Chapter 11 Solutions and Their properties

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Chapter 11 Solutions and Their properties
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What is a solution?
Sugar water
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• Solution
• 1. Homogeneous mixture
• 2. Transparent but may be colored
• 3. Contains particles with diameters in the
  range of 0.12 nm
• 4. Does not separate on standing

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other mixtures
Do not separate on standing
Typical colloids milk and fog
Typical suspensions Blood, paint, aerosol sprays
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Solution Formation

• Solute
• Dissolved substance, or smaller quantity
  substance
• Solvent
• Liquid dissolved in, larger quantity substance

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A Rule of Thumb Like dissolves
like Ionic/polar solute dissolves in ionic and
polar solvents. Non-polar solute dissolves in
non-polar solvents.
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Energy Changes and the Solution Process

• Three Types of interactions
• 1.      Solvent-solvent
• 2.      Solvent-solute
• 3.      Solute-solute
• Na and Cl- ion-ion attraction
• H2O and H2O dipole-dipole attraction
• Na and H2O ion-dipole attraction

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Any chemical reaction or physical process is
associated with a free-energy change DG. If DG
is negative the process is spontaneous If DG is 0
the process is at equilibrium If DG is positive
the process is non-spontaneous DG DH - T
DS DG Gibbs free-energy DH Heat of reaction
or process DS Entropy change, change of
randomness or disorder, temperature
dependent
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Entropy Changes in Solution Formation
Entropies of solutions are usually positive
because randomness increases
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Enthalpy change in enthalpy is not
predictable Some salts dissolve exothermic other
endothermic Example CaCl2 and MgSO4 dissolve
exothermic NH4NO3 dissolves endothermic Both
salts are used in hot packs and cold packs What
happens when we dissolve a substance?
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Enthalpy Change in Solution Formation
Exothermic -?Hsoln
The solutesolvent interactions ( ion-dipole
attraction) are stronger than solutesolute or
solventsolvent. Ions in solution are solvated,
in case of water hydrated Favorable
process Exothermic reaction.
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Enthalpy Change in Solution Formation
Endothermic ?Hsoln
The solutesolvent interactions are weaker than
solutesolute or solventsolvent. Unfavorable
process. Endothermic reaction
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Example 1

• Arrange the following in order of their expected
  increasing solubility in water
• Br2, KBr, C7H8 (toluene)

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Example 1

• Arrange the following in order of their expected
  increasing solubility in water
• Br2, KBr, C7H8 (toluene)

Toluene is non-polar and is insoluble in
water Br2 is non-polar but because of its size
its polarizable and is soluble KBr is an ionic
compound and is very soluble in water
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Summary

• Solution is a homogeneous mixture, which consists
  solute and solvent.
• Like dissolves like
• Energy changes in solution process
• A) ?Sgt0
• B) ?H can be either endothermic or exothermic

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Units of ConcentrationMolarity Mole Fraction
Mass percentage Molality.
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Molarity (M)
Advantage amounts of solute can be measured by
volume rather than by mass. Disadvantage Exact
concentration depends on temperature Because the
volume of a solution expands or contracts as the
temperature changes.
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Example To obtain a 0.1 M HCl solution Take
0.1 mole of HCl (1g 35.5g)/10 3.65 g And
fill it up to 1 Liter with water (Dont add
the 3.65 g to 1.00 L water!)
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Mole Fraction (x) mole of component X
---------------------------- total moles of
solution Example a solution prepared by
dissolving 1.00 mol of methyl alcohol in 90.0 g
of water, what is the mole fraction of each
component? 1.00 90 g water 5.00 mol
Xmethylalcohol --------------
1/6 1.00 5.00
5.00 XH2O -------------
5/6 1.00 5.00 Mole fractions
are not often used, more likely in gas mixtures
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• Mass percentage
• mass of component
• Mass ------------------------ x 100
• total mass of solution
• What is the mass percentage of glucose in a
  solution prepared by dissolving 10g of glucose
  into 100g of water?
• 10 g
• Mass glucose -------------- x 100 9.09
  mass
• 10g 100g

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For traces Parts per million ppm mass of
component ppm ------------------------
---- x 106 total mass of solution 1 ppm
1 mg/L Parts per billion ppb mass of
component ppb -----------------------
----- x 109 total mass of solution 1 ppb
1 mg/L or 1 mg/1000L
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Molality (m)

• moles of solute
• m -----------------------
• mass of solvent (kg)
• For a 1 m solution of KBr dissolve 1 mol KBr
  (119g) in 1 kg water.
• Advantage only masses, independent on temp.
• Disadvantage amounts must be measured by mass
• and not by volume

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What is the molality of a solution prepared by
dissolving 0.385 g of cholesterol, C27H46O in
40.0 g of chloroform, CHCl3? Cholesterol
386.7 amu chloroform 119.4 amu
What is the mole fraction of cholesterol in
the solution?
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What is the molality of a solution prepared by
dissolving 0.385 g of cholesterol, C27H46O in
40.0 g of chloroform, CHCl3? Cholesterol
386.7 amu chloroform 119.4 amu moles
cholesterol 0.385g / 386.7 Molality
----------------------------
----------------------- 0.0249 mol/kg kg
chloroform 0.04 kg What is the mole
fraction of cholesterol in the solution?
0.385g / 386.7 Xchloroform ---------------------
----------- 2.96 x 10-3 0.385g/386.7
40/119.4
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• Assuming that seawater is an aqueous solution of
  NaCl
• what is its molarity? The density of seawater is
  1.025 g/mL
• at 20?C and the NaCl concentration is 3.50 mass

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• Assuming that seawater is an aqueous solution of
  NaCl
• what is its molarity? The density of seawater is
  1.025 g/mL
• at 20?C and the NaCl concentration is 3.50 mass

3.5 mass 35 g NaCl in 1 kg solution 1 kg
solution m/d 1000/1.025 975.6 mL Molarity
35 g / (2335.5) 0.598
--------------------- ----------- 0.61 mol/L
0.61 M 0.9756 L 0.9756
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Summary
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Some Factors Affecting Solubility

• Solubility
• The amount of solute per unit of solvent needed
  to form a saturated solution
• A saturated solution is at equilibrium with
• undissolved solid.
• Dissolve
• Solute Solvent
  Solution
•   Crystallize

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Some Factors Affecting Solubility

• Unsaturated Contains less solute than a
  solvent has the capacity to dissolve.
• Supersaturated Contains more solute than would
  be present in a saturated solution.
• Crystallization The process in which dissolved
  solute comes out of the solution and forms
  crystals.

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• Effect of Temperature on Solubility
• Most solid substances become more soluble
• as temperature rises (not predictable)
• Solubility of NaCl for example nearly
  independent on temp.
• Most gases become less soluble
• as temperature rises (predictable)
•  

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• Effect of Pressure on Solubility
• 1. Liquids and solids No effect
• 2. Profound effect for gases.
• With increasing pressure more particles are
  forced into solution, because the particles try
  to escape from the applied force (Le Chatelier
  principle)
• Example opening a soda can or bottle.

If a stress is applied to a reaction mixture at
equilibrium, reaction occours in the direction
that relieves the stress
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Some Factors Affecting Solubility

• a) Equal numbers of gas molecules escaping
  liquid and returning to liquid
• b) Increase pressure, increase of gas
  molecules returning to liquid, solubility
  increases
• c) A new equilibrium is reached, where the
  s of escaping of returning

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The solubility of a gas in a liquid at a
given temperature is directly proportional to the
partial pressure of the gas over the solution.
Henrys Law solubility k x P k
constant characteristic of specific gas, mol/L
atm P partial pressure of the gas over the
solution
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Physical Behavior of Solutions Colligative
Properties

• H2O b.p. 100.0o C f.p. 0.0o C
• 1.00 m NaCl b.p. 101.0o C f.p. -3.7o C

o
o
Colligative properties Properties that depend on
the amount of a dissolved solute but not on its
chemical identity There are four main
colligative properties 1. Vapor pressure
lowering 2. Freezing point depression 3.
Boiling point elevation 4. Osmosis the
migration of solvent molecules through a
semipermeable membrane
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The vapor pressure of a solution is different
from the vapor of the pure solvent. Two
different cases 1. solute is non-volatile solute
has no vapor pressure of its own example
dissolving a solid vapor pressure of the solution
is always lower than that of the pure
solvent 2. solute is volatile solute has its
own vapor pressure example mixing 2 liquids
vapor pressure of the mixture is intermediate
between the vapor pressures of the two pure
liquids
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Vapor-pressure Lowering of Solutions Raoults Law

• Solutions with a Nonvolatile Solute

If the solute is nonvolatile and has no
appreciable vapor pressure of its own (solid
dissolved) the vapor pressure of the solution is
always lower that that of the pure solvent.
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Solutions with a Nonvolatile Solute!!!

• Raoults Law Psoln Psolv Xsolv
• Psoln vapor pressure of the solution
• Psolv vapor pressure of the pure solvent
• Xsolv mole fraction of the solvent in the
  solution
• Vapor pressure lowering is a colligative property
  (only
• dependent on amount of solute and not on its
  chemical identity!)
• For ionic substances calculate the total moles of
  
• solute particles, 1 mol NaCl will result in 1 mol
  Na and 1 mol
• Cl- 2 moles of particles
• 1 mol Na2SO4 will give 3 moles of particles

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Raoults Law applies to only Ideal solutions

• 1. Law works best when solute concentrations are
  low an when solute and solvent particles have
  similar intermolecular forces.
• 2. Further complication is that at higher
  concentrations
• ionic compounds are not 100 dissociated.
• Example
• 1 mol NaCl is only 90 dissociated
• 10 is undissociated
• resulting in less particles in solution than
  expected

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Example 9

• What is the vapor pressure (in mm Hg) of a
  solution prepared by dissolving 5.00 g of benzoic
  acid (C7H6O2) in 100.00 g of ethyl alcohol
  (C2H6O) at 35C? The vapor pressure of the pure
  ethyl alcohol at 35C is 100.5 mm Hg

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• Psoln Psolv Xsolv MM C7H6O2 122.12
  g/mol
• Psolv 100.5 mm Hg MM C2H6O 46.07 g/mol
•   1mol
• 5 g C7H6O2 x ---------- 0.0409 mol
• 122.12g
•  
• 100 g C2H6O x 1 mol/ 46.07 g 2.17 mol
• Xsolv 2.17 mol / (.0409 2.17 mol) .982
•  
• Psoln Psolv Xsolv
• 100.5 mm Hg .982 98.7 mm Hg

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Solutions with a Nonvolatile Solute

• Close-up view of part of the vapor pressure curve
  for a pure solvent and a solution of a
  nonvolatile solute. Which curve represents the
  pure solvent, and which the solution?
• Why?

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Reason for vapor pressure lowering DG DHvap
- T DS DHvap positive, disfavored DS
positive, favored DHvap is (nearly) the
same for a pure solvent and a solvent in a
solution DS is different solvent in a solution
has more disorder than pure solvent entropy of a
solution is higher than the pure solvent entropy
of the vapor in both cases the same Entropy
increase for vaporization from a solution is
smaller than vaporization from a pure
solvent Less entropy increase means less favored
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Solutions with a Volatile Solute!!

• For a mixture of 2 volatile liquids A and B the
  overall
• vapor pressure is the sum of the vapor pressure
  of the
• 2 components (Daltons law)
• Ptotal PA PB
• The vapor pressure for each component is
  calculated by
• Raoults law vapor pressure is equal to the mole
  fraction of A times the vapor pressure of pure A
• Ptotal PA PB (P0A XA) (P0B XB)
• PA vapor pressure of pure A XA mole
  fraction of A
• PB vapor pressure of pure B XB mole
  fraction of B

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Solutions with a Volatile Solute

• Close-up view of part of the vapor pressure
  curves for two pure liquids and a mixture of the
  two. Which curves represent the pure liquids,
  and which the mixture?

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Ptotal should be intermediate to A B Raoults
law applies only to ideal solutions Most real
solutions show deviations
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Example 10

• What is the vapor pressure ( in mm Hg) of a soln
  prepared by dissolving 25.0 g of ethyl alcohol
  (C2H5OH) in 100.0 g of water at 25C? The vapor
  pressure of pure water is 23.8 mm Hg and the
  vapor pressure of ethyl alcohol is 61.2 mm Hg at
  25C

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Example 10

• PH2O 23.8 mm Hg
• PC2H5OH 61.2 mm Hg
• XH2O mole fraction of A
• 25 g C2H5OH x 1 mol / 46.07 g .543 mol C2H5OH
• 100.0 g H2O x 1 mol/ 18 g 5.56 mol H2O
• XH2O 5.56 /(5.56 .543) .91
• XC2H5OH mole fraction of B
• XC2H5OH .543 / (.543 5.56) .09
• Ptot (23.8 x .91) (61.2 x .09) 27.2 mm Hg

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Boiling Point Elevation and Freezing Point
Depression of Solutions

• A solution has a lower vapor pressure than the
  pure liquid.
• To reach the atmospheric pressure (boiling point)
  the
• temperature must be higher.
• Tb Kb m Boiling point elevation
• Tf Kf m Freezing point depression
• Kb molal boiling-point elevation constant
• Kf molal freezing-point depression constant
• m molality

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Boiling Point Elevation and Freezing Point
Depression of Solutions
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Boiling Point Elevation and Freezing Point
Depression of Solutions

• 1. Red line is pure solvent
• 2. Green line solution of nonvolatile solute
• 3. Vapor pressure of solution is lower
• 4. Temp at which vapor pressure 1 atm for
  soln is higher
• 5. Boiling point of soln is higher by ?Tb
• 6. Liquid/vapor phase transition line is lower
  for soln
• 7. Triple point temp is lower for soln
• 8. Solid/liquid phase transition has shifted to
  a lower temp.
• 9. The freezing point of the soln is lower by
  ?Tf

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Molal boiling point elevation constant for
water 0.510C kg/mol A 1.00 molal solution of
glucose boils at 100.510C A 1.00 molal solution
of NaCl boils at 101.020C because we have twice
as many particles in the solution
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Example 11

• What is the normal boiling point in C of a
  solution prepared by dissolving 1.50 g of aspirin
  (C9H8O4) in 75.00 g of chloroform (CHCl3)? The
  normal boiling point of chloroform is 61.7 C and
  Kb of chloroform is 3.63 C kg/mol

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Example 11

• ?Tb Kb m
• m mole solute / kg solvent
• MM C9H8O4 180.16 g/mol
• 1.50 g C9H8O4 x 1 mol / 180.16 g .00833 mol
  C9H8O4
•  
• 75.00 g CHCl3 .07500 kg CHCl3
•  
• m .00833 mol C9H8O4 / .07500 kg CHCl3 .111 m
•  
• ?Tb 3.63 C kg/mol .111 mol/kg .403 C
•  
• Boiling point .403 C 61.7 C 62.1 C

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Osmosis and Osmotic Pressure

• Membranes are semipermeable materials
• They allow water and other small molecules to
• pass through, but they block the passage of
• larger molecules or ions.

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All living cells contain membranes and osmosis is
important in biological systems Osmosis provides
the primary means by which water is transported
into and out of cells Osmosis is responsible for
the ability of plant roots to suck up water from
the soil
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Osmosis
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Thermodynamic explanation Every system wants to
balance out the concentration One side pure
solvent Other side solution ordered system The
system tries to get into a more disordered more
randomness state The entropy will
increase Osmosis is similar to diffusion
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Osmosis Pressure

• 1. The amount of pressure necessary to achieve
  equilibrium
• 2. ? MRT
• ? osmotic pressure
• M molarity
• R gas constant, .08206 L atm/K mol
• T temperature in Kelvin

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Isotonic sodium chloride solution The total
concentration of dissolved particles inside red
blood cells is 0.30 M. What is the osmotic
pressure at body temp (310 k) ?
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Isotonic sodium chloride solution The total
concentration of dissolved particles inside red
blood cells is 0.30 M. What is the osmotic
pressure at body temp (310 k) ?
P MRT 0.30 mol/L x 0.08206 L atm/K mol x 310
K 7.63 atm
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All medical infusions must have the same osmotic
pressure Otherwise the blood cells would
burst! Therefore isotonic NaCl solutions are
injected What is the mass of an isotonic NaCl
solution? Since the molarity in blood cells is
0.3 M, we need 0.15 M NaCL (0.15 M Na and 0.15
M Cl-) Na 23.0 amu Cl 35.5 amu NaCl
58.5 amu 0.15 M NaCl 58.5 x 0.15 9 g/L
0.9 mass
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Example 12

• What osmotic pressure in atm would you expect for
  a solution of 0.125 M C6H12O6 that is separated
  from pure water by a semipermeable membrane at
  310 K?
• ? MRT
• (0.125 mol/L)(.08206 L atm/K mol)(310 K) 3.18
  atm

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Example 13

• A solution of unknown substance in water at 300 K
  gives rise to an osmotic pressure of 3.85 atm.
  What is the molarity of the solution?
• ? MRT
• M ?/RT
• M 3.85 atm / (.08206 L atm/K mol)(300 K)
• M .156 mol/L

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Some uses of colligative properties 1
Freezing-point depression - sprinkling of salt
to melt snow - antifreeze in automobile
cooling system - de-icing of airplane wings 2
Osmosis - desalination of seawater with
reverse osmosis 3 Molar mass determination
can use any four colligative properties most
accurate is osmotic pressure, since the
magnitude of osmosis effect is so great
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Example 14

• What is the molar mass of sucrose if a solution
  prepared by dissolving 0.822 g of sucrose in
  water and diluting to a volume of 300.0 mL has
  an osmotic pressure of 149 mm Hg at 298 K?

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• ? MRT
• 149 mm Hg x 1 atm / 760 mm Hg .196 atm
• M ? /RT
• .196 atm / (.08206 L atm/K mol)(298 K)
• .00802 mol/L
• .00802 mol/L x 1 L/1000 mL x 300 mL .00241 mol
•  
• MM mass of sucrose / moles of sucrose
• .822 g / .00241 mol 341.08 g/mol

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Summary