Notes, summaries, assignments, exams, and exercises for Chemistry for University

Gravimetric Analysis Fundamentals

Gravimetry is based on the law of mass action, essentially involving two experimental steps:

• Weight of the sample.
• Weight of the analyte or a known chemical substance of known composition containing the analyte.

Types of Gravimetric Analysis

Gravimetry by Volatilization

• The analyte is separated from other constituents of a sample by converting it into a known gas composition.
• The weight of this gas serves as a measure of the concentration of the analyte.

Gravimetry by Precipitation

• The analyte is separated from the components of a solution as a precipitate that is treated and converted into a stable compound of known composition.

Precipitators Agents

• Specific: They are rare; they react with a single chemical species.
• Selective:

Quantum Mechanics, E-k Diagrams & Effective Mass

• Schrödinger Equation: H * Ψ = E * Ψ, where H = V - (ħ^2 * ∇^2) / (2 * m).

  • 1D Infinite Well / H-Atom: Gives discrete energy states (E_n = -13.6 eV / n^2 for H-atom).

  • Crystal Lattice (spacing a): Multi-atom electron interactions split discrete states into a continuum of states (Bands: Ec, Ev) separated by a forbidden Bandgap (Eg).

• E-k Diagram (Reciprocal Space): Repeats every 2π / a; First Brillouin Zone is -π / a to +π / a.

  • 3D Parabolic Band: E(k) = E_min/max + (ħ^2 * k^2) / (2 * m*)

  • Effective Mass Derivation: Take 2nd derivative d^2E / dk^2 = ħ^2 / m* ⇒ m* = ħ^2 / (d^2E / dk^2)

  • Mobility & Current: μ = (q * τ) / m*, v = μ * E, and J = I / A = n * e * v = n * e * μ * E. (Sharper