Behaviour of solutes in solvents: solubility, Henry's law, Raoult's law, colligative properties, and activity coefficients for non-ideal mixtures. Operational substrate of analytical and biological chemistry.
solution-chemistry
Solubility
Maximum amount of a solute that dissolves in a given solvent at equilibrium under specified conditions, typically expressed as g/L, mol/L,…
Henry's law
At a fixed temperature, the partial pressure of a gas dissolved in a liquid is proportional to its mole fraction in the liquid: p_i = k_H…
Raoult's law
For an ideal liquid mixture, the partial vapour pressure of each component equals its pure-component vapour pressure times its mole…
Colligative properties
Solution properties depending only on the number (not the identity) of solute particles: vapour-pressure lowering, boiling-point elevation,…
Activity coefficient (γ)
Correction factor a_i = γ_i x_i relating the effective 'active' concentration of a species to its mole fraction for non-ideal solutions.…
Molarity (concentration)
Amount concentration: moles of solute per litre of solution. Unit: mol·L⁻¹ or M. The default concentration scale in aqueous chemistry.…
Osmosis and osmotic pressure
Net flow of solvent across a semipermeable membrane from a region of low solute concentration to one of high solute concentration, driven…
Debye-Hückel theory
Limiting law for activity coefficients: log γ± = -A|z+z⁻|√I. Ionic atmosphere + Debye length. Extends to extended DH + Davies equations for…
Osmotic pressure (van't Hoff)
Π = iMRT for dilute solutions. Colligative property; governs biological fluid balance, membrane separations, desalination (reverse osmosis).
Solubility product Ksp & common-ion effect
Ksp = [A⁺]ᵃ[B⁻]ᵇ for sparingly soluble salt. Common-ion effect suppresses solubility; complex formation enhances. Selective precipitation…
Ion solvation & coordination number
Hydration shells: Li+ (4), Na+ (4-6), K+ (6-8), Mg²+ (6), Ca²+ (6-8). Residence times (~ns to µs). Impacts mobility, biological selectivity.
Activity vs concentration
a = γc accounts for non-ideality. Pitzer equations for concentrated electrolytes. Thermodynamic standard states: 1 mol/kg (molal), Henry's…
Debye–Hückel (extended) theory
log γ = -A z² √I/(1+Ba√I); limiting law at low I; Davies, Pitzer extensions for higher concentrations.
Pitzer model of electrolyte activity
Virial expansion in ionic strength with binary/ternary parameters; accurate to seawater-high I; OLI, SeaFREAK codes.
Born model of ion solvation
ΔG_solv = -N_A z²e²/(8πε₀r)(1-1/ε); continuum dielectric; refined by Onsager, PCM, COSMO for molecular simulations.
Hofmeister series
SO₄²⁻ > Cl⁻ > Br⁻ > SCN⁻ chaotropic/kosmotropic ion effect on protein stability, solubility; modern views beyond surface tension.
Salting-in / salting-out
Ion-specific solubility change of macromolecules; Setschenow equation; mechanism for ammonium-sulfate protein precipitation.
Micelle formation & CMC thermodynamics
Amphiphile aggregation above CMC; critical packing parameter v/(a₀l_c); spherical, rod, bilayer predictions.
Solubility product K_sp
K_sp = Π a_i^ν_i for sparingly soluble salt; common-ion effect; pH dependence for hydroxides, carbonates.
Solvatochromic scales (E_T(30))
Solvent polarity index from λ_max of betaine dye; ~200 solvents ranked; H-bond donor acceptor α, β parameters.
Stability constants β_n
β_n = [ML_n]/([M][L]^n); tabulated for speciation calculations; pH-dependent equilibria determined by spectrophotometry, potentiometry.
Ion pairs & Bjerrum length
ℓ_B = e²/(4πε₀εk_BT); ions within ℓ_B form pairs; important in electrolyte theory at low ε.