Unit 2: Physical and Chemical Properties of Water and Aqueous Systems

Foundations of Water in Biochemistry

• Water is the most abundant molecule within living organisms and is fundamental to the existence of life. Life originated in an aqueous environment.
• It constitutes approximately $70 \, \%$ or more of the total body weight of all living organisms.
• The unique properties of water significantly influence biological chemistry, acting as the aqueous medium for functions such as metabolism.
• Water is often referred to as a universal solvent because it can dissolve or dissociate most compounds.
• Beyond its role as a solvent, water is a critical participant in metabolic processes, serving as both a reactant and a product in various reactions.

Noncovalent Interactions in Aqueous Systems

• Biological processes largely occur in an aqueous medium where biomolecules interact with water through weak, noncovalent interactions.
• Although these interactions are individually weak, they are collectively significant in maintaining the three-dimensional structures of proteins, nucleic acids, polysaccharides, and membrane lipids.
• The solubility of any substance in water is determined by the forces between the substance's functional groups and water molecules.

Molecular Structure of Water and Hydrogen Bonding

• A water molecule ($H_2O$) consists of two hydrogen atoms covalently bonded to one oxygen atom ($O$).
• The molecular geometry is derived from a tetrahedral arrangement:
  • Two corners of the tetrahedron are occupied by the bonding electron pairs (the $H$ atoms).
  • The other two corners are occupied by nonbonding electron pairs (unshared pairs) of the oxygen atom.
• These nonbonding electron pairs exert repulsive forces, pushing the hydrogen atoms closer together.
• Consequently, the $H-O-H$ bond angle is reduced to $104.5^{\circ}$, compared to the $109.5^{\circ}$ angle of a perfect tetrahedron. This results in a bent, angular, or V-shaped geometry.
• Electronegativity differences: The oxygen atom is more electronegative than the hydrogen atom, attracting the shared electron pairs more strongly toward its nucleus.
• This unequal sharing creates two electric dipoles along the $O-H$ bonds. The oxygen atom carries a partial negative charge ($\delta^{-}$), while each hydrogen atom carries a partial positive charge ($\delta^{+}$).
• A hydrogen bond is an electrostatic interaction between the $\delta^{-}$ oxygen of one water molecule and the $\delta^{+}$ hydrogen of another.
• Bond Distances:
  • The distance between participating atoms in a hydrogen bond is approximately $0.17\,nm$.
  • The distance of a covalent $H-O$ bond is approximately $0.096\,nm$.
• Each water molecule can theoretically form hydrogen bonds with up to four neighboring water molecules, a feature most evident in the crystal structure of ice.
• In a liquid state, hydrogen bonds are highly unstable and constantly break and reform, yet they provide the stability that allows water to remain liquid at room temperature.

Hydrogen Bonding in Biological Molecules

• Hydrogen bonding is not limited to water-water interactions; it occurs between water and biomolecules and within the biomolecules themselves.
• Electronegative atoms such as oxygen ($O$) and nitrogen ($N$) are the primary participants, typically found in amino groups ($-NH_2$) and hydroxyl groups ($-OH$).
• These bonds are crucial for the structural integrity of:
  • Polypeptides (Proteins): Hydrogen bonds form between polypeptide chains.
  • Nucleic Acids (DNA and RNA): Hydrogen bonds occur between nitrogenous bases (e.g., between Adenine and Thymine) to hold the two strands of DNA together.

Hydrophilic and Hydrophobic Interactions

• Hydrophilic ("water-loving"): These interactions occur between water and polar or charged molecules (e.g., glucose, amino acids). These substances readily dissolve in water by forming hydrogen bonds.
• Hydrophobic ("afraid of water"): These interactions involve non-polar molecules (e.g., lipids, oils) that are virtually insoluble in water. These molecules tend to aggregate or self-associate in an aqueous environment to minimize contact with water.
• Amphipathic Molecules: These contain both polar/charged groups (hydrophilic) and non-polar groups (hydrophobic).
  • Example: Phospholipids, which have a polar head group (containing phosphate) and a non-polar hydrocarbon tail.
  • In water, amphipathic molecules aggregate into micelles—spherical structures where the polar heads interact with the water and the non-polar tails cluster in the center. This behavior is fundamental to the formation of biological membranes.

Van der Waals Interactions

• These are the weakest of all intermolecular attractions, resulting from the attraction between the nuclei and electron clouds of atoms.
• When two uncharged atoms approach, the nucleus of one attracts the electron cloud of the other, creating transient or "induced" dipoles.
• These forces require an optimal distance between atoms known as the Van der Waals radius.
• They contribute to the specificity of enzyme-substrate interactions, antibody-antigen interactions, and protein folding.

Electrostatic Interactions

• These occur between polar or ionic compounds, such as sodium chloride ($NaCl$), which are held together by strong electrostatic forces in crystal form.
• Dissolution Process: The $\delta^{-}$ ends of water molecules attract $Na^{+}$ ions, while the $\delta^{+}$ ends attract $Cl^{-}$ ions.
• Water possesses a high dielectric constant, which weakens the electrostatic forces between ions, allowing them to dissociate and become hydrated or solvated (surrounded by water molecules).
• In biological systems, inorganic ions like $Na^{+}$, $K^{+}$, $Ca^{2+}$, $Mg^{2+}$, and $Cl^{-}$ do not exist freely but are bound by electrostatic interactions to the oppositely charged ends of water dipoles.

Unique Physical Properties of Water

• Melting and Boiling Points: The thermal energy required to break the extensive network of hydrogen bonds accounts for the melting point of ice and the high boiling point of water. Melting is a spontaneous process.
• Heat of Vaporization: This provides a measure of the energy needed to overcome attractive forces between molecules. High evaporation energy allows higher organisms to shed excess body heat through localized cooling (sweat).
• Dielectric Constant: The high value makes water an effective solvent for polar sugars and charged amino acids (e.g., lysine) by reducing their internal electrostatic attractions.
• Density: Water is unique because it is less dense as a solid (ice) than as a liquid. Maximum density occurs at $4\,^{\circ}C$. Consequently, ice floats on the surface of ponds, allowing aquatic life to survive in the liquid water beneath.
• Specific Heat: Water requires $4.814\,J$ to raise the temperature of $1\,g$ of $H_2O$ by $1\,^{\circ}C$. This high capacity helps organisms withstand sudden environmental temperature fluctuations.

Ionization of Water and the Concept of pH

Water molecules ionize to a limited extent, producing a proton ($H^{+}$) and a hydroxyl ion ($OH^{-}$): $H_2O \rightleftharpoons H^{+} + OH^{-}$

• Protons do not exist freely in solution; they immediately associate with water to form hydronium ions ($H_3O^{+}$), though they are conventionally represented as $H^{+}$.
• The equilibrium constant ($K_{eq}$) for water dissociation is: $K_{eq} = \frac{[H^{+}][OH^{-}]}{[H_2O]}$
• At $25\,^{\circ}C$, the value of $K_{eq}$ is $1.8 \times 10^{-16}\,M$.

The Ionic Product of Water ($K_w$)

• The molar concentration of pure water is calculated by dividing the mass of water in $1\,dm^3$ ($1000\,g$) by its molecular weight ($18\,g/mol$): $\frac{1000}{18} = 55.5\,M$
• By substituting these values into the equilibrium equation: $1.8 \times 10^{-16} = \frac{[H^{+}][OH^{-}]}{55.5}$$[H^{+}][OH^{-}] = 55.5 \times (1.8 \times 10^{-16}) = 1.0 \times 10^{-14}$
• The constant $K_w$ (ionic product of water) is defined as: $K_w = [H^{+}][OH^{-}] = 1.0 \times 10^{-14}\,M^2$ at $25\,^{\circ}C$.
• In pure water, $[H^{+}] = [OH^{-}]$. Therefore: $[H^{+}] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7}\,M$

pH Scale and Definitions

• S.P.L. Sorenson introduced the concept of pH in 1909 to express hydrogen ion concentration.
• Definition: pH is the negative logarithm of the hydrogen ion concentration (in $mol/dm^3$): $pH = -\log[H^{+}] = \log\frac{1}{[H^{+}]}$
• For pure water at $25\,^{\circ}C$: $pH = -\log(1.0 \times 10^{-7}) = 7.0$
• pOH: This describes basicity or hydroxyl ion concentration: $pOH = -\log[OH^{-}]$
• The pH Scale (0 to 14):
  • Neutral: $pH = 7$ ($[H^{+}] = [OH^{-}]$).
  • Acidic: $pH < 7$ ($[H^{+}] > [OH^{-}]$). Lower pH corresponds to higher $H^{+}$ concentration.
  • Basic/Alkaline: $pH > 7$ ($[OH^{-}] > [H^{+}]$).

Calculation Examples

• Example 1: Concentration of $H^{+}$ in $0.01\,M \, NaOH$
  • $[OH^{-}] = 0.01\,M = 10^{-2}\,M$
  • $[H^{+}] = \frac{K_w}{[OH^{-}]} = \frac{10^{-14}}{10^{-2}} = 1 \times 10^{-12}\,M$
• Example 2: Concentration of $OH^{-}$ in $0.1\,M \, HCl$
  • $[H^{+}] = 0.1\,M = 10^{-1}\,M$
  • $[OH^{-}] = \frac{10^{-14}}{10^{-1}} = 1 \times 10^{-13}\,M$

pH in Biological Systems

Biochemical reactions are highly sensitive to pH. Proteins and nucleic acids have functional groups that change charge based on pH levels, which can alter enzyme catalysis and cellular function.

pH Values of Organelles and Body Fluids:

• Mitochondria matrix: $7.5$
• Cytosol: $7.2$
• Nucleus: $7.2$
• Blood: $7.4$
• Peroxisomes: $7.0$
• Urine: $6.0$
• Saliva: $6.3-6.8$
• Human skin: $5.5$
• Lysosomes: $4.5$
• Gastric juice: $1.5$

Buffers and the Henderson-Hasselbalch Equation

• A buffer is an aqueous solution that resists changes in pH when small amounts of acid ($H^{+}$) or base ($OH^{-}$) are added. This resistance is called buffer action.
• Buffers typically consist of a conjugate acid-base pair.
  • Acidic buffer: Weak acid and its conjugate base (e.g., acetate buffer).
  • Alkaline buffer: Weak base and its salt.

Mechanism of Buffer Action (Acetate Buffer Example)

• Acetic acid ($HAc$) dissociates into a proton ($H^{+}$) and an acetate ion ($Ac^{-}$): $CH_3COOH \rightleftharpoons H^{+} + CH_3COO^{-}$
• If $H^{+}$ is added: It reacts with the conjugate base ($CH_3COO^{-}$) to form acetic acid, removing free protons from the solution.
• If $OH^{-}$ is added: It reacts with the acetic acid ($CH_3COOH$) to form water and acetate ions, removing free hydroxyl ions.

Important Biological Buffers

• Phosphate Buffer: An intracellular buffer. It is most effective at $pH \, 6.86$ and has a buffering range from $5.9$ to $7.9$.
• Bicarbonate Buffer: A physiological buffer in human blood that maintains blood at $pH \, 7.4$.

Derivation of the Henderson-Hasselbalch Equation

Consider a weak acid ($HA$) that ionizes: $HA \rightleftharpoons H^{+} + A^{-}$

1. The dissociation constant ($K_a$) is: $K_a = \frac{[H^{+}][A^{-}]}{[HA]}$

2. Solve for $[H^{+}]$: $[H^{+}] = K_a \times \frac{[HA]}{[A^{-}]}$

3. Take the negative logarithm of both sides: $-\log[H^{+}] = -\log\left(K_a \times \frac{[HA]}{[A^{-}]}\right)$$-\log[H^{+}] = -\log(K_a) - \log\frac{[HA]}{[A^{-}]}$

4. Substitute $pH = -\log[H^{+}]$ and $pK_a = -\log(K_a)$. Use the property $-\log\frac{x}{y} = +\log\frac{y}{x}$: $pH = pK_a + \log\frac{[A^{-}]}{[HA]}$

General Form:$pH = pK_a + \log\frac{[Base]}{[Acid]}$

This equation is used to calculate the pH of a buffer solution and the specific ratio of conjugate base to conjugate acid at a given pH.