Liquids, Solids, and Intermolecular Forces

Intermolecular Forces and the States of Matter in Zero-Gravity

Intermolecular attractive forces are the fundamental interactions existing among all particles that compose matter. The physical existence of condensed states—specifically solids and liquids—is determined by the magnitude of these intermolecular forces relative to the amount of thermal energy present in a sample. An illustrative example of these forces is observed in the behavior of water in a zero-gravity environment, such as a space station. In this environment, water molecules do not spill; instead, they stick together to form a floating, oscillating blob. This oscillation eventually ceases as the blob takes the shape of a near-perfect sphere, a direct consequence of intermolecular forces acting to minimize surface area.

Comparative Properties of the Three States of Matter

The properties of gas, liquid, and solid states vary significantly based on the relative strength of intermolecular forces compared to thermal energy:

• Gas State: Characterized by low density, an indefinite shape, and an indefinite volume. The intermolecular forces are weak relative to thermal energy. Particles have complete freedom of motion, are not held together, and are constantly in motion, colliding with each other and their container. There is substantial empty space between particles, leading to a molar volume much larger than that of solids or liquids. Gases are compressible and expand to fill any container.
• Liquid State: Characterized by high density, an indefinite shape, and a definite volume. The intermolecular forces are moderate relative to thermal energy. Particles are closely packed, making liquids incompressible, yet they possess the ability to move around one another. This allows liquids to flow and take the shape of the bottom of their container, though they lack the freedom to expand and fill the container entirely.
• Solid State: Characterized by high density, a definite shape, and a definite volume. The intermolecular forces are strong relative to thermal energy. Particles are packed closely in fixed positions, although they may vibrate. Because of this packing, solids are incompressible and do not flow, retaining their shape regardless of the container.

Structural Categorization of Solids and Phase Changes

Solids are further classified based on the arrangement of their constituent particles. Crystalline solids, such as salt and diamonds, feature particles arranged in an orderly, long-range geometric pattern. In contrast, amorphous solids, such as glass and plastic, consist of particles that do not demonstrate a regular geometric pattern over a long range.

Transitioning between these states requires a change in the kinetic energy of the particles or a change in their freedom of movement. Heating solids causes them to melt into liquids, while heating liquids causes them to boil into gases. Transitions can also be induced by pressure changes. Gases can be condensed into liquids by decreasing the temperature or increasing the pressure. Increasing pressure, often achieved by decreasing the gas volume, reduces the translational freedom of the particles. For most substances, the freezing point increases as the applied pressure increases.

The Nature and Trends of Intermolecular Attractions

Intermolecular attractions arise due to the forces between opposite charges. These include attractions between a positive ion and a negative ion, or the positive end of one polar molecule and the negative end of another. Even nonpolar molecules experience temporary charges. The strength of these attractions is governed by the magnitude of the charges (larger charges result in stronger attractions) and the distance between them (increased distance results in weaker attractions). Notably, intermolecular forces are generally much weaker than the bonding forces (covalent or ionic) that hold atoms together within a molecule because they involves smaller charges over larger distances.

There is a direct correlation between the strength of intermolecular forces and boiling points. Boiling a liquid requires the addition of enough energy to overcome all attractions between the particles without breaking the internal covalent bonds. Consequently, the stronger the intermolecular attractive forces, the higher the normal boiling point of the liquid will be.

Dispersion Forces and Molecular Factors

Dispersion forces, also known as London forces, are the result of temporary polarity caused by fluctuations in electron distribution within atoms and molecules. This creates an instantaneous dipole where a region with excess electron density acquires a partial negative charge ($\delta^-$) and a region with depleted density acquires a partial positive charge ($\delta^+$). These forces are present in all molecules and atoms. When an instantaneous dipole forms in one molecule, it induces a dipole in surrounding molecules.

The magnitude of the dispersion force depends on:

1. Polarizability: Determined by the volume of the electron cloud. A larger molar mass implies more electrons and a larger electron cloud, which increases polarizability and results in stronger attractions. For example, in noble gases, boiling points increase as molar mass increases.
2. Molecular Shape: Molecules with more surface-to-surface contact have larger induced dipoles. Straight-chain isomers (n-alkanes) have higher boiling points than branched-chain isomers because they allow for more contact between molecules.

Dipole–Dipole Forces and Solubility

Dipole–dipole forces exist in polar molecules that possess a permanent dipole due to their molecular shape and bond polarity. This permanent dipole increases the attractive forces between molecules, leading to higher boiling and melting points compared to nonpolar molecules of similar size. For instance, Acetonitrile ($CH_3CN$) has a molar mass of $41.05\,g/mol$ and a dipole moment of $3.92\,D$, resulting in a boiling point of $81.6^\circ C$. In contrast, propane ($CH_3CH_2CH_3$) has a similar molar mass ($44.09\,g/mol$) but a dipole moment of only $0.08\,D$, leading to a much lower boiling point of $-42^\circ C$.

Solubility is dictated by the principle that "like dissolves like." Polar substances dissolve in polar solvents (hydrophilic interactions), while nonpolar molecules dissolve in nonpolar solvents (hydrophobic interactions). Miscible liquids can dissolve in each other in any proportion. If the attractive forces between molecules of the same kind (e.g., water-water) are much stronger than the attractions for a different molecule (e.g., pentane), the liquids will be immiscible.

Hydrogen Bonding and Ion–Dipole Forces

Hydrogen bonding is a particularly strong type of dipole–dipole interaction that occurs when hydrogen is bonded to a highly electronegative atom (specifically fluorine, oxygen, or nitrogen). Because these atoms pull the bonding electrons away so strongly and hydrogen has no other electrons, the hydrogen nucleus (a proton) becomes de-shielded. This exposed proton creates a strong center of positive charge that attracts electron clouds on neighboring molecules. While very strong for an intermolecular force (responsible for the high boiling points of water and ethanol), hydrogen bonds are only about $2\%-5\%$ as strong as covalent bonds.

Ion–dipole forces occur in mixtures when ions from an ionic compound are attracted to the dipoles of polar molecules. This is the strongest type of intermolecular attraction found in mixtures and is the primary factor determining the solubility of ionic compounds in aqueous solutions.

Summary of Intermolecular Force Strengths

Note: Dispersion forces can become stronger than other forces in molecules with very high molar masses.

Physical Properties of Liquids: Surface Tension and Viscosity

Surface tension is the tendency of liquids to minimize their surface area. Molecules at the surface experience a net pull toward the interior because they lack neighbors above them, causing the surface to act like an "elastic skin." Stronger intermolecular forces result in higher surface tension. Increasing the temperature generally reduces surface tension as thermal energy overcomes the cohesive forces.

Viscosity is the resistance of a liquid to flow. It increases with the strength of intermolecular attractions and the length of the molecules (which increases surface contact). More spherical molecular shapes result in lower viscosity as the molecules can roll more easily.

Viscosity of n-Alkanes:

• n-Pentane ($C_5H_{12}$): $0.240\,cP$ (Molar mass: $72.15\,g/mol$)
• n-Hexane ($C_6H_{14}$): $0.326\,cP$ (Molar mass: $86.17\,g/mol$)
• n-Heptane ($C_7H_{16}$): $0.409\,cP$ (Molar mass: $100.2\,g/mol$)
• n-Octane ($C_8H_{18}$): $0.542\,cP$ (Molar mass: $114.2\,g/mol$)
• n-Nonane ($C_9H_{20}$): $0.711\,cP$ (Molar mass: $128.3\,g/mol$)

Capillary Action and Meniscus Formation

Capillary action is the ability of a liquid to rise up a thin tube against gravity, driven by the competition between cohesive forces (liquid-liquid attraction) and adhesive forces (liquid-tube attraction). Adhesive forces pull the edges of the liquid up the tube, and cohesive forces pull the rest of the liquid along. The liquid rises until gravity balances these forces. Thinner tubes result in higher rises. This competition also forms the meniscus. Water forms a concave meniscus in glass because adhesive forces to the glass are stronger than cohesive forces. Mercury forms a convex meniscus because its cohesive forces (metallic bonds) are stronger than its adhesion to glass.

Vaporization and Vapor Pressure

Molecules in a liquid are in constant motion with a distribution of kinetic energies proportional to temperature. Vaporization (evaporation) occurs when high-energy molecules at the surface overcome intermolecular attractions to escape into the gas phase. The rate of vaporization increases with surface area and temperature. Volatile liquids evaporate easily due to weak intermolecular forces, while nonvolatile liquids (like motor oil) do not.

Condensation is the opposite process, where gas molecules lose energy and are recaptured by the liquid. In a closed container, vaporization and condensation reach dynamic equilibrium. The pressure exerted by the vapor at this point is the vapor pressure. Weaker intermolecular forces lead to higher vapor pressure and higher volatility. Vapor pressure increases with temperature.

Boiling Point and Atmospheric Pressure

Boiling occurs when a liquid's vapor pressure equals the external (atmospheric) pressure, allowing bubbles to form throughout the liquid. The normal boiling point is the temperature where vapor pressure equals $1\,atm$. Because atmospheric pressure decreases at higher altitudes, the boiling point of water also decreases:

• Sea Level (Boston, MA): $1.0\,atm$, $100^\circ C$
• Denver, CO ($5,280\,ft$): $0.83\,atm$, $94^\circ C$
• Mount Whitney, CA ($14,505\,ft$): $0.60\,atm$, $87^\circ C$
• Denali, AK ($20,310\,ft$): $0.46\,atm$, $83^\circ C$
• Mount Everest, Tibet ($29,029\,ft$): $0.32\,atm$, $78^\circ C$

Sublimation, Fusion, and Phase Diagrams

Sublimation is the direct transition from solid to gas, while deposition is the transition from gas to solid. Fusion (melting) occurs when a solid is heated and molecules gain enough energy to partially overcome the forces holding them in place. The opposite of fusion is freezing.

Phase diagrams map the states of matter based on temperature and pressure:

• Lines: Represent state changes where two states coexist (e.g., the vaporization curve).
• Triple Point: The specific temperature and pressure where all three states coexist in equilibrium.
• Critical Point: The terminal point on the vaporization curve. Beyond the critical temperature ($T_c$), a gas cannot be condensed into a liquid regardless of pressure.
• Supercritical Fluid: Formed at or above the critical point where the meniscus disappears and the substance has properties of both a gas and a liquid.

Questions & Discussion

Conceptual Connection 12.1: Which state of matter is compressible? The answer is gas, because of the large amount of empty space between particles.

Conceptual Connection 12.3: Which halogen has the highest boiling point ($Cl_2$, $Br_2$, or $I_2$)?$I_2$ has the highest boiling point because it has the largest molar mass, leading to greater polarizability and stronger dispersion forces.

Determining Dipole-Dipole Attractions: Do they occur between $CH_2Cl_2$ molecules? To determine this, one must look at the Lewis structure and molecular shape. Because of the electronegativity differences ($C=2.5, H=2.1, Cl=3.0$) and the molecular geometry, $CH_2Cl_2$ is polar and thus experiences dipole-dipole attractions.

Conceptual Connection 12.4: Orientation of Acetonitrile ($CH_3CN$) interaction. Acetonitrile molecules will orient themselves so that the positive end of one molecule is near the negative end of the other.

Practice: Choose the substance in each pair that is a liquid at room temperature (highest boiling point).

1. Pair: $CH_3OH$ or $CH_3CHF_2$. Answer: $CH_3OH$ (due to hydrogen bonding).
2. Pair: $CH_3-O-CH_2CH_3$ or $CH_3CH_2CH_2NH_2$. Answer: $CH_3CH_2CH_2NH_2$ (due to hydrogen bonding via the amino group).

Conceptual Connection 12.5: Which substance has the highest boiling point ($CH_3OH$, $CO$, or $N_2$)?$CH_3OH$ (Methanol) has the highest boiling point because it can form hydrogen bonds.

Practice: Phases of $CO_2$ at specific conditions based on the phase diagram.

• $20.0^\circ C, 72.9\,atm$: Near the critical point.
• $-56.7^\circ C, 5.1\,atm$: Triple point (Solid, Liquid, and Gas coexist).
• $10.0^\circ C, 1.0\,atm$: Gas phase.
• $-78.5^\circ C, 1.0\,atm$: Solid/Gas boundary (Sublimation point).
• $50.0^\circ C, 80.0\,atm$: Supercritical fluid phase (above critical temperature of $31^\circ C$).