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24-Colligative Properties - 5.111 Lecture 24 COLLIGATIVE...

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Unformatted text preview: 5.111 Lecture # 24. COLLIGATIVE PROPERTIES [Pages FSS-FSS and 327-338 from the “Chemical Principles” textbook. 4‘11 edition, by Peter Atkins & Loretta Jones. Freeman, New York. 2008] Properties that depend only on the relative numbers of solute and solvent molecules and n_ot on the chemical nature of the solute. Important colligative properties: I. Lowering of the vapor pressure of the solvent; II. Raising of the boiling point of the solvent; III. Lowering of the fieezing point of the solvent; and IV. Osmosis. For colligative properties, we need measures of concentration that directly relate to the relative numbers of solute and solvent molecules (which molarity, M, is n_ot). They are: 0 Mole fraction, x xsolute : nsolute/ ( nsolute + nsolvent) Where nsoiute and nsolvem are the number of moles of the solute and solvent, respectively. 0 Molality molalitysolme = amount of solute (mol) / mass of solvent (kg) (2) Molality versus Molagity. Units of m. I. Vapor—Pressure Lowering Raoult’s Law — The vapor pressure of a solvent is proportional to its mole fraction in solution: P solvent = xsolvent' P0 solvent where Psolvem and Posolvem are the vapor pressure of the solvent in solution and of the pure solvent, respectively. Non-volatile solutes. Ideal solutions. Molecular rationale of Raoult’s law —— at equilibrium, Rateevapmtion = Ratecondensafion. Analysis — [Slide 24.1]. Thermodynamic basis of Raoult’s law. 0 For the liquid phase, Hsolution z 0 and Ssolution > 0. Why? Hence Gsolution decreases, i.e., when S T, G1. 0 Since at equilibrium Gt,apor = Gsolvem, Gvapor also decreases in solution and thus so does Psolvent- Non—ideal solutions obey Raoult’s law only at below ~O.l M for non-electrolyte solutions and at below ~0.01 M for electrolyte solutions. Why? Fig 8.2 Point to remember: The vapor pressure of a solvent is lowered by the presence of a non-volatile solute. This phenomenon gives rise to the phenomena discussed in sections 11 through IV below. 11. Boiling—Point Elevation Recall that (a) Pm,or increases with temperature, and (b) at the boiling point of a its P vapor = P atmospheric- Therefore, it will take a higher temperature for a solution, compared to the pure solvent, to reach the atmospheric pressure. This effect, i.e., T b > T b°, is called boiling- point elevation. Consider this effect thermodynamically — [Slide 24.2]. For an ideal solution of a non-electrolyte, Tb — T b0 = kb-molality (4) Where k1, is the boiling—point elevation constant. For example, for water kb = 0.51 K-m'l; hence for a 0.1 m solution of sucrose in water T b = 100.05°C (100°C + 0.51 K-m'l x 0.1 m), i.e., the effect is small. 111. Freezing—Point Lowering mg 9“. THEBEwnEmh 3V Alfiefimaggh E gowns—w “Eon-mfizom 23E. 2.5 2.5: 9:... !09 31? !I § “‘9 'Afijaua am; JE|Ow “‘9 'AfiJaua aax; JB|Ow hoam> .on~> o J m8 mm. m. "6 Md mm. mu "1' 1ulod 6u ’§ Recall that (a) Pvapor increases with temperature, and (b) at the freezing/melting point of a solid its Pvapor = Patmospheric. For example, pure ice and aqueous solution of, say, NaCl can coexist in equilibrium only if their vapor pressures are equal. But since the vapor pressure of water over aqueous solution of NaCl is lower than that over pure water, the vapor pressure of the ice must be Leg than if it were in equilibrium with pure water. Consequently, the temperature of the ice must be less than 0°C and hence the T f of the solution lower than T 3’. Thus freezing-point lowering gdepression), i.e., Tf°> Tf. Consider this effect thermodynamically — [Slide 24.3]. Analogously to 11., Tfo — Tf = kfmolality where kf is the freezing-point constant. The values of kf are typically much greater than those of kb —— [Slide 24.4] —— resulting in significant AT f (e. g., seawater freezes ~1.85°C lower than fresh water). Consequently, the freezing-point lowering phenomenon is practically important. Spreading salt on walkways and roads to melt ice. Note that for salts (such as NaCl) dissolved in water Tf" —— T f = i'kfmolality (6) 00w 9“. h .whsuflwnEw... 3V h .whsuerEw... A8 ” scummaav u mn:_oa-m:_uow."_m «15>.on . 14.; v 23%;“. 2.5: 23. d gzaau “'9 'ABJaua am; JB|OW “‘9 'AfiJaua aaglelow 'I'B'd'fiiiiié'é] wu m6 md mm in 1u 3.0 0.03 34 o .8ng vow NE SN 9‘ 6:23 23, BEN 3m wow 3223ch and 5on SN 3 maggot? m3 3n mam 3' 0283858 8&8 3m EN 5% mat 8:38 m3 2% NS, 3 0823 E4 gm 9% 3&1 3892w :LOEEQV Gov Ea :Loefié 60v Ema 2528 J mnmzom J wENoon 353280 3699:8on cam “Eom-m:m=om ad Ems. where z' is van’t Hoff” 3 factor which, in very dilute (i.e., ideal) aqueous solutions, for NaCl is 2. Why? For a saturated aqueous solution of NaCl, T f is -18°C. Consequences. Antifreezes, e. g., ethylene glycol: 50% (v/V) ethylene glycol in water has a T f of ~ —36°C (and a T b > 100°C due to II. as an extra benefit). IV. Q_s_r_n_qs_i§ Let’s place pure water in one beaker and the same volume of seawater in another, and then place both beakers under a bell jar. What will happen with time? Analysis based on a higher vapor pressure over pure water than over seawater. Now let’s instead separate pure water from seawater by a semipermeable membrane (what is it?) —- [Slide 24.5]. The same reasoning as above. Molecular and thermodynamic analyses. Osmosis: T he flow of solvent through a semipermeable membrane into a solution. Why does net solvent transfer eventually stop? Two reasons. Osmotic pressure, TE. The van’t Hoff equation: 7t = i RT ‘6 (7) where c is molarity of solution. Note that 7t is independent of the solvent or the solute. 5.x 9“. wcmEEwE wEmm—Ewnimm “cg—om mus—om Osmosis in living systems: consider erythrocytes [Slide 24.6]; plants; bacteria and meat preservation by NaCl; isotonic or “physiological” solutions (0 z 0.3 M). Reverse osmosis. [Slide 24.5] Desalination of water. Fig 8.32 ...
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