2.3: Weak Acids and Bases, pH and pKa

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Learning Goals (ChaptGPT o1, 1/25/25)

Below is a series of targeted learning goals designed to deepen understanding of acid–base equilibria, titration analyses, and the influence of environmental factors on ionizable groups in biomolecules.

• Understand Acid–Base Properties of Biomolecules and Water:

  • Describe how water acts as both a Brønsted–Lowry acid and base, including its autoionization into H₃O⁺ and OH⁻.
  • Explain how functional groups in biomolecules (e.g., carboxylic acids, phosphoric acids, amines) acquire or lose protons and how this alters their chemical properties.

• Master the Mathematical Foundations of Acid–Base Equilibria:

  • Derive and interpret the equilibrium constant expressions for the autoionization of water and for generic acid dissociation reactions.
  • Calculate pH and pKa values using the definitions pH=−log⁡[H3O+]pH = -\log [H_3O^+] and pKa=−log⁡KapK_a = -\log K_a, and understand their physical significance.

• Apply the Henderson–Hasselbalch Equation:

  • Use the Henderson–Hasselbalch equation to predict the protonation state of acids in solution under various pH conditions.
  • Interpret titration curves, identify key points such as the inflection point where pH=pKa, and understand the concept of buffering capacity.

• Analyze Titration Curves and Charge States:

  • Explain the stepwise protonation/deprotonation processes depicted in titration curves, including the behavior of monoprotic and polyprotic acids.
  • Predict the net charge on biomolecules (e.g., proteins) by applying titration principles to their ionizable functional groups.

• Explore Polyprotic Acid Behavior:

  • Define polyprotic acids and explain why each subsequent deprotonation has a higher pKa due to increasing charge repulsion.
  • Analyze complex titration curves for polyprotic acids and discuss the significance of multiple plateaus corresponding to different ionizable groups.

• Evaluate Environmental Effects on pKa Values:

  • Discuss how solvent composition (e.g., water vs. ethanol) and the microenvironment (e.g., protein interior vs. surface) influence the pKa of ionizable groups.
  • Use examples such as aspartic acid in different protein contexts to illustrate how nearby charged or hydrophobic groups alter intrinsic acid strength.

• Connect Acid–Base Chemistry to Biological Function:

  • Relate the protonation state of biomolecules to their biological functions, such as enzyme activity, ion transport, and protein–protein interactions.
  • Assess how shifts in pH can modulate biomolecular structure and function through changes in charge states.

• Develop Practical Skills in Quantitative Analysis:

  • Utilize experimental titration data and interactive models (e.g., spreadsheets, molecular visualizations) to quantitatively determine the pKa values and buffering ranges of various acids and bases.
  • Critically evaluate how titration data supports our understanding of acid–base equilibria in complex biological systems.

These learning goals reinforce theoretical concepts through quantitative reasoning and practical application, ensuring junior and senior biochemistry majors can integrate chemical principles with biological phenomena.

 

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 acidity/basicity of the environment. We have to turn to a bit of mathematics to determine that extent.

Reaction of water with self: 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, 10^-7 M of H₃O⁺ and OH^-.

You remember from introductory chemistry and life in general that pure water has a pH of 7. This pH derives 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 wrong value of 15.7 would make the pKa of water higher than that of methanol (15.3), which can't be since the methoxide anion is less stable due to electron release by the methyl group than OH^-.

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 change with different substituents on the acids. The stronger the acid, the weaker the conjugate base. This should make sense as a weak base is unlikely to reabstract 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 charge state of the acid. Since the 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 and much lower than the pKa of the acid. 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. So at low pH, the acid exists just as HA. Now consider adding an amount to NaOH to match the concentration of the ionizable proton. 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 up as the pKa is increased. 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 in the middle of the curve at the inflection point of the curve. Note 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-Hasselbach 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 determine the protonation quickly, 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 for each subsequent ionization is higher since removing a proton from an increasingly more 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 become phosphorylated after they are synthesized. Membrane lipids usually contain a phosphate group. A whole class of phospholipids are 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 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.

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 on a large macromolecule 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 negative charge to the protein and how the amine of the amino acid lysine, a weak base, contributes to 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 the concentration and depends only on the intrinsic stability of reactants with respect to the products. However, this is true only under a given set of 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 accounted for by the decrease in stability of the charged products, which are less shielded from each other by 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 huge, with the lowest being 0.5 (a buried Asp in the protein T4 Lysosome) and the highest being 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 determined experimentally to be 0.5, which is way stronger than 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 is a surface-exposed positively charged lysine side chain, which can stabilize a negative charge on the 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 based on hydrophobicity, which shows that nonpolar groups essentially surround the Asp 26 side chain. These would destabilize a negative charge on the D26, 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

Chapter Summary

This chapter deepens our understanding of acid–base chemistry as it applies to both water and biomolecules. The discussion begins by reinforcing the fundamental acid–base properties of water, highlighting its autoionization into hydronium (H₃O⁺) and hydroxide (OH⁻) ions. This sets the stage for quantitatively treating acid–base equilibria, introducing essential concepts such as pH, pKa, and the equilibrium constant (Kₐ). Students are reminded that the concentration of H₃O determines pH⁺, while the pKa value indicates the strength of an acid—the lower the pKa, the stronger the acid.

A major focus is placed on the Henderson–Hasselbalch equation, which provides a practical tool for predicting the ratio of deprotonated to protonated forms of an acid in solution. The chapter illustrates how this equation explains the behavior observed in titration curves, where the point at which pH equals pKa signifies a 50/50 mixture of ionized and unionized species. Through graphical representations and titration analyses, the text clarifies how small pH changes around the pKa minimally affect the pH and buffering capacity of biological systems.

The material expands to cover polyprotic acids—molecules that can donate more than one proton. It explains that each successive proton donation generally occurs at a higher pKa due to the increased difficulty of removing a proton from a more negatively charged species. This section underscores the complexity of titration curves for molecules with multiple ionizable groups, such as phosphoric acid and amino acids, where multiple plateaus may be observed.

Another critical topic is the effect of environmental factors on pKa values. Using examples such as aspartic acid in different protein microenvironments, the chapter demonstrates that the intrinsic pKa of a functional group can shift dramatically depending on local interactions, solvent polarity, and nearby charged residues. These variations are essential for understanding the precise control of protein structure, function, and enzyme activity in vivo.

Overall, the chapter integrates mathematical derivations with biochemical applications, equipping students with the tools to predict biomolecule charge states under various conditions. By connecting acid–base theory to biological function, the text reinforces how pH and protonation dynamics are fundamental to many processes in living systems—from enzyme catalysis to cellular signaling and metabolism.