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Zumdahl’s Chapter 11

Zumdahl’s Chapter 11. Solutions. Solution Composition Concentrations H solution Hess’s Law undersea Solubilities Henry’s Law: Gases and Raoult’s Law Temperature Effects. Colligative Properties T BP Elevation T FP Depression Osmotic Pressure van’t Hoff Factor

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Zumdahl’s Chapter 11

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  1. Zumdahl’s Chapter 11 Solutions

  2. Solution Composition Concentrations Hsolution Hess’s Law undersea Solubilities Henry’s Law: Gases and Raoult’s Law Temperature Effects Colligative Properties TBP Elevation TFP Depression Osmotic Pressure van’t Hoff Factor Colloids and Emulsions Chapter Contents

  3. Solution Composition • Molarity, M = moles solute / liter sol’n. • Cannot be accurately predicted for mixtures because partial molar volumes vary. • If volumes don’t add, masses and moles do! • Molality, m = moles solute / kg solvent • Not useful in titration unless density known. • Useful in colligative effects. • Mole fraction, XA = moles A / total moles

  4. Conc. of 50% by wt. NaOH • Density at 20°C is 1.5253 g cm3 •  each liter of solution weighs 1525.3 g • ½ that mass is NaOH, or 762.65 g • nNaOH = 762.65 g [ 1 mol/39.998 g ] = 19.067 • [NaOH] = 19.067M but also • 19.067 mol / 0.76265 kg H2O = 25.001mand • nwater = 762.65 g [ 1 mol/18.016 g ] = 42.332 • XNaOH =19.067 /(19.067+42.332)=0.31054

  5. 100 cc ea. H2O & C2H5OH • Want Proof? 50% by Volume 100 proof • Want Volume? Need densities! • At 20°C,  = 0.99823 & 0.79074 g/cc, resp. •  sol’n. mass = 99.823+79.074 = 178.897 g • By mass: 100%(79.074 / 178.897) = 44.201% • From tables:  = 0.92650 g/cc • V = 178.897 g/0.92650 g/cc = 193.09 cc •  It’s really 2 100cc / 193.09 cc = 103.58 proof

  6. Expand both solvent and solute • at the expense of H1 and H2 • in lost intermolecular • interactions. Conceptual Mixing Enthalpies • Merge the • expanded liquids • together recovering • H3 from the • new interactions. But even if it requires heat, mixing may well happen since entropy favors it! 3. If the exothermic mixing exceeds the endothermic expansion, there will be a net exo- thermic heat of solution.

  7. Underwater Hess’s Law • Unrelated to basket weaving. • Since solutions are fluid, they need not expand then mix, requiring “upfront” $$. • Instead they acquire AB interaction as they lose AA and BB ones; pay as you go. • Hess doesn’t care; the overall enthalpy change$ will be the same.

  8. Solubilities • It’s true that which of A or B is the solute or solvent is mere naming convention … • Which was the solute in that 50% cocktail? • Still solutes with low solubility are surely in the mole fraction minority. • And it is worthwhile asking what state parameters influence their solubility?

  9. Gas Solubilities • No doubt about it: pressure influences solubility. And directly. • CO2 in soft drinks splatter you with dissolution as you release the pressure above the liquid. • Henry’s Law codifies the relationship: • PA = kH•[A(aq)] (kH is Henry’s constant) • It applies only at low concentrations; so • It applies not at all to strongly soluble gases!

  10. Apply at opposite extremes. Raoult when X~1 Henry when X~0 So Raoult to solvent and Henry to solute. When XB is small, XB=[B]/55.51M for [water]=55.51M Henry’s OK with X. P°B P°A P k’H;B k’H;A XA 0 1 P = P° X P kH’ X Raoult’s and Henry’s Laws

  11. Raoult vs. Henry Difference • When X~1, the solvent is not perturbed by miniscule quantities of solute. Solvent vaporization is proportional to solvent molecules at solution’s surface. Raoult • When X~0, solute is in an utterly foreign environment, surrounded only by solvent. kH reflects the absence of A-A interaction, and Henry applies.

  12. Solubility and Temperature • Sometimes the AB interactions are so much weaker than AA or BB that A and B won’t mix even though entropy favors it. • Since T emphasizes entropy, some of the immiscible solutions mix at higher T. • Solidsolubilities normally rise with T. • Exceptions are known … like alkali sulfates.

  13. Gases Flee Hot Solutions • You boiled lab water to drive out its dissolved gases, especially CO2. • That’s why boiled water tastes “flat.” • Genghis Khan invented tea (cha) to flavor the water his warriors refused to boil for their health as they conquered Asia and Eastern Europe. • Increased T expands Vgas, making it more favored by entropy vs. dissolved gas. • This time, no exceptions!

  14. The Phase Diagram Mixing in a solute lowers solvent Pvapor So TBP must rise. Since the solvent’s solid suffers no Pvapor change, TFP must fall. Liquid span must increase in solution. P T Changed Phase Changes

  15. Elevating Depressions • Both colligative properties arise from the same source: Raoult’s Law. • Thermo. derivations of resulting T give: • Freezing Point Depression: • TFP = –Kf msolute where Kf~RTFP2 / Hfusion • Boiling Point Elevation: • TBP = +Kb msolute where Kb~RTBP2 / Hvap • Kf > Kb since Hfusion < Hvap

  16. Antifreeze / Summer Coolant are the same Ethylene glycol (1,2-Ethanediol) is soluble in the radiator water, non-corrosive, nonscaling, and raises the boiling point in summer heat while lower-ing freezing point in winter. “Road salt” is CaCl2 now since NaCl corrodes cars. Practical Phase Changes

  17. Colligative Utility • Ligare means “to bind.” These features are bound up with just numbers of moles. • NOT the identity of the molecules! • Indeed, Kf and Kb are seen not to depend on solute properties but on solvent ones. • So they’re used to count solute moles to convert weights to molar weights! • Not sensitive enough for proteins, MW~10 kg

  18. Exquisite Sensitivity • To count protein moles, we need Osmotic Pressure that is very sensitive to [solute]. • Solvent will diffuse across a membrane to dilute a concentrated solute solution. • If the solute is too large (protein!) to diffuse back, the volumemust increase. • Rising solution creates (osmotic) pressure to an equilibrium against further diffusion.

  19. MW by Osmotic Pressure,  • Thermodynamic derivation of the balance between  & diffusion on the equilibrium gives: V = nRT(!) or = MRT • E.g., 0.5 g in 50 cc yields 10 cm of pressure at 25°C (so RT = 24.5 atm L /mol) • 10 cm (1 ft/30.5 cm) (1 atm/33 ft) = .010 atm • [protein] =  / RT = 0.00041 mol/L • Wt = 0.5 g/0.05 L = 10 g/L MW = 24 kg

  20. Moles of What? • Doesn’t matter if property’s colligative. • Counts moles of ions if solute dissociates. • van’t Hoff Factor, i, measures ionization. • i multiplies molality in any of the colligative expressions to show apparent moles present. • It’s a stand-in for non-idealities too; pity. • So in 0.001mK3PO4, i should be nearly 4, and colligative properties see 0.004m?NO!

  21. Weak Electrolyte Corrections • PO43– is a conjugate base of HPO42– • Ka3 = 4.810–13so Kb1 = Kw/Ka3 = 0.021 for PO43– + H2O  HPO42– + OH– • Equilibrium lies to left, so start with [OH–] = [HPO42–] = 0.001–xand [PO43–] = x • (0.001–x)2 / x = 0.021 or x ~ 4.810–5 ~ 0 • Counting K+, total moles ~ 0.003+2(0.001) • Soi ~ 0.005/0.001 = 5not 4. (4.95 with care)

  22. Reverse Osmosis • If dilution across a semipermeable (keeps out solute) membrane builds pressure, • Pressure should be able to squeeze water back out of a solution! …if the membrane survives. • Desalination plants are critical in desert nations like the Gulf States & N. Africa. • Waste water is much more (salt) concentrated, an environmental hazard to local sea life unless ocean currents are swift enough to dilute it.

  23. When is a SolutionNot a Solution? • When it’s a problem?  • Insoluble materials precipitate out of a solution at a rate that increases with their mass. So smallparticlesstay suspended. • With particle sizes of 1 m to 1 nm such suspensions are called colloids. • Since visible ~ 0.5m, the larger colloids scatter visible light efficiently! (Tyndall effect)

  24. Taxonomy of Suspensions Dispersed Material Phase Dispersing Medium Phase

  25. – – + – + + – + – + + – – + + – + – Aqueous Colloids • Particles might be charged and stabilized (kept from coagulating) by electrostatics. • Even neutral ones will favor adjacency of one charge which develops double layer (an oppositely charged ionic shell) to stabilize the colloid. • “Salting out” destroys the colloid by over-whelming the repulsions with ionic strength. • Small, highly charged ions work best, of course.

  26. Surface Chemistry (liquids) • Colloid study, a subset of surface science. • Colloid molecules must be insoluble in the dispersing medium. • Solubility governed by “like dissolves like.” • But surface tensions play a role as well since solutes display surface excess concentration. • Interfaces between phases are not simply at the bulk concentrations; influences segregation.

  27. Surface Chemistry (solids) • Industrial catalysts for many processes are solids. • Atoms and molecules adhere, dissociate, migrate, reassociate, and desorb. • Efficiency scales with catalyst surface area. • Area measured by adsorbing monolayers of gas (N2 ) and observing discontinuities as monolayer is covered.

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