 ) = 1 .9 × 10 − 5 p K a = − log 10 K a = − log 10 ( 6.5 × 10 − 5 ) = − ( − 4.19 ) = 4.19 Benzoic acid is stronger than acetic acid. [Benzoic acid has a higher K a and a lower p K a .]