2.3: Weak Acids and Bases, pH and pKa

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Learning Goals 

(Learning goals written by Claude, Sonnet 4.6, Anthropic)

Acid-Base Equilibria and the Henderson-Hasselbalch Equation

• Define pKa as a concentration-independent measure of intrinsic acid strength, rank the common biochemical functional groups (alkanes, amines, alcohols, thiols, imidazoles, carboxylic acids, phosphoric acid) by relative acidity, and explain in thermodynamic terms why stronger acids produce weaker conjugate bases.
• Derive and apply the Henderson-Hasselbalch equation to calculate the ratio of protonated to deprotonated forms of a functional group at a given pH, and use the ±2 rule to rapidly estimate charge state without calculation.
• Interpret a titration curve for a monoprotic or polyprotic acid, identifying the equivalence point, the buffering region, and the relationship between the inflection point and pKa — and extend this analysis to triprotic biological acids such as phosphoric acid and polyprotic amino acids.

Charge State of Biomolecules

• Predict the protonation state and net charge of ionizable groups in small molecules and macromolecules (carboxylic acids, phosphates, amines, imidazoles, guanidinium groups) at physiological pH, and explain how phosphorylation of serine, threonine, or tyrosine side chains converts a neutral hydroxyl group into a doubly negative phosphoester.
• Explain how the charge state of ionizable groups in proteins governs their nucleophilicity, capacity for ion-ion interactions, and overall protein behavior — and connect these properties to the mechanistic roles of specific amino acid side chains in enzyme catalysis.

Environmental Modulation of pKa

• Explain why pKa values are sensitive to the local dielectric environment, and predict the direction of pKa shifts when an ionizable group is transferred from bulk aqueous solution to a nonpolar protein interior or to a solvent of lower dielectric constant.
• Rationalize large deviations of protein residue pKa values from their solution-phase reference values — including the extreme cases of Asp 70 in T4 lysozyme (pKa 0.5) and Asp 26 in thioredoxin (pKa 9.2) — in terms of nearby electrostatic interactions and the hydrophobicity of the surrounding microenvironment.

 

The previous section described the general acid/base properties of water. Many functional groups in both small and large biomolecules act as acids and bases. Common weak acids are carboxylic and phosphoric acid and their derivatives, which become negatively charged after donating a proton. Common weak bases are amines, which become positively charged on protonation. Such charge acquisition changes the properties of the acid or base. A protonated amine is no longer a nucleophile. A deprotonated carboxylic acid can now engage in an ion-ion IMF. The extent of deprotonation depends on the environment's acidity or basicity. We have to turn to a bit of mathematics to determine that extent.

Reaction of water with itself: Autoionization

As shown in the previous section, water can react with itself to produce H₃O⁺ and OH^- as illustrated in Figure \(\PageIndex{1}\).

Figure \(\PageIndex{1}\): Reaction of water with self

This autoionization reaction is often represented in a simpler form:

\[\ce{H2O <=> H^{+} + OH^{-}.}\nonumber \]

The equilibrium constant for this simplified reaction can be written as

\[
K_{e q}=\frac{\left[H^{+}\right]\left[O H^{-}\right]}{H_2 O}
\]

Given the known value of \(K_{eq}\) and the concentration of water (55 M), this can be simply rewritten as

\[K_a=55 K_{e q}=\left[H^{+}\right]\left[O H^{-}\right]=10^{-14}\]

(see discussion of the pKa of water below.)

Hence, pure, neutral water has equal but small concentrations of H₃O⁺ and OH^-, 10^-7 M.

You recall from introductory chemistry and everyday life that pure water has a pH of 7. This pH value is derived from the general formulas for both pH and a new quantity, pKa.

\[
\begin{gathered}
p H=-\log \left[H_3 O^{+}\right]=-\log \left(10^{-7}\right)=7 \\
p K_a=-\log K_a=-\log \left(10^{-14}\right)=14
\end{gathered}
\]

Note

Some texts incorrectly use 15.7 for the pKa of water. Here is a link to an explanation of why 14 is better. The incorrect value of 15.7 would make the pKa of water higher than that of methanol (15.3), which does not make sense since the methoxide anion is less stable due to electron release by the methyl group than the OH-anion.

Generic Bronsted acids with a dissociable proton can be written using the simplified chemical equation below.

\[\ce{HA <=> H^{+} + A^{-}} \nonumber \]

The equilibrium constant for this simplified reaction (leaving out water) can be written as

\begin{equation}
\begin{aligned}
& K_{e q}=\frac{\left[H^{+}\right]\left[A^{-}\right]}{H A} \\
K_a= & {[H A] K_{e q}=\left[H^{+}\right]\left[A^{-}\right] } \\
& p K_a=-\log K_a
\end{aligned}
\end{equation}

The pKa is a measure of the strength of an acid. The stronger the acid, the larger the Ka and the smaller the pKa.

Here is a table of pK_a values for common acids and functional groups. The pKa values of acids change with different substituents. The stronger the acid, the weaker the conjugate base. This should make sense as a weak base is unlikely to abstract a proton and return to its original acidic form. Likewise, the weakest acids produce the strongest conjugate bases, which would reprotonate to return to the weak acid state.

Group	Example	weaker acid	≈ pKa	Conjugate Base	stronger conj. base
alkane			50
amine			35
alkyne			25
alcohol			16
water			14
protonated amine			10
phenol			10
thiol			10
imidazole			7
carboxylic acid			5
hydrochloric acid			-8
		stronger acid			weaker conj. base

The Henderson-Hasselbalch Equation

We can find the pKa for small acids in solution in pKa tables. However, from a biochemical perspective, we often need to know the acid's charge state. Since pH is approximately constant in organisms (more on that later), we know the [H3O+]. Hence, we can calculate the ratio of \(A^- / HA\) using the Henderson-Hasselbalch equation (Equation 2.2.5), which is derived below.

\begin{equation}
\begin{gathered}
\mathrm{K}_{\mathrm{a}}=\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\
-\log \mathrm{K}_{\mathrm{a}}=-\log \left[\mathrm{H}^{+}\right]-\log \left(\left[\mathrm{A}^{-}\right] /[H A]\right) \\
\mathrm{pK}_{\mathrm{a}}=\mathrm{pH}-\log \left(\left[\mathrm{A}^{-}\right] /[\mathrm{HA}]\right)
\end{gathered}
\end{equation}

which gives the traditional Henderson-Hasselbalch equation below.

\begin{equation}
\mathrm{pH}=\mathrm{pK}_{\mathrm{a}}+\log \frac{\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]}
\end{equation}

You certainly would have performed titration curve analyses of acids in your chemistry class. What is the chemistry that occurs at each step? Let's assume the pH is low, well below the acid's pKa. From the Henderson-Hasselbalch equation, you would surmise that the ratio of A^-/HA is very small - that is, the acid is essentially fully protonated. That should also make intuitive sense. For a weak acid to be coaxed to give up a proton, a reasonably strong base (like OH^-) should be added. At low pH, the acid exists as HA. Now, consider adding a sufficient amount of NaOH to match the concentration of the ionizable protons. At that point in the titration, the mass balance would suggest that the acid in its protonated state is gone, and all that remains is A^-. What happens if just enough NaOH is added to react with half of the HA? The mass balance would tell us that A^-=HA, and at that point, the pH = pK_a of the acid.

The entire titration curve can be calculated from the Henderson-Hasselbalch equation. A graph of it is shown below.

The graph shifts upward as the pKa increases. The pH starts soaring at the end of the graph after the added hydroxide has reacted with the last ionizable proton. After that, the pH is determined by the concentration of the strong base OH^-. The graph is flattest at the inflection point. Note that at this pH, pH = pKa. In the middle of the curve, the pH changes least with the addition of small amounts of OH^-. This is the basis of buffering, which will be covered in the next section.

If you know the pH of a solution and the pKa of the ionizable group, you can very quickly estimate the functional group's average charge (protonation) state. Let's see what the Henderson-Hasselbalch equation (Equation 2.2.5) predicts under three specific pH states:

pH	log (A^-/HA)	(A^-/HA)	protonation state
2 units < pKa (more acidic, expect protonated)	-2 = log (A^-/HA)	0.01 = (A^-/HA) = 1/100	fn group about 99% protonated
2 units > pKa (more basic, expect deprotonated)	2 = log (A^-/HA)	100 = (A^-/HA) = 100/1	fn group about 99% deprotontaed
pH = pKa	0 = log (A^-/HA)	1 = (A^-/HA) = 50/59	fn group 50% protonated

From these simple examples, we have illustrated the +2 rule to determine the charge state. This rule is used to quickly determine the protonation state and, hence, the charge state of an acid and its conjugate base, and is extremely important to know and use (and easy to derive).  If the potential acid HA is a protonated amine (RNH₃⁺), the fully deprotonated state (RNH₂) is uncharged.  The fully deprotonated state has a -1 charge if it is a carboxylic acid.

Polyprotic Oxyacids

Acids that can donate more than one proton are called polyprotic acids. They are typically oxyacids, with the ionizable proton on an oxygen atom, which can form a reasonably stable oxyanion (negative on the oxygen) as the oxygen is electronegative and stabilizes the charge. The negative charge on the conjugate base of oxyacids is further stabilized by resonance delocalization involving the doubly bonded oxygen atom. Figure \(\PageIndex{2}\) shows two of the most biologically relevant oxyacids.

Figure \(\PageIndex{2}\): Reactions of polyprotic acids with water

The pKa of each subsequent ionization is higher because removing a proton from an increasingly charged molecular ion is more difficult. The titration plot of pH vs NaOH is similar to the graph above, but has multiple plateaus at pH=pKa,

Derivatives of phosphoric acid are found in all major classes of biomolecules. Nucleic acids contain a sugar-phosphate link in their backbone. Many proteins are phosphorylated after synthesis. Membrane lipids usually contain a phosphate group. A whole class of phospholipids is found in biomembranes.

Titration Curves for Polyprotic Acids

As we will see in a subsequent chapter, all amino acids have an amine and carboxylic acid group, and some have an additional ionizable side chain.  Each has its pKa values.  Those with three ionizable groups are triprotic acids, much like phosphoric acid.  Titration curves for polyprotic acids are more complex than those for monoprotic acids.  If the pKa values are separated enough, three general plateaus, each centered at the pKa value of the ionizable group, can be seen in their titration curves. If two of the groups are carboxylic acids, no clear plateau will be observed in the region of the titration curve for those groups.

Recent Updates:  4/13/26

Change parameters and pKa values in the interactive graph below to see the effects on the titration curve for a triprotic acid, such as H₃PO₄, phosphoric acid. The conjugate acid/base pairs, H₃PO₄/H₂PO₄-, H₂PO₄^-/HPO₄^2-, and HPO₄^2-/PO₄^3-, are ubiquitous in life.

Graph generated by Claude from spreadsheet below and uploaded to GitHub.

Click on the Excel file link to download a spreadsheet for triprotic acid titrations with sliders to interactively change pKa values, as shown in the image below.

 

Charge State of Biomolecules

The Henderson-Hasselbalch equation can be used to determine the charge state of ionizable functional groups (carboxylic and phosphoric acids, amines, imidazoles, guanidino groups), even in large macromolecules such as proteins, which contain carboxylic acids (weak acids) and amines (weak bases). Figure \(\PageIndex{3}\) shows how the weakly acidic aspartic and glutamic acids, two common amino acids found in proteins, contribute a negative charge to the protein and how the amine of the amino acid lysine, a weak base, contributes a positive charge.

Figure \(\PageIndex{3}\): Deprotonation/Protonation of weak amino acid side chains contributes to protein charge.

Other amino acids that contain an alcoholic function group can also become phosphorylated to produce a phosphoprotein, which converts a neutral ROH group to a phosphoester with a negative two charge, as shown in Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\): Phosphorylation of -OH containing side chains of proteins by ATP

pKa and Environment

The pKa is a measure of the equilibrium constant for the reaction. And, of course, you remember that ΔG^o = -RT ln Keq. Therefore, pKa is independent of concentration and depends only on the intrinsic stability of the reactants relative to the products. However, this is true only under specific conditions, such as temperature, pressure, and solvent composition.

Consider, for example, acetic acid, which in aqueous solution has a pKa of about 4.7. This weak acid dissociates only slightly to form H⁺ (in water, the hydronium ion, H₃O⁺, is formed) and acetate (Ac^-). These ions are moderately stable in water but reassociate readily to form the starting product. The pKa of acetic acid in 80% ethanol is 6.87. This can be attributed to the decrease in stability of the charged products, which are less shielded from each other due to the less polar ethanol. Ethanol has a lower dielectric constant than water. The pKa increases to 10.32 in 100% ethanol and a whopping 130 in air!

The pKa values of ionizable groups in proteins vary enormously as they depend on the microenvironment of the group. Consider the amino acid aspartic acid (Asp, D), which has a -CH₂CO₂H R-group or "side chain" similar to acetic acid. In a given protein, a given Asp side chain might be on the surface, but another in the same protein might be buried in the protein away from water. You would expect the pKa values for these two Asp side chains to differ. The average pKa for Asp side chains in 78 different proteins was 3.5, less than that of acetic acid (4.7), but not dramatically. However, the range of pKa values for Asp in these proteins was wide, with the lowest at 0.5 (a buried Asp in the protein T4 Lysosome) and the highest at 9.2 in the protein thioredoxin from E. coli.

Figure \(\PageIndex{5}\) shows an interactive iCn3D model of the surrounding environment of Asp 70 (D70) in T4 Lysoszyme. Its pKa has been experimentally determined to be 0.5, which is significantly stronger than that of acetic acid. The dotted cyan lines show ion-ion interactions between the -CH₂CO₂^- side chain of Asp 70 (D7) and the positively charged imidazolium group of histidine (H31) in the protein. The distance between the two charged groups is about 3.4 A.

Figure \(\PageIndex{5}\): Surrounding environment of Asp 70 (D70) in T4 Lysoszyme (2b6z). (Copyright; author via source).
Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...RRiVn6saN92tU6

The following model shows the surroundings of Asp 26 (D26) in E. coli thioredoxin.  This particular aspartic acid has a pKa of 9.2. The dark blue group represents a surface-exposed, positively charged lysine side chain that can stabilize the negative charge on Asp 26. Note, however, that it is much farther away than the imidazolium group in T4 lysozyme that stabilizes the negative charge on D70. The rest of the model is colored by hydrophobicity, indicating that nonpolar groups surround the Asp26 side chain. These would destabilize the negative charge on D26, thereby enhancing the stability of protonated (neutral) Asp and elevating its pKa to 9.2.

Figure \(\PageIndex{6}\): Surrounding environment of Asp 26 (D26) in E. Coli thioredoxin (5HR2). (Copyright; author via source).
Click the image for a popup or use this external link: https://structure.ncbi.nlm.nih.gov/i...i9BNNdbA2bmP5A

Summary

(Summary written by Claude, Sonnet 4.6, Anthropic)

This chapter develops a quantitative framework for understanding acid-base chemistry in biological systems, extending the general acid-base properties of water introduced previously to ionizable functional groups in biomolecules and to the macromolecular environments in which those groups reside.

The autoionization of water establishes the reference point for all aqueous acid-base chemistry: at neutrality, [H₃O⁺] = [OH⁻] = 10⁻⁷ M, giving a pH of 7. The pKa, defined as −log Ka, is a concentration-independent measure of acid strength determined entirely by the intrinsic relative stability of the protonated and deprotonated forms — a thermodynamic quantity directly related to ΔG° through the relationship ΔG° = −RT ln Keq. Across the functional groups most relevant to biochemistry, pKa values span an enormous range: from approximately −8 for HCl, through 5 for carboxylic acids, 7 for imidazoles, and 10 for thiols, phenols, and protonated amines, to 35 for amines and 50 for alkanes. This hierarchy reflects the ability of each conjugate base to stabilize negative charge through electronegativity, resonance delocalization, and inductive effects.

The Henderson-Hasselbalch equation (pH = pKa + log [A⁻]/[HA]) provides the central quantitative tool for relating pH, pKa, and the protonation state of any ionizable group. Its most practical consequence is the ±2 rule: a functional group is approximately 99% protonated when the pH is two units below its pKa and approximately 99% deprotonated when the pH is two units above it. At pH = pKa, the group is exactly 50% protonated. This rule allows rapid estimation of the charge state of any functional group in a biomolecule at physiological pH without computation. In titration curves, the Henderson-Hasselbalch equation accounts for the sigmoidal shape, the plateau regions where pH changes little with added base (the buffering regions), and the sharp rise at the equivalence point. Polyprotic acids — phosphoric acid and amino acids being the most biologically important — display multiple such plateaus, each centered at a distinct pKa, provided those pKa values are sufficiently separated. Phosphate derivatives occur in the backbone of nucleic acids, in membrane phospholipids, and as post-translational modifications of proteins; their multiple ionizable groups are central to their biological functions.

The charge states of biomolecules at physiological pH are directly read from the Henderson-Hasselbalch equation. At pH 7.4, carboxylic acid groups (pKa ~4-5) are overwhelmingly deprotonated and negatively charged, while protonated amines (pKa ~10) are predominantly protonated and positively charged. Imidazole groups (pKa ~7) are uniquely poised near neutrality, making histidine side chains exquisitely sensitive to small pH changes — a property widely exploited in enzyme active sites. Phosphorylation of serine, threonine, or tyrosine converts a neutral hydroxyl into a phosphoester carrying approximately two negative charges at physiological pH, a dramatic change in charge state that underlies much of cellular signaling logic.

Finally, the chapter establishes that pKa values in proteins are not fixed constants but vary substantially with the local microenvironment. Decreasing the solvent's dielectric constant — or burying a residue in a hydrophobic protein interior — destabilizes charged species and elevates their pKa. Conversely, a nearby positively charged residue stabilizes an adjacent negative charge, lowering pKa. These effects can be dramatic: the pKa of aspartate in proteins ranges from 0.5 (Asp 70 in T4 lysozyme, stabilized by a proximal histidinium ion) to 9.2 (Asp 26 in thioredoxin, destabilized by a hydrophobic environment), a span of nearly nine pH units compared to the solution reference value of approximately 4.7 for acetic acid. Understanding these microenvironment-dependent pKa shifts is essential for rationalizing enzyme mechanisms, protein stability, and the pH dependence of protein function.