Zumdahl’s Chapter 11
Chapter Contents
Solution CompositionConcentrations
Hsolution
Hess’s Law undersea
SolubilitiesHenry’s Law: Gases
and Raoult’s Law
Temperature Effects
Colligative PropertiesTBP Elevation
TFP Depression
Osmotic Pressure
van’t Hoff FactorColloids and
Emulsions
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 solventNot useful in titration unless density known.Useful in colligative effects.
Mole fraction, XA = moles A / total moles
Conc. of 50% by wt. NaOH
Density at 20°C is 1.5253 g cm3
each liter of solution weighs 1525.3 g½ that mass is NaOH, or 762.65 g
nNaOH = 762.65 g [ 1 mol/39.998 g ] = 19.067
[NaOH] = 19.067 M but also
19.067 mol / 0.76265 kg H2O = 25.001 m and
nwater = 762.65 g [ 1 mol/18.016 g ] = 42.332
XNaOH =19.067 /(19.067+42.332)=0.31054
100 cc ea. H2O & C2H5OH
Want Proof? 50% by Volume 100 proofWant 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
But even if itrequires heat,mixing may well happen since entropyfavors it!
Conceptual Mixing Enthalpies
1. Expand both solvent and solute at the expense of H1 and H2 in lost intermolecular interactions.
2. Merge the expanded liquids together recovering H3 from the new interactions.
3. If the exothermic mixing exceeds the endothermic expansion, there will be a net exo- thermic heat of solution.
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.
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?
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; soIt applies not at all to strongly soluble gases!
Raoult’s and Henry’s LawsApply at opposite
extremes.Raoult when X~1Henry when X~0So Raoult to solvent
and Henry to solute.
When XB is small, XB=[B]/55.51M for [water]=55.51MHenry’s OK with X.
XA0 1
P
P°B
P°A
k’H;B k’H;A
P = P° X P kH’ X
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.
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.
Solid solubilities normally rise with T.Exceptions are known … like alkali sulfates.
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!
Changed Phase Changes
The Phase DiagramMixing 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
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 ~ RTBP
2 / Hvap
Kf > Kb since Hfusion < Hvap
Practical Phase ChangesAntifreeze / Summer
Coolant are the sameEthylene 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.
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
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 volume must increase.Rising solution creates (osmotic) pressure
to an equilibrium against further diffusion.
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/LWt = 0.5 g/0.05 L = 10 g/L MW = 24 kg
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 0.001m K3PO4 , i should be nearly 4, and colligative properties see 0.004m? NO!
Weak Electrolyte Corrections
PO43– is a conjugate base of HPO4
2–
Ka3 = 4.810–13 so Kb1 = Kw/Ka3 = 0.021 for PO4
3– + H2O HPO42– + OH–
Equilibrium lies to left, so start with [OH–] = [HPO4
2–] = 0.001–x and [PO43–] = x
(0.001–x)2 / x = 0.021 or x ~ 4.810–5 ~ 0Counting K+, total moles ~ 0.003+2(0.001)So i ~ 0.005/0.001 = 5 not 4. (4.95 with care)
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.
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 small particles stay 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)
Taxonomy of Suspensions
Solid Liquid Gas
Solid Solid Suspension
e.g., pigmented plastics
Solid Emulsion e.g., opal or
pearl or butter
Solid Foam e.g.,styrofoam
coffee cups
Liquid Sol or paste
e.g., toothpaste
Emulsion
e.g., milk or Sauce Bernaise
Foam
e.g., suds; fire extinguisher
Gas Solid Aerosol
e.g., smoke, dust
Liquid Aerosol
e.g. fog, atomizer spray
fahgedaboudit
Dispersed Material Phase
Dis
pers
ing
Med
ium
Pha
se
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.
+ +++ ++ +
++
–
––
–
– –––
–
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.
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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