Physical Chemistry Concepts: Definitions and Applications

Posted on Apr 2, 2025 in Chemistry

Nernst Distribution Law

The Nernst Distribution Law describes the equilibrium distribution of a solute between two immiscible liquid phases. It states that at a constant temperature, the ratio of the concentrations of the solute in the two liquids is constant, provided the solute has the same molecular form in both phases.

Limitations include deviations due to solute association or dissociation in one phase, and non-ideal behavior at higher concentrations. Modifications often involve using activities instead of concentrations or considering the distribution coefficient (partition coefficient) which accounts for different solute forms.

Surface Tension

Surface tension is a property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules. It represents the energy required to increase the surface area of a liquid by a unit amount.

Classification of interfaces involving liquids:

  • Liquid-gas (Surface Tension)
  • Liquid-liquid (Interfacial Tension)
  • Liquid-solid (Interfacial Tension)

Common methods for determination include:

  • Capillary rise method
  • Pendant drop method
  • Wilhelmy plate method

Analysis of Complexes

Methods for the analysis and characterization of complexes (e.g., metal-ligand complexes) include:

  • pH Titration: Used to determine stability constants by monitoring pH changes during complex formation.
  • Spectrophotometry (UV-Vis, IR, NMR): Measures absorbance or other spectral properties that change upon complexation.
  • Chromatography (e.g., Ion Exchange, Size Exclusion): Separates complexed species from free components.

pH titration, specifically, involves measuring the pH of a solution containing the interacting species as a function of the volume of a titrant (acid or base) added.

Solubility of Gases in Liquids

Several factors affect the solubility of gases in liquids:

  • Temperature: Generally, gas solubility decreases as temperature increases.
  • Pressure: Gas solubility increases proportionally with the partial pressure of the gas above the liquid (Henry’s Law).
  • Nature of the Gas and Liquid: Chemical similarities (e.g., polarity) influence solubility. Gases that react with the solvent show higher solubility.
  • Presence of Other Solutes: Dissolved salts often decrease gas solubility (‘salting out’).

Raoult’s Law and Deviations

Raoult’s Law states that the partial vapor pressure of a solvent above an ideal solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution (Psolvent = Xsolvent * P0solvent).

Deviations from Raoult’s Law occur in real solutions due to non-ideal behavior arising from differences in intermolecular forces between solute-solvent, solute-solute, and solvent-solvent molecules. Positive deviations occur when interactions between unlike molecules are weaker than between like molecules, leading to higher vapor pressure. Negative deviations occur when interactions between unlike molecules are stronger, leading to lower vapor pressure.

Polymorphism in Solids

Polymorphism is the ability of a solid material to exist in more than one crystalline form or structure. These different forms, called polymorphs, have the same chemical composition but differ in their crystal lattice arrangements, leading to variations in physical properties like solubility, melting point, and stability.

Dissociation Constants

Dissociation constants (e.g., acid dissociation constant, Ka; base dissociation constant, Kb) quantify the extent to which a compound (like an acid or base) dissociates into its constituent ions in a solution at equilibrium. They are equilibrium constants for the dissociation reaction.

Applications include:

  • Calculating the pH of solutions containing weak acids or bases.
  • Preparing buffer solutions with specific pH values.
  • Predicting drug absorption and behavior in pharmaceutical formulations and biological systems.

Crystal Structure Analysis

Methods used to determine the arrangement of atoms within a crystalline solid include:

  • X-ray Diffraction (XRD): The primary technique for determining crystal structure, lattice parameters, and identifying crystalline phases based on diffraction patterns.
  • Infrared (IR) Spectroscopy: Provides information about chemical bonds and functional groups, which can differ between polymorphs.
  • Microscopy (e.g., Polarized Light Microscopy, SEM): Visualizes crystal habit (shape) and morphology, which can be indicative of the crystal form.

Principles of Diffusion

Diffusion is the net passive movement of particles (atoms, ions, or molecules) from a region of higher concentration to a region of lower concentration. This movement is driven by the random thermal motion of particles and continues until the concentration is uniform throughout the system (equilibrium).

Adsorption Isotherms

Adsorption isotherms describe the equilibrium relationship between the amount of a substance (adsorbate) adsorbed onto a solid surface (adsorbent) and its concentration or pressure in the surrounding fluid (gas or liquid) at a constant temperature. Examples include Langmuir and Freundlich isotherms.

Spreading Coefficient

The spreading coefficient (S) is a measure of the tendency of a liquid (e.g., oil) to spread spontaneously over another liquid or a solid surface. It is calculated from the surface and interfacial tensions involved (S = γsub – γliq – γint, where sub=substrate, liq=spreading liquid, int=interface). A positive or zero value indicates spontaneous spreading.

HLB (Hydrophile-Lipophile Balance)

HLB (Hydrophile-Lipophile Balance) is an empirical scale (typically 0-20) used to characterize surfactants based on the relative strength of their hydrophilic (water-loving) and lipophilic (oil-loving) portions. It helps predict surfactant properties like solubility and suitability for specific applications (e.g., emulsifiers, detergents, wetting agents).

Surface Active Agents (Surfactants)

Surface active agents, commonly known as surfactants, are amphiphilic molecules containing both hydrophilic and lipophilic parts. They preferentially adsorb at interfaces (e.g., air-water, oil-water) and lower the surface tension or interfacial tension.

Fundamental Gas Laws

Gas laws describe the macroscopic behavior of gases in relation to pressure (P), volume (V), temperature (T), and amount (n). Key fundamental laws include:

  • Boyle’s Law: At constant temperature, the volume of a fixed amount of gas is inversely proportional to its pressure (P₁V₁ = P₂V₂).
  • Charles’ Law: At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature (V₁/T₁ = V₂/T₂).
  • Avogadro’s Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas (V₁/n₁ = V₂/n₂).

Factors Affecting Solubility

The solubility of a solute in a solvent depends on several factors:

  • Temperature: Solubility of solids usually increases with temperature, while gas solubility typically decreases.
  • Pressure: Significantly affects gas solubility (increases with pressure – Henry’s Law), but has little effect on solid or liquid solubility.
  • Nature of Solute and Solvent: The principle of “like dissolves like” applies; polar solutes dissolve better in polar solvents, and nonpolar solutes in nonpolar solvents.
  • Presence of Other Solutes: Can increase or decrease solubility through effects like complexation or the common ion effect.

Capillary Rise Method for Surface Tension

The capillary rise method is an experimental technique for measuring the surface tension of a liquid. It involves observing the height to which a liquid rises (or falls, if non-wetting) inside a narrow capillary tube due to surface tension forces balancing the weight of the liquid column. The surface tension can be calculated using the Jurin’s Law equation.

Buffered Isotonic Solutions

A buffered isotonic solution is a solution designed for biological or pharmaceutical applications (like injections or eye drops) that meets two criteria:

  1. Isotonic: It has the same osmotic pressure as a specific biological fluid (e.g., blood plasma, tear fluid), preventing cell damage due to water movement.
  2. Buffered: It contains a buffer system (a weak acid and its conjugate base, or vice versa) that resists significant changes in pH upon addition of small amounts of acid or base, maintaining stability.

Fundamental States of Matter

The three fundamental states (or phases) of matter are distinguished by their structural arrangement and particle motion:

  • Solid: Particles are tightly packed in fixed positions; has a definite shape and volume.
  • Liquid: Particles are close together but can move past one another; has a definite volume but takes the shape of its container.
  • Gas: Particles are far apart and move randomly and rapidly; has no definite shape or volume, filling its container.

Gibbs Phase Rule

The Gibbs Phase Rule relates the number of degrees of freedom (F) of a system at thermodynamic equilibrium to the number of components (C) and the number of phases (P) present. The rule is expressed as: F = C – P + 2 (for systems where pressure and temperature are variables). Degrees of freedom represent the number of independent intensive variables (like temperature, pressure, concentration) that can be varied without changing the number of phases in equilibrium.

Methods for pH Determination

Common methods for measuring the pH (acidity or alkalinity) of an aqueous solution include:

  • pH Meter: An electronic instrument (potentiometric method) that measures the voltage difference between a pH-sensitive electrode and a reference electrode. Offers high accuracy.
  • pH Indicator Paper/Strips: Paper impregnated with indicators that change color at specific pH values. Provides a quick estimate.
  • pH Indicator Solutions: Liquid indicators added to the solution that change color depending on the pH. Used visually or in titrations.
  • Acid-Base Titration: Determining the concentration of an acid or base by neutralizing it with a solution of known concentration, often using a pH meter or indicator to find the endpoint. pH can be calculated at various points.

Surface Tension vs. Interfacial Tension

Both measure the energy per unit area at an interface, but:

  • Surface Tension (γ): Specifically refers to the tension at the interface between a liquid and a gas (usually air). It arises from the imbalance of cohesive forces experienced by molecules at the surface compared to the bulk liquid.
  • Interfacial Tension (γint): Refers to the tension at the interface between two immiscible liquids, or between a liquid and a solid. It arises from the imbalance of both cohesive (within each phase) and adhesive (between phases) forces at the boundary.

Protein-Drug Binding Interactions

Protein-drug binding is the phenomenon where drug molecules associate reversibly (or sometimes irreversibly) with proteins in the body, primarily plasma proteins like albumin and alpha-1-acid glycoprotein, but also tissue proteins. This binding affects the drug’s distribution, metabolism, excretion, and pharmacological activity, as typically only the unbound (free) fraction of the drug is pharmacologically active and available to cross membranes.

Surface Tension Measurement Methods

Common laboratory techniques for determining the surface tension of liquids include:

  • Capillary Rise Method: Measures the height a liquid climbs in a narrow tube.
  • Pendant Drop Method: Analyzes the shape of a drop hanging from a tip.
  • Wilhelmy Plate Method: Measures the force required to pull a thin plate (usually platinum) through the liquid surface.
  • (Other methods include Du Noüy ring, drop volume, bubble pressure)

Fick’s Laws of Diffusion

Fick’s Laws describe the process of diffusion quantitatively:

  • Fick’s First Law: Relates the diffusive flux (J, the amount of substance crossing a unit area per unit time) to the concentration gradient (dC/dx). It states that flux is proportional to the negative of the gradient: J = -D (dC/dx), where D is the diffusion coefficient.
  • Fick’s Second Law: Describes how the concentration changes over time at a specific location due to diffusion. It is a partial differential equation: ∂C/∂t = D (∂²C/∂x²) (in one dimension).

Critical Solution Temperature (CST)

The Critical Solution Temperature (CST) is the specific temperature at which two partially miscible liquids become fully miscible in all proportions. There are two types:

  • Upper Critical Solution Temperature (UCST): The temperature above which the two liquids are completely miscible. Below the UCST, they form two separate phases within a certain composition range.
  • Lower Critical Solution Temperature (LCST): The temperature below which the two liquids are completely miscible. Above the LCST, they separate into two phases. Some systems exhibit both UCST and LCST.