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.