Liquids, Solids, and Intermolecular Forces Flashcards

Molecular Comparison of Solids, Liquids, and Gases

• Fundamental States of Matter:

  • Matter exists in three primary states—solid, liquid, and gas—defined by the arrangement of particles (atoms, molecules, or ions), their kinetic energy, and the relative strength of intermolecular forces holding them together.

  • Quantitative comparison of water states at $1\text{ atm}$:

    • Gas (Steam at $100\,^\circ\text{C}$): Density = $5.90 \times 10^{-4}\,g\,cm^{-3}$, Molar Volume = $30.6\,dm^3\,mol^{-1}$.

    • Liquid (Water at $20\,^\circ\text{C}$): Density = $0.998\,g\,cm^{-3}$, Molar Volume = $18.0\,cm^3\,mol^{-1}$.

    • Solid (Ice at $0\,^\circ\text{C}$): Density = $0.917\,g\,cm^{-3}$, Molar Volume = $19.6\,cm^3\,mol^{-1}$.

• Solids:

  • Shape and Volume: Definite shape and definite volume.

  • Particle Arrangement: Particles are packed closely together in fixed positions, vibrating about fixed points without translational freedom.

  • Intermolecular Forces: Strong relative to thermal kinetic energy, preventing flow.

  • Compressibility: Incompressible due to minimal distance between constituent particles.

  • Structural Classifications:

    • Crystalline Solids: Particles arrange in distinct, repeating geometric three-dimensional patterns with long-range order. Examples include sodium chloride ($NaCl$) and diamond.

    • Amorphous Solids: Particles display no long-range order or geometric symmetry. Examples include glass, rubber, and plastic.

• Liquids:

  • Shape and Volume: Definite volume, but indefinite shape. Liquids adapt to the shape of their container.

  • Particle Arrangement: Particles are in close contact with one another but retain translational freedom to move past adjacent particles.

  • Intermolecular Forces: Moderate relative to thermal kinetic energy, allowing fluidity while maintaining cohesion.

  • Compressibility: Virtually incompressible due to high packing density.

• Gases:

  • Shape and Volume: Indefinite shape and indefinite volume. Gases expand to occupy the entire volume and shape of their container.

  • Particle Arrangement: Particles are separated by large intermolecular distances with complete freedom of motion.

  • Intermolecular Forces: Weak relative to thermal kinetic energy, allowing independent particle motion.

  • Compressibility: Highly compressible because the vast majority of gaseous volume consists of empty space.

• Summary of State Properties:

  • Gas: Low Density, Indefinite Shape, Indefinite Volume, Weak Intermolecular Force Strength.

  • Liquid: High Density, Indefinite Shape, Definite Volume, Moderate Intermolecular Force Strength.

  • Solid: High Density, Definite Shape, Definite Volume, Strong Intermolecular Force Strength.

• Phase Transitions and Environmental Factors:

  • Altering a substance's physical state requires changing particle kinetic energy (via temperature) or altering intermolecular spacing/freedom (via pressure).

  • Heating increases thermal kinetic energy, converting solids to liquids (melting) and liquids to gases (boiling).

  • Cooling lowers thermal energy, promoting condensation or freezing.

  • Increasing pressure forces particles together, condensing gases into liquids or solidifying liquids.

  • Propane Tank Case Study: In a pressurized liquefied propane tank, propane exists in liquid-gas equilibrium ($C_3H_8(l) \rightleftharpoons C_3H_8(g)$). Opening the valve lowers internal pressure, allowing liquid propane to rapidly vaporize into gaseous propane ($C_3H_8(g)$).

  • Molecular Integrity During Phase Change: Vapor emitted from boiling liquid water consists entirely of intact gaseous water molecules ($H_2O(g)$). Phase changes disrupt intermolecular attractions without breaking covalent intramolecular bonds.

Nature and Types of Intermolecular Forces

• Overview of Intermolecular Forces:

  • Intermolecular forces are electrostatic attractions between separate molecules, atoms, or ions.

  • Intermolecular forces are significantly weaker than intramolecular chemical bonds (covalent, ionic, or metallic bonds).

  • The strength of intermolecular forces directly dictates physical properties including state of matter, boiling point, melting point, viscosity, and surface tension.

  • Stronger attractive forces require higher thermal energy to overcome, yielding higher boiling and melting points.

  • Hierarchy of Intermolecular Attraction Strengths:         $\text{Ion-Dipole Forces} > \text{Hydrogen Bonding} > \text{Dipole-Dipole Forces} > \text{London Dispersion Forces}$

• London Dispersion Forces (London Forces):

  • Definition: Temporary, fluctuating dipoles created by instantaneous fluctuations in electron distribution within atoms or molecules.

  • Mechanism: An instantaneous dipole in one atom distorts the electron cloud of an adjacent atom, inducing a complementary dipole that results in electrostatic attraction.

  • Universality: Present in all atoms, nonpolar molecules, and polar molecules.

  • Factors Governing Magnitude:

    • Polarizability: The ease with which an electron cloud can be distorted. Larger molar mass and greater total number of electrons expand the volume of the electron cloud, increasing polarizability and dispersion force magnitude.

    • Noble Gas Boiling Point Trend:

      • Helium ($He$): Molar mass = $4.00\,g\,mol^{-1}$, Boiling point = $4.2\,K$.

      • Neon ($Ne$): Molar mass = $20.18\,g\,mol^{-1}$, Boiling point = $27\,K$.

      • Argon ($Ar$): Molar mass = $39.95\,g\,mol^{-1}$, Boiling point = $87\,K$.

      • Krypton ($Kr$): Molar mass = $83.80\,g\,mol^{-1}$, Boiling point = $120\,K$.

      • Xenon ($Xe$): Molar mass = $131.30\,g\,mol^{-1}$, Boiling point = $165\,K$.

    • Molecular Shape and Surface Area Contact: Extended molecules offer a larger surface area for intermolecular contact, enhancing dispersion forces compared to compact, spherical isomers of identical molar mass.

      • $n\text{-Pentane}$ ($C_5H_{12}$): Linear structural isomer, Molar mass = $72.15\,g\,mol^{-1}$, Boiling point = $36.1\,^\circ\text{C}$.

      • $Neopentane$ ($C_5H_{12}$): Spherical structural isomer, Molar mass = $72.15\,g\,mol^{-1}$, Boiling point = $9.5\,^\circ\text{C}$.

  • Case Study of Diatomic Iodine ($I_2$):

    • Diatomic iodine ($I_2$) is nonpolar with a linear symmetric geometry.

    • Lacks permanent dipoles or hydrogen bonding capabilities.

    • Intermolecular cohesion occurs strictly through London dispersion forces driven by large, highly polarizable electron clouds.

• Dipole-Dipole Forces:

  • Definition: Electrostatic attraction between permanent partial positive charges ($\delta+$) and partial negative charges ($\delta-$) in polar molecules.

  • Polar molecules align to maximize attractive head-to-tail interactions while minimizing repulsive like-charge interactions.

  • For substances of similar molecular weight, polar molecules exhibit higher boiling points and melting points than nonpolar molecules due to dipole-dipole contributions.

  • Comparative Analysis:

    • Formaldehyde ($CH_2O$): Polar, Molar mass = $30.03\,g\,mol^{-1}$, Boiling point = $-19.5\,^\circ\text{C}$, Melting point = $-92\,^\circ\text{C}$.

    • Ethane ($C_2H_6$): Nonpolar, Molar mass = $30.07\,g\,mol^{-1}$, Boiling point = $-88\,^\circ\text{C}$, Melting point = $-183\,^\circ\text{C}$.

  • Acetonitrile ($CH_3CN$) Interaction Geometry: Electrostatic potential maps demonstrate that antiparallel and head-to-tail alignments yield optimal net attraction between permanent dipole moments.

• Solubility and Intermolecular Forces:

  • Principle of Miscibility: "Like dissolves like".

  • Polar liquids are miscible with polar solvents; nonpolar liquids are miscible with nonpolar solvents.

  • Hydrophilic Functional Groups: $-OH$, $-CHO$, $-C=O$, $-COOH$, $-NH_2$, $-Cl$.

  • Hydrophobic Functional Groups: $C-H$, $C-C$.

  • Pentane and Water Immiscibility: Nonpolar pentane ($C_5H_{12}$) cannot form favorable attractive interactions with polar water ($H_2O$). Water's strong hydrogen bonding network excludes pentane molecules, driving phase separation.

• Hydrogen Bonding:

  • Definition: An unusually strong, specialized dipole-dipole force occurring when hydrogen is directly bonded to small, highly electronegative atoms: Nitrogen ($N$), Oxygen ($O$), or Fluorine ($F$).

  • Mechanism: The extreme electronegativity difference severely shifts electron density away from hydrogen, leaving an unshielded proton core ($\delta+$) strongly attracted to lone pair electrons on adjacent $N$, $O$, or $F$ atoms ($\delta-$).

  • Comparison of Structural Isomers ($C_2H_6O$, Molar Mass = $46.07\,g\,mol^{-1}$):

    • Ethanol ($CH_3CH_2OH$): Contains an $-OH$ bond capable of hydrogen bonding. Boiling point = $78.3\,^\circ\text{C}$, Melting point = $-114.1\,^\circ\text{C}$.

    • Dimethyl Ether ($CH_3OCH_3$): Lacks $-OH$ bonds (interacts via dipole-dipole and dispersion forces only). Boiling point = $-22.0\,^\circ\text{C}$, Melting point = $-138.5\,^\circ\text{C}$.

  • Hydride Boiling Point Trends (Groups 4A vs 6A):

    • Group 4A hydrides ($CH_4$, $SiH_4$, $GeH_4$, $SnH_4$) are nonpolar; boiling points increase steadily down the group with molar mass due to dispersion forces.

    • Group 6A hydrides ($H_2O$, $H_2S$, $H_2Se$, $H_2Te$) show an anomalous spike for $H_2O$ ($100\,^\circ\text{C}$) compared to $H_2S$ ($-60\,^\circ\text{C}$) due to extensive hydrogen bonding in liquid water.

• Ion-Dipole Forces:

  • Definition: Electrostatic attraction between an ion (cation or anion) and the permanent dipole of a polar molecule.

  • Strength: Strongest among all intermolecular force classifications.

  • Solvation Role: Dissolution of ionic lattices in water involves orientation of water dipoles around ions: oxygen ends ($\delta-$) hydrate cations ($Na^+$), while hydrogen ends ($\delta+$) hydrate anions ($Cl^-$).

• Dominant Intermolecular Force Summary Table:

  • Methane ($CH_4$): Nonpolar, London dispersion forces dominate (symmetrical geometry).

  • Methanol ($CH_3OH$): Polar, Hydrogen bonding dominates (contains $O-H$ bond).

  • Chloroform ($CHCl_3$): Polar, Dipole-dipole forces dominate (permanent dipole without $N-H$, $O-H$, or $F-H$).

  • Benzene ($C_6H_6$): Nonpolar, London dispersion forces dominate (symmetrical planar ring).

  • Ammonia ($NH_3$): Polar, Hydrogen bonding dominates (contains $N-H$ bonds and N lone pair).

  • Sulfur Dioxide ($SO_2$): Polar, Dipole-dipole forces dominate (bent shape gives permanent dipole without H).

Liquid Properties in Action: Surface Tension, Viscosity, and Capillary Action

• Surface Tension:

  • Definition: The energy required to increase the surface area of a liquid by a unit amount (expressed in $mJ\,m^{-2}$).

  • Molecular Origin: Bulk molecules experience uniform attractive forces in all directions from surrounding neighbors. Surface molecules lack upper neighbors, experiencing a net inward cohesive force toward the bulk.

  • Geometric Consequence: Liquids minimize surface area by forming spherical droplets, as spheres minimize surface-area-to-volume ratios.

  • Quantitative Benchmarks at $20\,^\circ\text{C}$:

    • Water ($H_2O$): Surface tension = $72.8\,mJ\,m^{-2}$ (strong hydrogen bonding).

    • Benzene ($C_6H_6$): Surface tension = $28.0\,mJ\,m^{-2}$ (weak dispersion forces).

  • Determinants: Stronger intermolecular forces produce higher surface tension. Raising temperature lowers surface tension by increasing molecular kinetic energy, enabling molecules to overcome attractive potential barriers.

• Viscosity:

  • Definition: A fluid's internal resistance to flow.

  • Units: Measured in Poise ($1\,P = 1\,g\,cm^{-1}\,s^{-1}$) or centipoise ($1\,cP = 10^{-2}\,P$).

  • Benchmark Value: Water viscosity = $1.002\,cP$ at $20\,^\circ\text{C}$.

  • Comparative Fluidity: Honey exhibits high viscosity ($\approx 10000\,cP$ at $20\,^\circ\text{C}$) compared to water ($1.002\,cP$) because its concentrated sugar constituents (glucose, fructose) form extensive hydrogen bonding networks that inhibit molecular motion.

  • Governing Factors:

    • Intermolecular Forces: Direct relationship; stronger forces yield higher viscosity.

    • Temperature: Inverse relationship; heating increases average kinetic energy, lowering viscosity.

      • Water Viscosity vs Temperature:

        • $20\,^\circ\text{C}: 1.002\,cP$

        • $40\,^\circ\text{C}: 0.653\,cP$

        • $60\,^\circ\text{C}: 0.467\,cP$

        • $80\,^\circ\text{C}: 0.355\,cP$

        • $100\,^\circ\text{C}: 0.282\,cP$

    • Molecular Length and Geometry: Flexible, long-chain molecules entangle, increasing viscosity. Spherical shapes roll easily, exhibiting lower viscosity.

      • Straight-Chain Hydrocarbon Series at $20\,^\circ\text{C}$:

        • $n\text{-Pentane}$ ($C_5H_{12}$, $72.15\,g\,mol^{-1}$): $0.240\,cP$

        • $n\text{-Hexane}$ ($C_6H_{14}$, $86.17\,g\,mol^{-1}$): $0.326\,cP$

        • $n\text{-Heptane}$ ($C_7H_{16}$, $100.2\,g\,mol^{-1}$): $0.409\,cP$

        • $n\text{-Octane}$ ($C_8H_{18}$, $114.2\,g\,mol^{-1}$): $0.542\,cP$

        • $n\text{-Nonane}$ ($C_9H_{20}$, $128.3\,g\,mol^{-1}$): $0.711\,cP$

• Capillary Action, Cohesion, and Adhesion:

  • Definition: The ability of a liquid to flow upward against gravity within a narrow tube.

  • Interplay of Forces:

    • Cohesive Forces: Intermolecular attraction between identical liquid molecules.

    • Adhesive Forces: Attraction between liquid molecules and the solid walls of the tube.

  • Meniscus Formations:

    • Concave Meniscus: Forms when adhesive forces exceed cohesive forces (e.g., Water in glass). Water adheres to polar glass silica ($SiO_2$), creeping up the walls.

    • Convex Meniscus: Forms when cohesive forces exceed adhesive forces (e.g., Mercury in glass). Metallic cohesion within mercury dominates over adhesion to glass.

  • Capillary Radius Effect: Liquid column height rises higher in narrower tubes.

Vaporization, Vapor Pressure, and Phase Equilibria

• Vaporization Dynamics and Energetics:

  • Definition: Surface phase transition wherein liquid molecules with kinetic energy exceeding the intermolecular binding energy break free into the gas phase.

  • Factors Increasing Vaporization Rate: Greater surface area, elevated temperature, and weaker intermolecular forces.

  • Thermal Distribution (Maxwell-Boltzmann): Only a small high-energy kinetic tail of molecules escapes at ambient temperatures. Increasing temperature broadens the kinetic energy distribution, increasing the escaping fraction.

  • Energetics: Endothermic phase change ($\Delta H_{vap} > 0$). Liquid loses high-energy molecules, causing evaporative cooling unless heat is supplied.

  • Condensation: Exothermic reverse phase change ($\Delta H_{cond} = -\Delta H_{vap}$) where gas molecules collide with liquid surfaces, losing energy and re-entering the liquid state.

  • Volatility Classifications:

    • Volatile Liquids: Evaporate readily due to weak intermolecular forces (e.g., gasoline, acetone, diethyl ether).

    • Nonvolatile Liquids: Exhibit low vapor pressures and slow evaporation due to strong intermolecular forces (e.g., motor oil, glycerol).

• Heat of Vaporization ($\Delta H_{vap}$):

  • Definition: The energy required to vaporize one mole of liquid at constant pressure.

  • Enthalpy values of select liquids at their normal boiling points and at $25\,^\circ\text{C}$:

    • Water ($H_2O$): Normal bp = $100\,^\circ\text{C}$, $\Delta H_{vap} = 40.7\,kJ\,mol^{-1}$ at bp, $\Delta H_{vap} = 44.0\,kJ\,mol^{-1}$ at $25\,^\circ\text{C}$.

    • Isopropyl Alcohol ($C_3H_8O$): Normal bp = $82.3\,^\circ\text{C}$, $\Delta H_{vap} = 39.9\,kJ\,mol^{-1}$ at bp, $\Delta H_{vap} = 45.4\,kJ\,mol^{-1}$ at $25\,^\circ\text{C}$.

    • Acetone ($C_3H_6O$): Normal bp = $56.1\,^\circ\text{C}$, $\Delta H_{vap} = 29.1\,kJ\,mol^{-1}$ at bp, $\Delta H_{vap} = 31.0\,kJ\,mol^{-1}$ at $25\,^\circ\text{C}$.

    • Diethyl Ether ($C_4H_{10}O$): Normal bp = $34.6\,^\circ\text{C}$, $\Delta H_{vap} = 26.5\,kJ\,mol^{-1}$ at bp, $\Delta H_{vap} = 27.1\,kJ\,mol^{-1}$ at $25\,^\circ\text{C}$.

  • Sample Stoichiometric Heat Calculation:

    • Calculating mass of water vaporized at $100\,^\circ\text{C}$ given $155\,kJ$ heat input:             $\text{moles } H_2O = \frac{155\,kJ}{40.7\,kJ\,mol^{-1}} = 3.808\,mol$             $\text{mass } H_2O = 3.808\,mol \times 18.02\,g\,mol^{-1} = 68.6\,g\,H_2O$

• Dynamic Equilibrium and Vapor Pressure:

  • In a closed vessel, the rate of evaporation initially exceeds the rate of condensation. As gas density increases, condensation accelerates until rate of evaporation = rate of condensation (Dynamic Equilibrium).

  • Vapor Pressure: Partial pressure exerted by gas molecules in dynamic equilibrium with their liquid phase.

  • Boiling Point: The temperature at which liquid vapor pressure equals surrounding atmospheric pressure.

  • Normal Boiling Point: Temperature at which liquid vapor pressure equals exactly $1\,atm$ ($760\,torr$).

  • Altitude and Atmospheric Pressure Dependence:

    • Mount Everest ($29,032\,ft$): Pressure = $0.32\,atm$, Water Boiling Point = $78\,^\circ\text{C}$.

    • Denali ($20,310\,ft$): Pressure = $0.46\,atm$, Water Boiling Point = $83\,^\circ\text{C}$.

    • Mount Whitney ($14,505\,ft$): Pressure = $0.60\,atm$, Water Boiling Point = $87\,^\circ\text{C}$.

    • Denver ($5,280\,ft$): Pressure = $0.83\,atm$, Water Boiling Point = $94\,^\circ\text{C}$.

    • Boston ($20\,ft$): Pressure = $1.0\,atm$, Water Boiling Point = $100\,^\circ\text{C}$.

• Quantitative Modeling: Clausius-Clapeyron Equation:

  • Exponential Form:         $P_{vap} = \beta \exp\left(-\frac{\Delta H_{vap}}{R T}\right)$         Where $P_{vap}$ is vapor pressure, $\beta$ is a structural constant, $\Delta H_{vap}$ is heat of vaporization ($J\,mol^{-1}$), $R = 8.314\,J\,mol^{-1}\,K^{-1}$ is the gas constant, and $T$ is absolute temperature in Kelvin ($K$).

  • Linearized Form:         $\ln(P_{vap}) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T}\right) + \ln(\beta)$         Plotting $\ln(P_{vap})$ versus $\frac{1}{T}$ yields a straight line with slope $m = -\frac{\Delta H_{vap}}{R}$ and y-intercept $b = \ln(\beta)$.

  • Two-Point Form:         $\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right)$         Used to calculate vapor pressure or boiling point at non-standard conditions.

Phase Transitions, Heating Curves, and Phase Diagrams

• Sublimation and Fusion:

  • Sublimation: Direct phase change from solid to gas ($\text{Solid} \rightarrow \text{Gas}$), bypassing the liquid phase. Requires energy input ($\Delta H_{sub} > 0$). Example: Dry ice ($CO_2(s)$).

  • Deposition: Exothermic direct phase change from gas to solid ($\text{Gas} \rightarrow \text{Solid}$).

  • Fusion (Melting): Phase change from solid to liquid ($\text{Solid} \rightarrow \text{Liquid}$). Endothermic process ($\Delta H_{fus} > 0$).

  • Freezing (Crystallization): Exothermic reverse phase change from liquid to solid ($\Delta H_{crystallization} = -\Delta H_{fus}$).

  • Hess's Law Enthalpy Relation:         $\Delta H_{sub} = \Delta H_{fus} + \Delta H_{vap}$

• Heat of Fusion ($\Delta H_{fus}$):

  • Definition: Heat energy required to melt one mole of solid at constant pressure.

  • Relative Magnitude: $\Delta H_{fus}$ is significantly smaller than $\Delta H_{vap}$ because melting only requires partially disrupting long-range order, whereas vaporization requires breaking all intermolecular forces completely.

• Comprehensive Heating Curve of Water ($1.00\,mol$ from $-25.0\,^\circ\text{C}$ to $125.0\,^\circ\text{C}$):

*   **Segment 1: Heating ice from $-25.0\,^\circ\text{C}$ to $0.0\,^\circ\text{C}$:**
    *   Formula: $q_1 = m C_{s,ice} \Delta T$
    *   Parameters: $m = 18.0\,g$, $C_{s,ice} = 2.09\,J\,g^{-1}\,^\circ\text{C}^{-1}$, $\Delta T = 25.0\,^\circ\text{C}$.
    *   Calculation: $q_1 = (18.0\,g) \times (2.09\,J\,g^{-1}\,^\circ\text{C}^{-1}) \times (25.0\,^\circ\text{C}) = 941\,J = 0.941\,kJ$.
*   **Segment 2: Melting ice at $0.0\,^\circ\text{C}$ (Phase Change):**
    *   Formula: $q_2 = n \Delta H_{fus}$
    *   Parameters: $n = 1.00\,mol$, $\Delta H_{fus} = 6.02\,kJ\,mol^{-1}$.
    *   Calculation: $q_2 = (1.00\,mol) \times (6.02\,kJ\,mol^{-1}) = 6.02\,kJ$.
*   **Segment 3: Warming liquid water from $0.0\,^\circ\text{C}$ to $100.0\,^\circ\text{C}$:**
    *   Formula: $q_3 = m C_{s,liq} \Delta T$
    *   Parameters: $m = 18.0\,g$, $C_{s,liq} = 4.18\,J\,g^{-1}\,^\circ\text{C}^{-1}$, $\Delta T = 100.0\,^\circ\text{C}$.
    *   Calculation: $q_3 = (18.0\,g) \times (4.18\,J\,g^{-1}\,^\circ\text{C}^{-1}) \times (100.0\,^\circ\text{C}) = 7520\,J = 7.52\,kJ$.
*   **Segment 4: Vaporizing liquid water at $100.0\,^\circ\text{C}$ (Phase Change):**
    *   Formula: $q_4 = n \Delta H_{vap}$
    *   Parameters: $n = 1.00\,mol$, $\Delta H_{vap} = 40.7\,kJ\,mol^{-1}$.
    *   Calculation: $q_4 = (1.00\,mol) \times (40.7\,kJ\,mol^{-1}) = 40.7\,kJ$.
*   **Segment 5: Heating steam from $100.0\,^\circ\text{C}$ to $125.0\,^\circ\text{C}$:**
    *   Formula: $q_5 = m C_{s,steam} \Delta T$
    *   Parameters: $m = 18.0\,g$, $C_{s,steam} = 2.01\,J\,g^{-1}\,^\circ\text{C}^{-1}$, $\Delta T = 25.0\,^\circ\text{C}$.
    *   Calculation: $q_5 = (18.0\,g) \times (2.01\,J\,g^{-1}\,^\circ\text{C}^{-1}) \times (25.0\,^\circ\text{C}) = 905\,J = 0.905\,kJ$.
*   **Total Energy Input:**

        $q_{total} = q_1 + q_2 + q_3 + q_4 + q_5 = 0.941 + 6.02 + 7.52 + 40.7 + 0.905 = 56.086\,kJ$

• Phase Diagrams:

  • Map of stable physical states as a function of pressure ($P$) and temperature ($T$).

  • Structural Regions: Distinct areas correspond to Solid, Liquid, and Gas phases.

  • Boundary Curves:

    • Sublimation Curve: Solid-gas equilibrium boundary.

    • Fusion Curve: Solid-liquid equilibrium boundary.

    • Vaporization Curve: Liquid-gas equilibrium boundary.

  • Triple Point: Unique temperature and pressure at which solid, liquid, and gas phases coexist simultaneously in thermodynamic equilibrium (For water: $T = 0.01\,^\circ\text{C}$, $P = 4.58\,torr$).

  • Critical Point: Terminal point of the vaporization curve at critical temperature ($T_c$) and pressure ($P_c$). Beyond this point, liquid and gas boundaries vanish, forming a Supercritical Fluid.

  • Anomalous Fusion Curve of Water:

    • Most substances possess a positive fusion curve slope ($\frac{dP}{dT} > 0$), as solid states are denser than liquid states.

    • Water exhibits a negative fusion curve slope ($\frac{dP}{dT} < 0$) because ice is less dense than liquid water due to an open hexagonal hydrogen-bonded structure. Applying pressure to ice at $0\,^\circ\text{C}$ induces melting into liquid water.