Biochemistry: Chapter 1 — Water, pH, and Buffers

1.1 The Chemistry of Water: Polarity, Hydrogen Bonding & Solvent Power #

Water (H_2O) is the universal chemical medium in which all biological processes occur. Far from being a passive solvent, water actively participates in biochemical reactions and dictates the folding, assembly, and stability of all biological macromolecules.

The oxygen atom in water is significantly more electronegative (chi = 3.44) than the two hydrogen atoms (chi = 2.20). Because of the two unshared electron lone pairs on oxygen, water adopts an asymmetric bent molecular geometry with a bond angle of 104.5°. This asymmetric charge distribution creates a permanent electric dipole moment (1.85 Debye), with a partial negative charge (δ^–) centered on oxygen and partial positive charges (δ⁺) on each hydrogen.

                  δ-
                 :O:
                /   
            δ+ H     H δ+
           [Bent Geometry: 104.5°]

1.1.1 The Hydrogen-Bond Network #

In liquid water, the partially positive hydrogen atom of one water molecule is electrostatically attracted to an unshared electron pair of an adjacent oxygen atom, forming a hydrogen bond.

• Each water molecule can participate in a maximum of four hydrogen bonds (two donated via hydrogens, two accepted via oxygen lone pairs).
• In crystalline ice, all four hydrogen bonds are statically fixed, generating a rigid, open, low-density hexagonal lattice.
• Upon melting into liquid water, roughly 15% of these bonds break, allowing water molecules to pack more closely. Consequently, liquid water is denser than solid ice—an anomalous physical property that prevents oceans, lakes, and rivers from freezing solid from the bottom up.
• In liquid water, hydrogen bonds have an average lifetime of only 1 to 20 picoseconds (10^-12 s), forming a fluctuating, highly dynamic tetrahedral network.

1.1.2 Water as a Polar Solvent: Dielectric Shielding #

Water readily dissolves crystalline ionic salts (such as NaCl) because of its exceptionally high dielectric constant (varepsilon ≈ 78.5 at 25°C). According to Coulomb’s Law:

F = (q₁ q₂ / 4 π varepsilon₀ varepsilon r²)

Water’s high dielectric constant diminishes the electrostatic force of attraction between oppositely charged ions by nearly eighty-fold. Water molecules orient their dipoles around individual ions, forming ordered hydration shells (ion-dipole interactions). The negative oxygens cluster around cations (Na⁺), while positive hydrogens cluster around anions (Cl^–), neutralizing charges and overcoming the lattice energy of the crystal.

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1.2 The Hydrophobic Effect: The Thermodynamic Engine of Macromolecular Folding #

Nonpolar substances (such as hydrocarbons, aliphatic amino acid side chains, and fatty acid tails) are virtually insoluble in water. They do not possess permanent dipoles or full charges, and cannot participate in hydrogen bonding.

When a nonpolar solute is placed into water, it does not repel water molecules through repulsive forces. Rather, water molecules adjacent to the nonpolar surface must reorient their hydrogen-bonding geometry to satisfy their own hydrogen bonds, creating an ordered, ice-like clathrate cage surrounding the nonpolar molecule.

1.2.1 The Thermodynamic Balance Sheet (Δ G = Δ H – TΔ S) #

The formation of ordered water cages carries a severe entropy penalty (Δ S_water < 0), making the dissolution of nonpolar molecules thermodynamically unfavorable (Δ G > 0).

When multiple nonpolar molecules coalesce and aggregate together:

1. The total nonpolar surface area exposed to water is dramatically reduced.

2. The ordered water cages collapse, liberating hundreds of immobilized water molecules back into the disordered, high-entropy bulk solvent.

3. This liberation produces a massive favorable gain in entropy (Δ S > 0), rendering the overall Gibbs free energy negative:

Δ G = Δ H – TΔ S < 0

> The Fundamental Rule: The hydrophobic effect is not caused by direct attractive forces between hydrocarbon chains, but by the thermodynamic imperative of water molecules to maximize their conformational entropy. This entropic driver powers the folding of globular proteins, the spontaneous self-assembly of lipid bilayers, and the high-affinity binding of drugs to enzyme active sites.

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1.3 Acid-Base Equilibria & The Henderson–Hasselbalch Equation #

Pure water undergoes slight autoionization:

H_2O ⇌ H⁺ + OH^– quad (more precisely, 2H_2O ⇌ H_3O⁺ + OH^–)

The ion product of water at 25°C is:

K_w = [H⁺][OH^–] = 1.0 × 10^-14 M²

The pH scale is defined as the negative logarithm of hydrogen ion concentration:

pH = -log₁₀ [H⁺]

Because the autoionization of water is an endothermic process (Δ H > 0), K_w increases with temperature. At human physiological body temperature (37°C), K_w ≈ 2.4 × 10^-14 M², which places true neutrality ([H⁺] = [OH^–]) at pH 6.8. Consequently, normal human arterial blood at pH 7.4 is slightly alkaline relative to neutral water at body temperature.

1.3.1 Derivation of the Henderson–Hasselbalch Equation #

Consider the dissociation of a weak Bronsted acid HA:

HA ⇌ H⁺ + A^–

The acid dissociation constant (K_a) is expressed as:

K_a = ([H⁺][A^–] / [HA])

Taking the negative logarithm (-log₁₀) of both sides:

-log₁₀ K_a = -log₁₀ [H⁺] – log₁₀≤ft(([A^–] / [HA])right)

Substituting pK_a = -log₁₀ K_a and pH = -log₁₀[H⁺]:

pH = pK_a + log₁₀≤ft(([A^–] / [HA])right)

#### Core Quantitative Buffer Rules:

• When the conjugate base and weak acid concentrations are equal ([A^–] = [HA]), log₁₀(1) = 0, so pH = pK_a. At this exact midpoint, buffer capacity (β) is maximal.
• When pH = pK_a + 1, the ratio [A^–]/[HA] = 10:1 (90.9% conjugate base).
• When pH = pK_a – 1, the ratio [A^–]/[HA] = 1:10 (9.1% conjugate base).
• A weak acid/base pair functions as an effective buffer only within pK_a ± 1.0 pH unit. Beyond this range, one species is too depleted to neutralize added acid or base.

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1.4 Physiological Buffering in Blood and Cells #

Human arterial plasma must remain strictly between pH 7.35 and 7.45. Fluctuations outside the range of 6.8–7.8 are fatal due to enzyme inactivation and protein denaturation.

1.4.1 The Open Bicarbonate System #

The primary extracellular buffer in human blood is the bicarbonate buffer system:

CO₂ (gas) ⇌ CO₂ (dissolved) + H_2O xrightleftharpoons{Carbonic Anhydrase} H_2CO3 ⇌ H⁺ + HCO₃^–

Because true carbonic acid (H_2CO3) is present in negligible concentrations (≈ 1/400th of dissolved CO₂), clinical medicine combines dissolved CO₂ and H_2CO3 into a single effective concentration with an apparent pK_a‘ ≈ 6.10.

At first glance, a buffer with pK_a = 6.10 should be ineffective at pH 7.40, because pH 7.4 is 1.3 units above its pK_a. It works brilliantly because it operates as an open physiological system:

1. Lungs (Respiratory Compensation): Dissolved CO₂ is volatile. The lungs continuously expire CO₂ gas, holding arterial P_CO2 constant at ≈ 40 mmHg. If excess metabolic acid enters the blood, peripheral chemoreceptors trigger hyperventilation within minutes, exhaling CO₂, pulling the equilibrium leftward, and eliminating protons.

2. Kidneys (Renal Compensation): The renal proximal tubules continuously reabsorb filtered bicarbonate and synthesize new HCO₃^–, maintaining plasma [HCO₃^–] at ≈ 24 mM.

Applying the Henderson–Hasselbalch equation (with solubility coefficient α = 0.03 mM/mmHg):

pH = 6.10 + log₁₀≤ft(frac{[HCO₃^–]}{0.03 × P_CO2}right) = 6.10 + log₁₀≤ft((24 mM / 1.2 mM)right) = 6.10 + log₁₀(20) = 6.10 + 1.30 = 7.40

1.4.2 Intracellular Buffering: Phosphate and Histidine #

Inside the cytoplasm and organelles:

• Phosphate Buffer: H_2PO4^– ⇌ H⁺ + HPO₄^2- has a pK_a = 6.86, matching the cytosolic pH (6.9–7.2).
• Histidine Residues on Proteins: The imidazole side chain of histidine has a pK_a near 6.0–7.0. Hemoglobin contains 38 histidine residues per tetramer, serving as the dominant non-bicarbonate buffer in whole blood.

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1.5 Curiosity Spark & Clinical Insights #

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1.6 Key Takeaways & High-Yield Summary #

• Anomalous properties: Water’s high boiling point, surface tension, and dielectric constant (varepsilon ≈ 78.5) arise from dynamic tetrahedral hydrogen-bonding networks.
• Hydrophobic effect: Driven by the entropic liberation of ordered water cages (Δ S > 0), powering macromolecular folding and membrane self-assembly.
• Henderson–Hasselbalch equation: pH = pK_a + log([A^–]/[HA]). Buffering capacity is maximal when pH = pK_a.
• Open bicarbonate buffering: Operates at pH 7.4 despite pK_a = 6.1 because alveolar ventilation controls P_CO2 and renal tubules control [HCO₃^–].

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1.7 Review & Self-Assessment Questions #

1. Calculate the arterial blood pH in a patient whose blood gas shows P_CO2 = 50 mmHg and [HCO₃^–] = 25 mM. Identify the disorder.

• Answer: Dissolved CO₂ = 0.03 × 50 = 1.5 mM. Using Henderson-Hasselbalch: pH = 6.10 + log(25 / 1.5) = 6.10 + log(16.67) = 6.10 + 1.22 = 7.32. This represents acute respiratory acidosis (hypoventilation causing CO₂ retention).

2. Why does hyperventilation induce acute lightheadedness, numbness, and carpopedal spasm (tetany)?

• Answer: Hyperventilation excessively blows off CO₂, causing acute respiratory alkalosis (pH > 7.45). In alkalotic blood, protons dissociate from serum albumin’s histidine residues. Negatively charged albumin then binds free ionized calcium (Ca²⁺), causing acute hypocalcemia. Lowered extracellular calcium lowers the threshold for neuronal action potential firing, triggering involuntary neuromuscular tetany.

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