Biochemistry Flashcards: Water, Noncovalent Interactions, pH, and Buffer Systems

Biological Role and Fundamental Properties of Water

• Role in Evolution and Life Support:

  • Life evolved in water, which provided essential shielding against ultraviolet (UV) radiation.

  • Living organisms typically consist of $70\text{--}90\%$ water.

  • Ingestion and elimination mechanisms maintain fluid balance, accounting for approximately $50\%$ of total body weight.

  • Bulk metabolic and chemical reactions occur within an aqueous environment.

  • Water acts as a crucial structural determinant, forcing proteins to fold into active conformations, stabilizing nucleic acid double-stranded structures, and driving lipid bilayer self-assembly.

• Body Fluid Compartments:

  • Intracellular Fluid (ICF): Fluid located inside the cells (cytoplasm).

  • Extracellular Fluid (ECF): Subdivided into two main compartments:

    • Interstitial Fluid (IF): Fluid present in the tissue spaces between cells.

    • Blood Plasma: Liquid component of blood inside blood vessels.

  • Materials and nutrients exchange between blood plasma and surrounding tissue cells by passing through the interstitial fluid within capillaries.

Molecular Structure and Polarity of Water

• Chemical Formula and Electron Configuration:

  • Chemical formula: $H_2O$.

  • Governed by the octet rule; central oxygen ($O$) has atomic number $8$ with electron configuration $1s^2\,2s^2\,2p^4$.

  • The outer shell orbital contains four electron pairs:

    • Two pairs form covalent single bonds linking two hydrogen ($H$) atoms to the central oxygen atom.

    • Two pairs remain as nonbonding lone pairs.

• Geometry and Bond Angles:

  • Water exhibits a distorted tetrahedral geometry based on $sp^3$ hybridized atomic orbitals.

  • The $H\text{--}O\text{--}H$ bond angle is approximately $105^\circ$, which is slightly smaller than the ideal tetrahedral angle of $109.5^\circ$ due to lone pair repulsion.

• Electronegativity and Dipole Moment:

  • Oxygen possesses a significantly higher electronegativity than hydrogen.

  • Oxygen attracts the shared covalent bonding electrons closer to its nucleus, creating partial positive charges ($\delta^+$) on the two hydrogen atoms and a partial negative charge ($\delta^-$) on the oxygen atom.

  • This permanent charge asymmetry generates a net dipole moment, enabling water to function simultaneously as both a hydrogen bond donor and a hydrogen bond acceptor.

Principles and Dynamics of Hydrogen Bonding

• Definition and Nature:

  • A hydrogen bond is a strong electrostatic, noncovalent interaction between uncharged but polar molecules.

  • Occurs between an acid (proton donor) and a base (proton acceptor).

  • Requires a hydrogen atom covalently bonded to an electronegative atom ($O$ or $N$), generating a $\delta^+$ charge that interacts with the nonbonding lone pair of another electronegative atom ($O$ or $N$).

• Bond Strength and Energetics:

  • Single hydrogen bond energy between neutral atoms is $4\text{--}6\,kJ\,mol^{-1}$.

  • Single hydrogen bond energy involving one charged atom is $6\text{--}10\,kJ\,mol^{-1}$.

  • Hydrogen bonds in water have a bond energy of approximately $20\,kJ\,mol^{-1}$, which is significantly weaker than covalent $O\text{--}H$ bonds ($420\,kJ\,mol^{-1}$).

  • Hydrogen bonds are longer and weaker than covalent bonds.

• Directionality and Geometry:

  • Hydrogen bonds are strongest when the bonded atoms are oriented linearly ($180^\circ$ angle) to maximize electrostatic interaction.

  • Nonlinear or angled alignments weaken the interaction.

• Cooperativity and Physical Impact:

  • Hydrogen bonding in water is highly cooperative, with individual bond lifetimes ranging between $1$ and $20\,ps$ ($1\times 10^{-12}\text{--}20\times 10^{-12}\,s$).

  • Continuous formation and destruction of the hydrogen-bonded network gives water high cohesion, high adhesion, an anomalously high boiling point, an anomalously high melting point, and a large surface tension.

• States of Matter:

  • Ice (Solid State): Forms a regular hexagonal crystal lattice with low system entropy. Each water molecule forms the maximum of $4.0$ hydrogen bonds. Ice has a lower density than liquid water, allowing ice to float.

  • Liquid Water: Higher thermal entropy permits rapid molecular movement. Averages $3.4$ hydrogen bonds per water molecule at room temperature.

  • Water Vapor (Gas State): High kinetic energy completely overcomes hydrogen bonding; $0$ hydrogen bonds exist per molecule.

• Historical Reference:

  • In $1939$, chemist Linus Pauling stated in The Nature of the Chemical Bond: "I believe that as the methods of structural chemistry are further applied to physiological problems, it will be found that the significance of the hydrogen bond for physiology is greater than that of any other single structural feature."

Solutes, Polarity, and Solubility Characteristics

• Solubility Rule: "Like dissolves like." Polar solutes dissolve in polar solvents; nonpolar solutes do not.

• Good Solvents (Polar and Charged Substances):

  • Water readily dissolves charged or polar molecules capable of establishing hydrogen bonds.

  • Examples: Amino acids and peptides (e.g., glycine, aspartate), small alcohols (e.g., ethanol, glycerol), carbohydrates (e.g., glucose), metabolic intermediates (e.g., lactate), and phosphorylated lipid headgroups.

• Poor Solvents (Nonpolar Substances):

  • Water is an ineffective solvent for nonpolar substances that cannot form hydrogen bonds.

  • Examples: Nonpolar gases ($N_2$, $O_2$, $CO_2$), aromatic moieties (e.g., benzene rings, phenylalanine side chains), and aliphatic chains (e.g., long hydrocarbon tails, waxes).

• Solubilities of Common Gases in Water:

  • Nitrogen ($N_2$): Nonpolar; solubility is $0.018\,g\,dm^{-3}$ at $40\,^\circ C$

  • Oxygen ($O_2$): Nonpolar; solubility is $0.035\,g\,dm^{-3}$ at $50\,^\circ C$

  • Carbon Dioxide ($CO_2$): Nonpolar; solubility is $0.97\,g\,dm^{-3}$ at $45\,^\circ C$

  • Ammonia ($NH_3$): Polar; solubility is $900\,g\,dm^{-3}$ at $10\,^\circ C$

  • Hydrogen Sulfide ($H_2S$): Polar; solubility is $1860\,g\,dm^{-3}$ at $40\,^\circ C$

• Biological Gas Transport Mechanisms:

  • Because $O_2$ and $CO_2$ are nonpolar and poorly soluble in water, specialized biological mechanisms transport them:

    • Oxygen Transport: Carried through the blood bound to water-soluble carrier proteins (hemoglobin and myoglobin).

    • Carbon Dioxide Transport: Hydrated into carbonic acid ($H_2CO_3$) and transported primarily as soluble bicarbonate ($HCO_3^-$) ions, either free in plasma or bound to hemoglobin.

Classification of Noncovalent Interactions

• Definition: Noncovalent interactions do not involve sharing electron pairs between atoms. They are weaker than covalent bonds and reversible.

• Four Major Types:

  • 1. Ionic (Coulombic) Interactions:

    • Electrostatic forces occurring between permanently charged species or between an ion and a permanent dipole.

    • Includes attractive forces between opposite charges and repulsive forces between like charges.

  • 2. Hydrogen Bonds:

    • Electrostatic attractions between uncharged, polar groups containing hydrogen bound to electronegative donor and acceptor atoms.

  • 3. van der Waals Interactions:

    • Weak, non-specific electrostatic interactions between any two atoms in close proximity, regardless of polarity.

    • Attractive Component (London Dispersion Forces): Depends on atomic polarizability; dominates at longer distances ($0.4\text{--}0.7\,nm$).

    • Repulsive Component (Steric Repulsion): Depends on atomic size and electron cloud overlap; dominates at very short distances.

    • van der Waals Contact Distance: The distance corresponding to minimum potential energy where attractive and repulsive forces balance.

    • Biological Significance: Universal across all atoms; provides steric complementarity, stabilizes macromolecular structures (e.g., base stacking in DNA), and facilitates polarizable ligand binding.

  • 4. Hydrophobic Effect:

    • Complex thermodynamic phenomenon involving the association of nonpolar groups in aqueous solutions.

Thermodynamics and Biological Significance of the Hydrophobic Effect

• Thermodynamic Origin (Entropy Driven):

  • Entropy ($S$) measures the degree of randomness or disorder in a system. High entropy is thermodynamically favored.

  • Bulk liquid water possesses high entropy due to continuous hydrogen bond turnover.

  • When a nonpolar solute enters water, it cannot form hydrogen bonds. Water molecules surrounding the nonpolar solute are forced to form a highly ordered constraint cage around the hydrophobic molecule, resulting in local low entropy (\Delta S < 0).

  • Low entropy is thermodynamically unfavorable. To minimize this entropy loss, nonpolar molecules aggregate or cluster together. Aggregation reduces the total hydrophobic surface area exposed to water, releasing trapped water molecules back into bulk solution, thereby increasing total system entropy (\Delta S > 0).

• Amphipathic Compounds:

  • Amphipathic molecules possess dual polar and nonpolar regions (e.g., fatty acids with a polar head and a nonpolar tail).

  • In aqueous environments, amphipathic molecules form structured clusters called micelles or lipid bilayers:

    • Hydrophobic tails are sequestered into an internal core away from water.

    • Hydrophilic heads face outward, forming hydrogen bonds with water.

  • Comparison: Purely nonpolar liquids (like oil) lack polar heads and separate into distinct macroscopic layers in water. Soluble polar molecules (like glucose) dissolve completely as single molecules surrounded by hydrogen-bonding water shells.

• Biological Significance:

  • Drives the formation of cellular membranes and lipid bilayers.

  • Drives globular protein folding by burying hydrophobic amino acid side chains (e.g., leucine, isoleucine, valine, phenylalanine) into the interior core while exposing hydrophilic side chains to the surface.

  • Creates hydrophobic binding pockets in enzymes and receptors, facilitating the binding of nonpolar substrates and hydrophobic ligands (such as steroid hormones).

  • Guides rational drug design by structuring pharmaceuticals to bind into hydrophobic target sites.

• Macromolecular Stabilization Summary:

  • Macromolecular tertiary structures are collectively stabilized by hydrogen bonds, ionic bonds, hydrophobic interactions, van der Waals forces, and covalent disulfide bridges ($\text{--}S\text{--}S\text{--}$).

Colligative vs. Noncolligative Properties of Solutions

• Noncolligative Properties:

  • Depend directly on the chemical nature and identity of the dissolved solute.

  • Examples: Viscosity, surface tension, taste, and color.

• Colligative Properties:

  • Depend strictly on the concentration of solute particles (osmolarity) per unit volume, independent of their chemical identity.

  • Examples: Boiling point elevation, melting/freezing point depression, vapor pressure reduction, and osmotic pressure.

• Cellular Osmolarity and Tonicity:

  • The cytoplasm is a highly concentrated solution of metabolites, ions, and macromolecular proteins (such as albumin in plasma), creating high osmotic pressure.

  • Isotonic Environment: External solute concentration equals cytosolic solute concentration. Water moves equally in both directions; cells maintain volume and shape.

  • Hypertonic Environment: External solute concentration is higher than inside the cell. Water exits the cell, leading to cell shrinkage (crenation).

  • Hypotonic Environment: External solute concentration is lower than inside the cell. Water enters the cell, increasing internal osmotic pressure and causing cell swelling and membrane bursting (lysis).

Autoionization of Water and the Kw Constant

• Autoionization Reaction:

  • Water undergoes rapid, reversible autoionization acting simultaneously as an acid and a base:         $H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-$

  • Simplified representation:         $H_2O \rightleftharpoons H^+ + OH^-$

  • Acid ($H_2O$) donates a proton to form its conjugate base, hydroxide ($OH^-$).

  • Base ($H_2O$) accepts a proton to form its conjugate acid, hydronium ($H_3O^+$).

• Protons in Solution:

  • Free protons ($H^+$) do not exist in bulk liquid water. They are hydrated instantaneously to form hydronium ($H_3O^+$) ions.

  • Because autoionization equilibrium lies overwhelmingly to the left, pure water contains very few ions and exhibits low electrical conductivity (resistance of $18\,M\Omega\cdot cm$).

• Quantitative Derivation of Ionic Product of Water ($K_w$):

  • Equilibrium constant expression:         $K_{eq} = \frac{[H^+][OH^-]}{[H_2O]}$

  • Experimental measurement at $25\,^\circ C$ yields $K_{eq} = 1.8 \times 10^{-16}\,M$

  • Derivation of Molarity of Pure Water ($[H_2O]$):

    • $1\,L$ of water = $1000\,cm^3$.

    • Density of water = $1.0\,g\,cm^{-3}$, so mass of $1\,L$ water = $1000\,g$

    • Molar mass of $H_2O$ = $18\,g\,mol^{-1}$

    • Moles of water = $\frac{1000\,g}{18\,g\,mol^{-1}} = 55.55\,mol$

    • Molarity $[H_2O] = \frac{55.55\,mol}{1\,L} = 55.5\,M$

  • Calculation of $K_w$:         $K_w = K_{eq} \times [H_2O] = (1.8 \times 10^{-16}\,M) \times (55.5\,M) = 1.0 \times 10^{-14}\,M^2$

  • In pure neutral water, $[H^+] = [OH^-]$:         $[H^+] = [OH^-] = \sqrt{1.0 \times 10^{-14}\,M^2} = 1.0 \times 10^{-7}\,M$

The pH Scale and Acid-Base Calculations

• Definition of pH:

  • Defined as the negative logarithm (base $10$) of the hydrogen ion concentration:         $pH = -\log_{10}[H^+]$

• Relationship Between pH and pOH:

  • Starting from $K_w$:         $[H^+][OH^-] = 1.0 \times 10^{-14}\,M^2$

  • Taking the negative logarithm of both sides:         $-\log_{10}[H^+] - \log_{10}[OH^-] = -\log_{10}(1.0 \times 10^{-14})$         $pH + pOH = 14$

• Logarithmic Scale Dynamics:

  • Because pH is a negative logarithmic scale, an increase in $[H^+]$ produces a decrease in pH.

  • A change of $1.0$ pH unit represents a $10$-fold change in hydrogen ion concentration.

  • A neutral solution has $[H^+] = 10^{-7}\,M$, corresponding to $pH = 7.0$.

  • Negative pH values are mathematically and physically possible in extremely concentrated strong acids (e.g., for $6\,M\,HCl$, $pH = -\log_{10}(6) = -0.78$).

• pH Values of Common Biological and Household Liquids:

  • $1.0\,M\,HCl$: $0.0$

  • Gastric juice: $\sim 1.5\text{--}2.0$

  • Lemon juice: $\sim 2.2\text{--}2.4$

  • Cola, vinegar: $\sim 3.0$

  • Red wine: $\sim 3.5$

  • Beer: $\sim 4.5$

  • Black coffee: $\sim 5.0$

  • Milk, saliva: $\sim 6.5$

  • Pure water ($25\,^\circ C$): $7.0$

  • Human blood, tears: $7.4$

  • Seawater, egg white: $\sim 8.0$

  • Baking soda solution ($NaHCO_3$): $\sim 8.5$

  • Household ammonia: $\sim 11.5$

  • Household bleach: $\sim 12.5$

  • $1.0\,M\,NaOH$: $14.0$

Dissociation of Weak Acids, Ka, and pKa

• Definitions:

  • Acid: Proton donor ($HA$).

  • Base: Proton acceptor ($A^-$).

  • Conjugate Acid-Base Pair: A proton donor and its corresponding proton acceptor, differing by exactly one proton ($H^+$).

• Acid Dissociation Constant ($K_a$):

  • For the reversible dissociation $HA \rightleftharpoons H^+ + A^-$:         $K_a = \frac{[H^+][A^-]}{[HA]}$

  • $pKa$ is defined as the negative logarithm of $K_a$:         $pKa = -\log_{10} K_a$

• Acid Strength Relationships:

  • Strong Acids: Fully dissociate in aqueous solution. Characterized by large $K_a$ values, small/negative $pKa$ values, and very low affinity for their protons.

  • Weak Acids: Dissociate only partially in water. Characterized by small $K_a$ values, large positive $pKa$ values, and high affinity for their protons.

• Monoprotic vs. Polyprotic Acids:

  • Monoprotic Acid: Can donate only one proton per molecule (e.g., acetic acid: $CH_3COOH \rightleftharpoons CH_3COO^- + H^+$). Features one $K_a$ and one $pKa$ ($pKa = 4.76$).

  • Diprotic Acid: Can donate two protons sequentially (e.g., carbonic acid $H_2CO_3$, glycine). Features two distinct $K_a$ and $pKa$ values.

  • Triprotic Acid: Can donate three protons sequentially (e.g., phosphoric acid $H_3PO_4$). Features three distinct $K_a$ and $pKa$ values:

    • $pKa_1 = 2.14$ ($H_3PO_4 \rightleftharpoons H_2PO_4^- + H^+$)

    • $pKa_2 = 6.86$ ($H_2PO_4^- \rightleftharpoons HPO_4^{2-} + H^+$)

    • $pKa_3 = 12.4$ ($HPO_4^{2-} \rightleftharpoons PO_4^{3-} + H^+$)

• Protonation Rules Relative to pKa:

  • When pH < pKa: The ambient solution is rich in protons; the protonated acid form ($HA$) predominates.

  • When pH > pKa: The ambient solution is depleted of protons; the deprotonated conjugate base form ($A^-$) predominates.

  • When $pH = pKa$: Exactly $50\%$ of the molecule exists in the protonated form and $50\%$ in the deprotonated form ($[HA] = [A^-]$).

Derivation and Application of the Henderson-Hasselbalch Equation

• Step-by-Step Derivation:

  • 1. Begin with the expression for the acid dissociation constant:         $K_a = \frac{[H^+][A^-]}{[HA]}$

  • 2. Rearrange the equation to isolate the hydrogen ion concentration ($[H^+]$):         $[H^+] = K_a \cdot \frac{[HA]}{[A^-]}$

  • 3. Take the negative logarithm ($-\log_{10}$) of both sides:         $-\log_{10}[H^+] = -\log_{10} K_a - \log_{10}\left(\frac{[HA]}{[A^-]}\right)$

  • 4. Substitute the definitions $pH = -\log_{10}[H^+]$ and $pKa = -\log_{10} K_a$:         $pH = pKa - \log_{10}\left(\frac{[HA]}{[A^-]}\right)$

  • 5. Invert the argument inside the logarithm to change the minus sign to a plus sign:         $pH = pKa + \log_{10}\left(\frac{[A^-]}{[HA]}\right)$

  • 6. Generalized Henderson-Hasselbalch Equation:         $pH = pKa + \log_{10}\left(\frac{[\text{conjugate base}]}{[\text{weak acid}]}\right)$

Buffer Systems, Titration Curves, and Buffering Region

• Definition and Function of Buffers:

  • Buffers are aqueous solutions composed of a mixture of a weak acid and its conjugate base.

  • They resist changes in pH when small amounts of acid ($H^+$) or base ($OH^-$) are added.

• Mechanism of Buffering Action (e.g., Acetic Acid / Acetate Buffer):

  • Addition of OH^-$:* Added hydroxide ions react with free H^+$to form$H_2O$. Acetic acid ($CH_3COOH$) dissociates to replenish$H^+ ions, neutralizing the base.\n * *Addition of H^+$: Added hydrogen ions react with acetate ions ($CH_3COO^-$) to form acetic acid ($CH_3COOH$), preventing a decrease in pH.

• Titration Curves & Midpoint Dynamics:

  • A titration curve plots pH on the y-axis against added equivalents of strong base ($OH^-$) on the x-axis.

  • Exhibits a characteristic sigmoidal shape.

  • Midpoint of Titration: Occurs when exactly $0.5$ equivalents of base are added. At this point, $[HA] = [A^-]$, meaning $\log_{10}(1) = 0$, and $pH = pKa$.

  • Buffering Region: The region extending $1.0$ pH unit above and $1.0$ pH unit below the $pKa$ ($pH = pKa \pm 1.0$). Within this region, the system possesses maximal buffering capacity.

  • Buffering capacity is completely lost if the pH deviates by more than $1.0$ unit from the $pKa$.

• Comparison of Weak Acid Titration Curves:

  • Acetic Acid ($CH_3COOH$): $pKa = 4.76$; effective buffering range $3.76\text{--}5.76$

  • Di-hydrogen Phosphate ($H_2PO_4^-$): $pKa = 6.86$; effective buffering range $5.86\text{--}7.86$

  • Ammonium ($NH_4^+$): $pKa = 9.25$; effective buffering range $8.25\text{--}10.25$

Biological and Laboratory Buffer Systems

• In Vivo Biological Buffers:

  • Phosphate Buffer System:

    • Operates in the cytoplasm of cells, where phosphate concentrations are in the millimolar range.

    • Active conjugate acid-base pair: $H_2PO_4^- \rightleftharpoons HPO_4^{2-} + H^+$ with $pKa = 6.86$, making it effective near cellular pH.

  • Histidine:

    • Amino acid side chain containing an imidazole ring with a $pKa \approx 6.0$, serving as an efficient biological buffer at physiological neutral pH.

  • Bicarbonate Buffer System:

    • Primary buffer system maintaining blood plasma pH near $7.4$.

    • Based on coupled reversible equilibria between gaseous carbon dioxide, dissolved carbon dioxide, carbonic acid, and bicarbonate:             $CO_2(g) \rightleftharpoons CO_2(aq)$             $CO_2(aq) + H_2O(l) \rightleftharpoons H_2CO_3(aq)$             $H_2CO_3(aq) \rightleftharpoons H^+(aq) + HCO_3^-(aq)$

    • Respiratory Regulation: Dissolved $CO_2$ levels in lung capillaries equilibrium are adjusted by breathing rate:

      • Hyperventilation (exhaling excess $CO_2$): Shifts equilibrium to the left, consuming $H^+$ ions and raising blood pH (preventing/correcting acidosis).

      • Hypoventilation/rebreathing (retaining $CO_2$): Shifts equilibrium to the right, generating $H^+$ ions and lowering blood pH (preventing/correcting alkalosis).

• In Vitro Synthetic Laboratory Buffers:

  • Often composed of zwitterionic sulfonic acids of cyclic amines designed to maintain stable experimental pH without interfering with biological assays:

    • HEPES: $4\text{-(2-hydroxyethyl)-1-piperazineethanesulfonic acid}$

    • PIPES: $1,4\text{-piperazinediethanesulfonic acid}$

    • CHES: $2\text{-(cyclohexylamino)ethanesulfonic acid}$

Quantitative Practice Problems and Step-by-Step Solutions

• Problem 1: Hydroxide Ion Calculation

  • Question: Calculate the concentration of $OH^-$ in a solution where $[H^+] = 1.0 \times 10^{-5}\,M$.

  • Solution Steps:

    • 1. Use the ionic product of water: $K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\,M^2$

    • 2. Substitute given values: $1.0 \times 10^{-5}\,M \times [OH^-] = 1.0 \times 10^{-14}\,M^2$

    • 3. Isolate $[OH^-]$: $[OH^-] = \frac{1.0 \times 10^{-14}\,M^2}{1.0 \times 10^{-5}\,M} = 1.0 \times 10^{-9}\,M$

• Problem 2: pH Calculation for a Strong Base

  • Question: A solution is prepared by dissolving $0.01\,mol$ of $NaOH$ in $1.0\,L$ of water. What is the pH of the solution?

  • Solution Steps:

    • 1. $NaOH$ is a strong base that fully dissociates: $[OH^-] = \frac{0.01\,mol}{1.0\,L} = 0.01\,M = 1.0 \times 10^{-2}\,M$

    • 2. Calculate pOH: $pOH = -\log_{10}(1.0 \times 10^{-2}) = 2.0$

    • 3. Calculate pH: $pH = 14 - pOH = 14 - 2.0 = 12.0$

• Problem 3: Henderson-Hasselbalch Buffer Calculation

  • Question: What is the pH of an acetate buffer containing a conjugate base to acid ratio ($[A^-]/[HA]$) of $10:1$, given that the $pKa$ of acetic acid is $4.76$?

  • Solution Steps:

    • 1. Apply Henderson-Hasselbalch: $pH = pKa + \log_{10}\left(\frac{[A^-]}{[HA]}\right)$

    • 2. Substitute ratio: $pH = 4.76 + \log_{10}(10)$

    • 3. Evaluate logarithm: $\log_{10}(10) = 1.0$

    • 4. Calculate final pH: $pH = 4.76 + 1.0 = 5.76$

• Problem 4: Predominant Forms of Phosphoric Acid Across pH Values

  • Question: Determine the predominant molecular form of phosphoric acid ($pKa_1 = 2.14, pKa_2 = 6.86, pKa_3 = 12.4$) at pH values $2.14$, $5.0$, $6.86$, $10.0$, and $12.4$.

  • Solution Steps:

    • At pH = 2.14: $pH = pKa_1$; exact $50:50$ mixture of $H_3PO_4$ and $H_2PO_4^-$.

    • At pH = 5.0: $pH$ is between $pKa_1$ ($2.14$) and $pKa_2$ ($6.86$); the fully predominant form is $H_2PO_4^-$.

    • At pH = 6.86: $pH = pKa_2$; exact $50:50$ mixture of $H_2PO_4^-$ and $HPO_4^{2-}$.

    • At pH = 10.0: $pH$ is between $pKa_2$ ($6.86$) and $pKa_3$ ($12.4$); the fully predominant form is $HPO_4^{2-}$.

    • At pH = 12.4: $pH = pKa_3$; exact $50:50$ mixture of $HPO_4^{2-}$ and $PO_4^{3-}$.

Questions & Discussion

• Clarification on Hydrogen Bonds in Water vs. Ice:

  • Question: How is it possible for liquid water to have $3.4$ hydrogen bonds per molecule?

  • Answer: The value $3.4$ represents a statistical average over time across all liquid water molecules. Because liquid water molecules are in continuous thermal motion, hydrogen bonds rapidly break and reform on a picosecond scale ($1\text{--}20\,ps$). In solid ice, fixed crystal geometry allows each water molecule to maintain full, static $4.0$ hydrogen bonds simultaneously.

• Identifying Conjugate Acids and Bases in Pairs:

  • Question: How do you determine which species is the conjugate acid versus the conjugate base in a polyprotic pair?

  • Answer: Always compare the relative number of hydrogen atoms (protons). In any given pair, the species with the greater number of protons is the conjugate acid (proton donor), while the species with fewer protons is the conjugate base (proton acceptor).