Theory and Practice of Physical Pharmacy Chapter 1 and forward- Summary

GASEOUS STATE: Gases have no definite shape or volume and are compressible fluids, filling the entire container. Their high kinetic energy minimizes intermolecular forces, leading to large intermolecular distances. Vapors, existing below critical temperature, can be liquefied by compression alone. Temperature and pressure influence whether a substance exists as a gas, liquid, or solid.

Ideal Gas Law:

Several significant laws explain gas behavior:

  • Boyle's Law: At constant temperature, gas volume (V) is inversely proportional to pressure (P). V∝1PV \propto \frac{1}{P}

  • Charles' Law: At constant pressure, gas volume (V) is directly proportional to temperature (T). V∝TV \propto T

  • Gay-Lussac's Law: At constant volume, the pressure (P) of a gas is directly proportional to temperature (T). P∝TP \propto T

  • Avogadro's Law: At constant temperature and pressure, gas volume (V) is directly proportional to the number of moles (n). V∝nV \propto n

Ideal Gas Law:

Combining the above gives the ideal gas law: PV=nRTPV = nRT, where R is the gas constant. R is determined experimentally by plotting PV against P and extrapolating to zero pressure. R=PVnTR = \frac{PV}{nT} ; R=0.08206LatmmoleKR = 0.08206 \frac{L atm}{mole K} at 1 atmospheric pressure and 0°C.

Molecular Weight Determination:

Molecular weight (M) can be calculated using: PV=gRTMPV = \frac{gRT}{M}, or M=gRTPVM = \frac{gRT}{PV}, where g is the mass of the gas.

Real Gases:

Deviations from ideal behavior occur at lower temperatures and/or higher pressures. The van der Waals equation corrects for these deviations: (P+aV2)(V−b)=nRT(P + \frac{a}{V^2})(V - b) = nRT. The constant 'a' accounts for cohesive forces, and 'b' accounts for the excluded volume of gas molecules. At low pressures, where volume is large, the equation reduces to the ideal gas law.

LIQUID STATE:

Liquids have properties intermediate between gases and solids. They assume the shape of a container and distribute pressure evenly but do not always fill the container or compress significantly. Density is close to that of solids, but molecules have greater freedom to move.

Properties of Liquids:

  1. Random molecular motion, but less than gases, explains incompressibility and higher density.

  2. Kinetic energy and vapor pressure increase with temperature.

  3. Intermolecular attraction is 106 times stronger than in gases, preventing spontaneous separation.

Attractive Forces influencing phenomena:

Viscosity, surface tension, and vapor pressure.

Surface Tension:

Molecules at the surface experience a net inward pull due to unbalanced forces, causing the surface to contract and behave as if in tension.

Viscosity:

Resistance to flow due to shearing effect when one liquid layer moves past another.

Vapour Pressure:

Evaporation occurs when molecules gain enough energy to escape into the vapor phase. Condensation is the reverse process. At equilibrium, the rates of evaporation and condensation are equal. The Clausius-Clapeyron equation expresses the relationship between vapor pressure and absolute temperature:
log⁡P<em>1P</em>2=ΔH2.303R(1T<em>1−1T</em>2)\log \frac{P<em>1}{P</em>2} = \frac{{\Delta}H}{2.303R} (\frac{1}{T<em>1} - \frac{1}{T</em>2}), where '1H is the molar heat of vaporization.

SOLID STATE:

Solids have a stable shape and volume due to strong intermolecular forces.

Properties of Solids:

  1. Rigid with definite shape.

  2. Nearly incompressible.

  3. Slow diffusion compared to liquids or gases.

  4. Most melt upon heating, while some sublime.

Crystalline Solids:

Molecules are arranged in a repeating, ordered pattern. The melting point is the temperature at which the crystal lattice breaks. Unit cells are the smallest repeating units; examples include cubic, hexagonal, and triclinic. Crystalline solids have definite and rigid shapes, with interfacial angles remaining constant (law of constancy of interfacial angles).

Types of Crystalline Solids:

  1. Molecular crystals: Held by weak van der Waals forces. Soft, compressible, with low melting and boiling points; poor conductors (e.g., dry ice).

  2. Covalent crystals: Atoms are bonded by covalent bonds. Hard, incompressible, nonvolatile with very high melting points; poor conductors (e.g., diamond).

  3. Ionic crystals: Composed of positive and negative ions. Hard and brittle with high melting and boiling points; conduct electricity when melted or dissolved in polar solvents (e.g., sodium chloride).

  4. Metallic crystals: Positive kernels dispersed in a sea of mobile valence electrons. Can be hard or soft; good conductors of heat and electricity (e.g., copper).

Polymorphism:

The ability of a compound to crystallize in multiple forms with different lattice arrangements. Polymorphs have varying stabilities and properties like X-ray diffraction, melting point, and solubility. Polymorph formation depends on factors like supersaturation, temperature, and solvent. Examples include enantiotropic (reversibly changed with temp/pressure) and monotropic (one form unstable) polymorphs.

Solvates and Hydrates:

Crystalline solids may contain stoichiometric amounts of solvent (solvates) or water (hydrates) within the crystal lattice. Anhydrous forms lack water.

Amorphous Solids:

Lack long-range order and resemble liquids. Possess higher molecular mobility, entropy, and enthalpy than crystalline forms of the same material (supercooled liquids). Polycrystalline solids appear isotropic even though individual crystals are anisotropic.

Liquid Crystal State (Mesophase):

A state between crystalline solid and liquid states with molecules aligned along a common axis but arranged randomly within layers. Exhibits polymorphism and anisotropy (properties depend on measurement direction). Types include nematic, smectic, and cholesteric.

Supercritical Fluid State:

Formed from a gas above its critical temperature and pressure, it possesses properties intermediate between those of liquids and gases. Can effuse through solids and dissolve materials. Lacks surface tension. Applications include extraction, chromatography, and crystallization. Carbon dioxide and water are common examples.

States of Matter Changes:

-Liquefaction of Gases: Achieved by decreasing temperature and increasing pressure.
-Boiling Point: Temperature at which vapor pressure equals atmospheric pressure. The heat absorbed is the latent heat of vaporization.
-Melting Point: Temperature at which solid changes to liquid; the energy provided is the latent heat of fusion.

Phase Rule:

Proposed by J. Willard Gibbs, it relates the degrees of freedom (F), number of phases (P), and number of components (C) in a system at equilibrium: F=C−P+2F = C - P + 2. For condensed systems, the equation is F=C−P+1F = C - P + 1

Two-Component Systems examples:

  • Liquids: Water and phenol mixtures exhibiting partial miscibility depending on concentration and temperature. Has upper consulate temperature.

  • Solids and Liquids: Eutectic mixtures.

Three-Component Systems:

Represented by triangle diagrams with vertices representing 100% concentration of each component.