Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 2 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Homework Set # 21 Atkins & de Paula, 8e Chap 21 (pp only) Exercises: all part (b) unless noted: 2, 6, 7, 8, 11, 13, 15, 17

Objectives: Describe the motion of all types of particles in all types of fluids Concentrate of transportation properties: Diffusion ≡ migration of matter down a concentration gradient Thermal conduction ≡ migration of energy down a temperature gradient Electrical conduction ≡ migration of charge along a potential gradient Viscosity ≡ migration of linear momentum down a velocity gradient

Fig The flux of particles down a concentration gradient Fick’s first law of diffusion: If the concentration gradient varies steeply with position, then diffusion will be fast

The Phenomenological Equations Flux (J) ≡ the quantity of that property passing through a given area per unit time Matter flux – molecules m -2 s -1 Energy flux – J m -2 s -1 e.g., J(matter) ∝ dN/dz and J(energy) ∝ dT/dz Since matter flows from high to low concentration: where D ≡ diffusion coefficient in m -2 s -1

The Phenomenological Equations Since energy flows from high to low temperature: where κ ≡ coefficient of thermal conductivity in J K -1 m -1 s -1

Laminar (smooth) flow: If the entering layer has high linear momentum, it accelerates the layer If the entering layer has low linear momentum, it retards the layer Fig The viscosity of a fluid arises from the transport of linear momentum

The Phenomenological Equations where η ≡ coefficient of viscosity in kg m -1 s -1 So the viscosity of a gas increases with temperature!

Fig The experimental temperature dependence of water As the temperature is increased, more molecules are able to escape from the potential wells of their neighbors; the liquid then becomes more fluid Molecular Motion in Liquids

Conductivities of electrolyte solutions Conductance, G, of a solution ≡ the inverse of its resistance: G = 1/R in units of Ω -1 Since G decreases with length, l, we can write: where κ ≡ conductivity and A ≡ cross-sectional area Conductivity depends on number of ions, so molar conductivity ≡ Λ m = κ/c with c in molarity units

Fig The concentration dependence of the molar conductivities of (a) a strong and (b) a weak electrolyte Λ m = κ/c Strong electrolyte – molar conductivity depends only slightly on concentration Weak electrolyte – molar conductivity is normal at very low concentrations but falls sharply to low values at high concentrations

Weak electrolyte solutions Only slightly dissociated in solution The marked concentration dependence of their molar conductivities arises from displacement of the equilibrium towards products a low concentrations HA (aq) + H 2 O (l) ⇌ H 3 O + (aq) + A − (aq) where α ≡ degree of dissociation

Weak electrolyte solutions At infinite dilution, the weak acid is fully dissociated (α = 100%) ∴ Its molar conductivity is At higher concentrations α << 100% and molar conductivity is