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2.Properties of Colloidal Dispersion Shape & Size Determination Colloidal size : • particle with linear dimension between 10-7 cm (10 AO) and 10-4 cm (1 ) 1 - 1000 nm • particle weight/ particle size etc. Shapes of Colloids : linear, spherical, rod, cylinder spiral sheet 1 Molar Mass ( for polydispersed systems) • Number averaged • Weight averaged • • • • • • Viscosity averaged Surface averaged Volume averaged Second moment Third moment Radius of gyration niMi Mn i n i i Number averaged Molar Mass 2 2.1 Colligative Propery In solution • • • • Vapor pressure lowering Boiling point elevation Freezing point depression Osmotic pressure P = ikpm Tb = ikbm Tf = ikfm = imRT (m = molality, i = van’t Hoff factor) In colloidal dispersion Osmotic pressure 3 Osmosis the net movement of water across a partially permeable membrane from a region of high solvent potential to an area of low solvent potential, up a solute concentration gradient 4 Osmotic pressure the hydrostatic pressure produced by a solution in a space divided by a semipermeable membrane due to a differential in the concentrations of solute For colloidal dispersion The osmotic pressure π can be calculated using the Macmillan & Mayer formula π = 1 [1 + Bc + B’c2 + …] cRT M M M2 = gh 5 Molar Mass Determination Dilute dispersion h = RT [1 + Bc ] c Where gM M c = g dm-3 or g/100 cm-3 M = Mn = number-averaged molar mass B = constants depend on medium h (cm g-1L) c Slope = intercept x B/Mn Intercept = c (g L-1) RT g Mn 6 Estimating the molar volume From the Macmillan & Mayer formula : B = ½NAVp where B = Virial coefficient NA = Avogadro # Vp = excluded volume, the volume into which the center of a molecule can not penetrate which is approximately equals to 8 times of the molar volume Example/exercise : Atkins 7 Osmotic pressure on blood cells Donnan Equlibrium : activities product of ions inside = outside 8 Donnan equilibrium activity a = C Where a = activity = activity coefficient C = molar conc. log = - kz2 aNaCl, L = a NaCl, R (aNa+)L(aCl-)L = (a Na+ )R(a Cl-)R Reverse Osmosis a separation process that uses pressure to force a solvent through a membrane that retains the solute on one side and allows the pure solvent to pass to the other side Look for its application : drinking and waste water purifications, aquarium keeping, hydrogen production, car washing, food industry etc. Pressure 10 2.2 Kinetic property : Brownian Motion either the random movement of particles suspended in a fluid or the mathematical model used to describe such random movements, often called a Wiener process. The mathematical model of Brownian motion has several real-world applications. An often quoted example is stock market fluctuations. 2 x = 2Dt D = diffusion coefficient 2.2 Kinetic property : Diffusion the random walk of an ensemble of particles from regions of high concentration to regions of lower concentration Einstein Relation (kinetic theory) where and D = Diffusion constant, μ = mobility of the particles kB = Boltzmann's constant, T = absolute temperature. The mobility μ is the ratio of the particle's terminal drift velocity to an applied force, μ = vd / F. Diffusion of particles For spherical particles of radius r, the mobility μ is the inverse of the frictional coefficient f, therefore Stokes law gives f = 6r where η is the viscosity of the medium. Thus the Einstein relation becomes This equation is also known as the Stokes-Einstein Relation. Fick’s Law • 1st law J = -D • 2nd law 1st Law 2nd Law where Flux mole m-2 s-1 = molar concentration = chemical potential D = diffusion coefficient 2.2 Kinetic property : Viscosity a measure of the resistance of a fluid to deform under shear stress where: is the frictional force, r is the Stokes radius of the particle, η is the fluid viscosity, and is the particle's velocity. Viscosity Measurement R P = - PR4t 8VL = o t oto = viscosity of dispersion o = viscosity of medium Unit:Poise (P) 1 P = 1 dyne s-1 cm-2 = 0.1 N s m-2 L Viscometer [c P] [ c P] liquid nitrogen @ 77K 0.158 honey 2,000–10,000 acetone 0.306 molasses 5,000–10,000 methanol 0.544 benzene 0.604 molten glass 10,000–1,000,000 ethanol 1.074 10,000–25,000 mercury 1.526 chocolate syrup nitrobenzene 1.863 chocolate propanol 1.945 ketchup sulfuric acid 24.2 olive oil 81 peanut butter glycerol 934 castor oil 985 * 45,000–130,000 * shortening 50,000–100,000 * ~250,000 ~250,000 Intermolecular forces Intermolecular forces • intermolecular forces are forces that act between stable molecules or between functional groups of macromolecules. • Intermolecular forces include momentary attractions between molecules, diatomic free elements, and individual atoms. • These forces includes London Dispersion forces, Dipole-dipole interactions and Hydrogen bonding,. Einstein Theory = o (1+2.5) -1 = sp = 2.5 , sp : specific viscosity o = volume fraction of solvent replaced by solute molecule = NAcVh MV where c = g cm-3 vh=hydrodynamic volume of solute Einstein Theory = o (1+2.5) -1 = sp = 2.5 , sp : specific viscosity o = NAcVh MV [] = lim sp = 2.5 , [] : intrinsic viscosity c c Mark-Houwink equation [] = K(Mv)a K - types of dispersion a – shape & geometry of molecule Assignment 2 (3-5 students per group) 1. At 25 oC D of Glucose = 6.81x10-10 m of water = 8.937x103 P s-1 of Glucose = 1.55 g cm-3 Use the Stokes law to calculate the molecular mass of glucose, suppose that glucose molecule has a spherical shape with radius r 5 points Assignment 2 2. Use the data below for Polystyrene in Toluene at 25 oC, calculate its molecular mass c/g cm-3 0 2.0 4.0 6.0 8.0 10.0 /10-4kg m-1s-1 5.58 6.15 6.74 7.35 7.98 8.64 Given : K and a in the Mark-Houwink equation equal 3.80x10-5 dm-3/g and 0.63, respectively (5 points) Due Date : 21 Aug 2009