Gases & colligative properties

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Gases colligative properties

• Ch.14

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Gases dissolving in liquids

• Pressure and temperature influence gas solubility
• Solubility directly proportional to gas pressure
• Henrys Law
• Sg kHPg
• Sg gas solubility (M mol/L)
• kH Henrys law constant (unique to each gas
  M/mm Hg)
• Pg partial pressure of gaseous solute (mm Hg)

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Increase partial pressure ? increase solubility
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Example

• 27.0 g of acetylene gas dissolves in 1.00 L of
  acetone at 1.00 atm partial pressure of
  acetylene.
• If the partial pressure of acetylene is increased
  to 6.00 atm, what is the solubility of acetylene
  in acetone in mol/L? MW of acetylene 26.037
  g/mol

• 27.0 g x (mol/26.037 g) x (1/1.00 L) 1.04 M
• Sg kHPg
• 1.04 M kH x 1.00 atm
• kH 1.04 M/atm
• Sg (1.04 M/atm) x 6.00 atm
• 6.24 M
• Could also solve this by
• (Sg1/Pg1) (Sg2/Pg2)
• How did I come up with this?

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Problem

• The partial pressure of oxygen gas, O2, in air at
  sea level is 0.21 atm.
• Using Henrys Law, calculate the molar
  concentration of oxygen gas in the surface water
  (at 20C) of a lake saturated with air given that
  the solubility of O2 at 20C and 1.0 atm pressure
  is 1.3810-3 M.

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Solution
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They call it pop in the Midwest

• Drinks carbonated under high pressure
• Above 90 atm
• Under CO2 atmosphere
• Once bottle opened, partial pressure of gas above
  soda plummets
• CO2 solubility decreases drastically
• Gas bubbles out of soln
• Once the fizz is gone, it can never be regained
• Truly, one of the existential tragedies of this
  universe

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The bends

• Deeper diving has higher pressures
• Must use breathing tank
• If it contains N2 then higher pressure forces N2
  to dissolve in higher amounts in blood
• If ascension too fast, lower pressure causes N2
  to start bubbling out of blood too quickly
• Rupturing of arteries
• Excruciatingly painful death
• Must be rushed to hyperbaric chamber
• Tanks now dont use N2, but He
• Why?

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Effects of temp on solubility

• Obviously, as temp increases, solubility
  decreases
• Since increasing heat causes gases to dissolve
  out (endothermic)
• ? dissolving gases is an exothermic process

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Another look at gas solubility Le Châteliers
Principle

• Explains temperature relevance of solubility
• For systems in equilibrium, change in one side
  causes system to counteract on other side
• Gas liquid solvent ? sat. soln heat
• So add heat, rxn goes to left by kicking out gas
• Add gas, rxn goes to right by saturating soln
  giving off heat

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Solubility of solids based on temperature

• In general, solubility increases w/ increasing
  temp
• But exceptions
• No general behavior pattern noted

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Crystals

• One can separate impure dissolved salts by
  reducing temperature
• Impurity or desired product crystallizes out at
  specific temp as solubility collapses

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Colligative properties

• Vapor and osmotic pressures, bp, and mp are
  colligative properties
• Depend on relative of solute and solvent
  particles

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Vapor Pressure

• Remember
• Equilibrium vapor pressure
• Pressure of vapor when liq and vapor in
  equilibrium at specific temp
• Vapor pressure of soln lower than pure solvent
  vapor pressure
• Vapor pressure of solvent ?? relative of
  solvent molecules in soln
• i.e., solvent vapor pressure ? solvent mole
  fraction

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Raoults Law

• Psolution Xsolvent ? Psolvent
• So if 75 of molecules in soln are solvent
  molecules (0.75 Xsolvent)
• Vapor pressure of solvent (Psolvent) 75 of
  Psolvent

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Problem

• The vapor pressure of pure acetone (CH3COCH3) at
  30C 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.

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Solution
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Problem

• The vapor pressure of pure liquid CS2 is 0.3914
  atm at 20C. 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.

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Solution
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Limitations of Raoults Law

• Doesnt take into consideration attractive forces
  in solns
• For ideal soln (to right), forces between
  solute/solvent molecules forces w/in pure
  solvent
• Thus, Ptot PA PB
• Like graph to right
• Fine for similarly constructed molecules
  (hydrocarbons)
• London dispersion forces are weakest

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Solute-solvent gt solv-solv

• Decreases vapor pressure
• decreased volatility
• Get lower vapor pressure than calculated
• Ex
• CHCl3 C2H5OC2H5
• H on former H-bonds to latter
• Does it increase or decrease the latters IMF?

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Solute-solvent lt solv-solv

• Increases vapor pressure
• increased volatility
• Get higher vapor pressure than calculated
• Ex
• C2H5OH and H2O
• Former disrupts H-bonding of latter
• Does it increase or decrease the latters IMF?

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Nonvolatile solute added to solvent

• Salts
• Lower vapor pressure of solvent
• Make solvent less volatile

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Nonvolatile solute added to solvent

• Raises bp
• Lowers mp
• Why?
• Adding more nonvolatile solute or increasing
  solute molality
• decreases vapor pressure even more
• Phase diagram to right
• Pure water (black)
• Adulterated water (pink)

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Bp and molality relationship

• ?Tbp Kbp ? msolute
• Kbp molal boiling pt elevation constant for
  solvent (C/m)
• Bp elevation, ?Tbp, directly proportional to
  solute molality

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Antifreeze

• Propylene glycol
• 1,2-propanediol
• Formerly used ethylene glycol
• Phased out
• Poisonous
• Lowers melting pt
• Increases boiling pt
• Reduces risk of radiator boiling over
• Appreciated during the summer months in the desert

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Example

• Pure toluene (C7H8) has a normal boiling point of
  110.60C.
• A solution of 7.80 g of anthracene (C14H10) in
  100.0 g of toluene has a boiling point of
  112.06C.
• Calculate Kb for toluene.

• ?Tbp Kbp ? msolute
• ?Tbp 112.06C - 110.60C 1.46C
• 7.80g x (mol/178.23g) 4.38 x 10-2 mol
• (4.38 x 10-2 mol/0.1000 kg) 0.438 m
• 1.46C/0.438 m 3.33C/m

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Freezing point depression

• Similarly, ?Tfp Kfp ? msolute
• Kfp molal fp depression constant (C/m)
• Antifreeze CaCl2

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Problem

• Barium chloride has a freezing point of 962C 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 937C.
• Determine the molecular weight of the unknown
  substance.

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Solution
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Solutions containing ions their colligative
properties

• Colligative properties based on amount of
  solute/solvent
• Molality of ions depend on number of constituents
  in cmpd
• Different for ionic vs. covalent cmpds
• Ex
• NaCl ionizes into two ions
• So 0.5 m NaCl has 0.5 x 2 m 1 mtot
• Benzene doesnt ionize
• So 0.5 m benzene 0.5 mtot
• Using equation w/out above factor will lead to
  values that are off

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How to correct for it the vant Hoff factor

• i the number of solute particles after
  dissolving
• Colligative properties are larger for
  electrolytes than for nonelectrolytes of the same
  molality
• Why? (Hint solve the below)
• Give the i-values for methanol, CaSO4, BaCl2
• ?Tfp (measured) Kfp ? m ? i

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Problem

• How many grams of Al(NO3)3 must be added to 1.00
  kg of water to raise the boiling point to 105.0C
• Kb 0.51 C/m
• MW 212.9962 g/mol

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solution
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Osmosis

• Net movement of water (solvent) from area of
  lower solute concentration to area of higher
  solute concentration across a semi-permeable
  membrane
• Bio101

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More

• Pressure of column of soln pressure of water
  moving through membrane
• Osmotic pressure pressure made by column of
  soln diff of heights
• ? cRT
• c mol/L M
• R 0.08206 L ? atm/(mol ? K) ? ideal gas law
• T in Kelvin
• ? atm
• Useful for measuring MM of biochemical
  macromolecules
• Proteins and carbs