Gases & colligative Gases & colligative propertiesproperties

Ch.14Ch.14

Gases dissolving in liquidsGases dissolving in liquids Pressure and temperature influence gas Pressure and temperature influence gas

solubilitysolubility Solubility directly proportional to gas pressureSolubility directly proportional to gas pressure

Henry’s LawHenry’s Law:: SSgg = k = kHHPPgg SSg g = gas solubility (M = mol/L) = gas solubility (M = mol/L) kkH H = Henry’s law constant (unique to each gas; = Henry’s law constant (unique to each gas;

M/mm Hg)M/mm Hg) PPgg = partial pressure of gaseous solute (mm = partial pressure of gaseous solute (mm

Hg)Hg)

Increase partial pressure Increase partial pressure increase solubilityincrease solubility

Example Example 27.0 g of acetylene gas 27.0 g of acetylene gas

dissolves in 1.00 L of dissolves in 1.00 L of acetone at 1.00 atm acetone at 1.00 atm partial pressure of partial pressure of acetylene. acetylene.

If the partial pressure If the partial pressure of acetylene is of acetylene is increased to 6.00 atm, increased to 6.00 atm, what is the solubility of what is the solubility of acetylene in acetone in acetylene in acetone in mol/L? MW of acetylene mol/L? MW of acetylene = 26.037 g/mol= 26.037 g/mol

1.1. 27.0 g x (mol/26.037 g) 27.0 g x (mol/26.037 g) x (1/1.00 L) = 1.04 Mx (1/1.00 L) = 1.04 M

2.2. SSgg = k = kHHPPgg

3.3. 1.04 M = k1.04 M = kHH x 1.00 atm x 1.00 atm 1.1. kkHH = 1.04 M/atm = 1.04 M/atm

4.4. SSgg = (1.04 M/atm) x 6.00 atm = (1.04 M/atm) x 6.00 atm

1.1. = = 6.24 M6.24 M Could also solve this by:Could also solve this by:

– (S(Sg1g1/P/Pg1g1) = (S) = (Sg2g2/P/Pg2g2))

– How did I come up with How did I come up with this?this?

ProblemProblem

The partial pressure of oxygen gas, O2, in air at sea level is 0.21 atm. – Using Henry’s Law, calculate the molar

concentration of oxygen gas in the surface water (at 20°C) of a lake saturated with air given that the solubility of O2 at 20°C and 1.0 atm pressure is 1.38•10-3 M.

Solution Solution

32

42

S1.38 10 M

1.0atm 0.21atm

S 2.9 10 M

They call it “pop” in the They call it “pop” in the MidwestMidwest

Drinks carbonated under high pressureDrinks carbonated under high pressure– Above 90 atmAbove 90 atm

– Under COUnder CO22 atmosphere atmosphere

Once bottle opened, partial pressure of gas Once bottle opened, partial pressure of gas above soda plummetsabove soda plummets– COCO22 solubility decreases drastically solubility decreases drastically

– Gas bubbles out of solnGas bubbles out of soln Once the fizz is gone, it can never be regainedOnce the fizz is gone, it can never be regained

– Truly, one of the existential tragedies of this Truly, one of the existential tragedies of this universeuniverse

The bendsThe bends

Deeper diving has higher pressuresDeeper diving has higher pressures– Must use breathing tankMust use breathing tank– If it contains NIf it contains N22 then higher pressure forces N then higher pressure forces N22

to dissolve in higher amounts in bloodto dissolve in higher amounts in blood If ascension too fast, lower pressure causes If ascension too fast, lower pressure causes

NN22 to start bubbling out of blood too quickly to start bubbling out of blood too quickly – Rupturing of arteriesRupturing of arteries

Excruciatingly painful deathExcruciatingly painful death– Must be rushed to hyperbaric chamberMust be rushed to hyperbaric chamber

Tanks now don’t use NTanks now don’t use N22,, but Hebut He– Why?Why?

Effects of temp on solubilityEffects of temp on solubility

Obviously, as temp Obviously, as temp increases, solubility increases, solubility decreasesdecreases

Since increasing Since increasing heat causes gases heat causes gases to dissolve out to dissolve out (endothermic)(endothermic) dissolving gases dissolving gases

is an exothermic is an exothermic processprocess

Another look at gas solubility: Another look at gas solubility: Le Châtelier’s PrincipleLe Châtelier’s Principle

Explains temperature relevance of Explains temperature relevance of solubilitysolubility

For systems in equilibrium, change in one For systems in equilibrium, change in one side causes system to counteract on other side causes system to counteract on other side:side:

Gas + liquid solvent Gas + liquid solvent sat. soln + heat sat. soln + heat– So add heat, rxn goes to left by kicking out gasSo add heat, rxn goes to left by kicking out gas– Add gas, rxn goes to right by saturating soln & Add gas, rxn goes to right by saturating soln &

giving off heatgiving off heat

Solubility of solids based on Solubility of solids based on temperaturetemperature

In general, In general, solubility increases solubility increases w/ increasing tempw/ increasing temp– But exceptionsBut exceptions– No general behavior No general behavior

pattern notedpattern noted

CrystalsCrystals

One can separate One can separate impure dissolved impure dissolved salts by reducing salts by reducing temperaturetemperature– Impurity or desired Impurity or desired

product crystallizes product crystallizes out at specific temp out at specific temp as solubility as solubility collapsescollapses

Colligative propertiesColligative properties

Vapor and osmotic pressures, bp, Vapor and osmotic pressures, bp, and mp are colligative propertiesand mp are colligative properties– Depend on relative # of solute and Depend on relative # of solute and

solvent particlessolvent particles

Vapor PressureVapor Pressure Remember: Remember:

– Equilibrium vapor pressureEquilibrium vapor pressure Pressure of vapor when liq and vapor in equilibrium Pressure of vapor when liq and vapor in equilibrium

at specific tempat specific temp Vapor pressure of soln lower than pure Vapor pressure of soln lower than pure

solvent vapor pressuresolvent vapor pressure Vapor pressure of solvent Vapor pressure of solvent relative # of relative # of

solvent molecules in solnsolvent molecules in soln– i.e., solvent vapor pressure i.e., solvent vapor pressure solvent mole solvent mole

fractionfraction

Raoult’s LawRaoult’s Law

PPsolutionsolution = X = Xsolventsolvent P P°°solventsolvent

So if 75% of molecules in soln are So if 75% of molecules in soln are solvent molecules (0.75 = solvent molecules (0.75 = XXsolventsolvent))– Vapor pressure of solvent (Vapor pressure of solvent (PPsolventsolvent) = 75% ) = 75%

of of PP°°solventsolvent

Problem Problem

The vapor pressure of pure acetone (CH3COCH3) at 30°C is 0.3270 atm. Suppose 15.0 g of benzophenone, C13H10O (MW = 182.217 g/mol), is dissolved in 50.0 g of acetone (MW = 58.09 g/mol). – Calculate the vapor pressure of acetone

above the resulting solution.

Solution Solution

0.2986atmatm3270.0913.0PXP

913.00.0823mol0.861mol

mol861.0X

mol861.058.09g

mol50.0g :solvent

mol0823.0182.217g

mol15.0g :solute

solventsolventsolution

solvent

ProblemProblem

The vapor pressure of pure liquid CS2 is 0.3914 atm at 20°C. When 40.0 g of rhombic sulfur (a naturally occurring form of sulfur) is dissolved in 1.00 kg of CS2, the vapor pressure falls to 0.3868 atm. – Determine the molecular formula of

rhombic sulfur.

Solution Solution

8

sulfur rhombic

sulfur rhombic

3

solvent

solvent

solventsolventsolution

S

898.7sulfur 32.066g

mol

mol

256gmol

256g

0.156mol

g0.40

156.0mol

mol13.1mol

13.1mol0.9882

mol1.1376.143g

molg101.001.00kg :solvent

9882.0X

atm3914.0Xatm3868.0

PXP

Limitations of Raoult’s LawLimitations of Raoult’s Law Doesn’t take into Doesn’t take into

consideration attractive consideration attractive forces in solnsforces in solns

For For ideal soln ideal soln (to right), (to right), forces between forces between solute/solvent molecules = solute/solvent molecules = forces w/in pure solventforces w/in pure solvent

– Thus, PThus, Ptottot = P = PAA + P + PBB

– Like graph to rightLike graph to right Fine for similarly Fine for similarly

constructed molecules constructed molecules (hydrocarbons)(hydrocarbons)– London dispersion forces London dispersion forces

are weakestare weakest

Solute-solvent Solute-solvent > solv-solv> solv-solv Decreases vapor Decreases vapor

pressurepressure– decreased volatilitydecreased volatility

Get lower vapor Get lower vapor pressure than pressure than calculated calculated

Ex:Ex:– CHClCHCl33 & C & C22HH55OCOC22HH55

H on former H-bonds H on former H-bonds to latterto latter

– Does it increase or Does it increase or decrease the latter’s decrease the latter’s IMF?IMF?

Solute-solvent Solute-solvent < solv-solv< solv-solv Increases vapor Increases vapor

pressurepressure– increased volatilityincreased volatility

Get higher vapor Get higher vapor pressure than pressure than calculated calculated

Ex:Ex:– CC22HH55OH and HOH and H22OO– Former disrupts H-Former disrupts H-

bonding of latterbonding of latter Does it increase or Does it increase or

decrease the latter’s decrease the latter’s IMF?IMF?

Nonvolatile solute added to Nonvolatile solute added to solventsolvent

SaltsSalts– Lower vapor pressure of solventLower vapor pressure of solvent– Make solvent less volatileMake solvent less volatile

Nonvolatile solute added to Nonvolatile solute added to solventsolvent

Raises bpRaises bp Lowers mpLowers mp

– Why?Why? Adding more Adding more

nonvolatile solute or nonvolatile solute or increasing solute increasing solute molalitymolality– decreases vapor decreases vapor

pressure even morepressure even more Phase diagram to rightPhase diagram to right

– Pure water (black)Pure water (black)– Adulterated water Adulterated water

(pink)(pink)

Bp and molality relationshipBp and molality relationship

TTbpbp = K = Kbpbp mmsolutesolute

KKbp bp = molal boiling pt elevation = molal boiling pt elevation constant for solventconstant for solvent ((°C/°C/mm))

Bp elevation, Bp elevation, TTbpbp, directly , directly proportional to solute molalityproportional to solute molality

Antifreeze Antifreeze Propylene glycolPropylene glycol

– 1,2-propanediol1,2-propanediol– Formerly used ethylene Formerly used ethylene

glycol glycol Phased outPhased out Poisonous Poisonous

– Lowers melting pt Lowers melting pt – Increases boiling ptIncreases boiling pt– Reduces risk of radiator Reduces risk of radiator

“boiling over”“boiling over”– Appreciated during the Appreciated during the

summer months in the summer months in the desertdesert

Example Example

Pure toluene (C7H8) has a normal boiling point of 110.60°C.

A solution of 7.80 g of anthracene (C14H10) in 100.0 g of toluene has a boiling point of 112.06°C.

– Calculate Kb for toluene.

1.1. TTbpbp = K = Kbpbp mmsolutesolute

2.2. TTbpbp = 112.06 = 112.06°C - 110.60°C = 1.46°C

3. 7.80g x (mol/178.23g) = 4.38 x 10-2 mol

4. (4.38 x 10-2 mol/0.1000 kg) = 0.438 m

5. 1.46°C/0.438 m = 3.33°C/m

Freezing point depressionFreezing point depression

Similarly, Similarly, TTfpfp = K = Kfpfp mmsolutesolute

KKfp fp = molal fp depression constant = molal fp depression constant ((°C/°C/mm))

Antifreeze & CaClAntifreeze & CaCl22

ProblemProblem

Barium chloride has a freezing point of 962°C and a Kf of 108 °C/m.

A solution of 12.0 g of an unknown substance dissolved in 562 g of barium chloride gives a freezing point of 937°C.– Determine the molecular weight of the

unknown substance.

Solution Solution

mol

g92

0.13mol

12.0g

0.13solute moles

solvent 0.562g

solute moles23.0

23.0

C108C25T

C25C937C962T

m

mm

Solutions containing ions: Solutions containing ions: their colligative propertiestheir colligative properties

Colligative properties based on amount of Colligative properties based on amount of solute/solventsolute/solvent

Molality of ions depend on Molality of ions depend on number of number of constituents in cmpdconstituents in cmpd

Different for ionic vs. covalent cmpdsDifferent for ionic vs. covalent cmpds Ex:Ex:1.1. NaCl ionizes into two ionsNaCl ionizes into two ions

– So 0.5So 0.5 m m NaCl has 0.5 x 2 NaCl has 0.5 x 2 mm = 1 = 1 mmtottot

2.2. Benzene doesn’t ionizeBenzene doesn’t ionize– So 0.5 So 0.5 mm benzene = 0.5 benzene = 0.5 mmtottot

Using equation w/out above factor will lead to Using equation w/out above factor will lead to values that are offvalues that are off

How to correct for it: the How to correct for it: the van’t Hoff factorvan’t Hoff factor

ii = = the number of solute particles after dissolving Colligative properties are larger for Colligative properties are larger for

electrolytes than for nonelectrolytes of the electrolytes than for nonelectrolytes of the same molalitysame molality– Why? (Hint: solve the below)Why? (Hint: solve the below)

Give the Give the ii-values for: methanol, CaSO-values for: methanol, CaSO44, BaCl, BaCl22

TTfpfp (measured) = K (measured) = Kfpfp mm ii

Problem Problem

How many grams of Al(NOHow many grams of Al(NO33))33 must be must be added to 1.00 kg of water to raise added to 1.00 kg of water to raise the boiling point to 105.0the boiling point to 105.0°C°C

KKbb = 0.51 °C/ = 0.51 °C/mm MW = 212.9962 g/molMW = 212.9962 g/mol

solutionsolution

needed )Al(NO g530mol

212.9962g2.5mol

2.5solute moles

solvent 1.00kg

solute moles5.2

5.2

4C0.51

C5.0

C5.0C100.0-C105.0T

33

m

mm

OsmosisOsmosis

Net movement of water (solvent) Net movement of water (solvent) from area of lower solute from area of lower solute concentration to area of higher concentration to area of higher solute concentration across a semi-solute concentration across a semi-permeable membranepermeable membrane– Bio101Bio101

More… More… Pressure of column of soln = pressure of water Pressure of column of soln = pressure of water

moving through membranemoving through membrane Osmotic pressureOsmotic pressure = pressure made by column = pressure made by column

of soln = diff of heightsof soln = diff of heights = cRT= cRT c = mol/L = Mc = mol/L = M R = 0.08206 L R = 0.08206 L atm/(mol atm/(mol K) K) ideal gas law ideal gas law T = in KelvinT = in Kelvin = atm= atm Useful for measuring MM of biochemical Useful for measuring MM of biochemical

macromoleculesmacromolecules– Proteins and carbsProteins and carbs