Solutions

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Solutions

• Zumdahl
• Chapter 11

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What is a solution ?

• A special type of Mixture
• Single phase
• More than one distinguishable chemical
  constituent present
• Homogeneous
• Examples
• solid solutions --- alloys
• liquid solutions --- soda

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Solution Composition

• 1. Molarity (M)
• 2. Mass (weight) percent
• 3. Mole fraction (cA)
• 4. Molality (m)

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Calculating Solution Composition (example 11.1)
1.00 g ethanol

100.0 g water
Moles
Molarity
Molality
Mole Fraction
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Calculating Solution Composition (example 11.1)
1.00 g ethanol

100.0 g water
Mass
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Sample Exercise 11.2 What are m, mass , and x
of 3.75 M sulfuric acid in a aqueous solution
with density 1.230?
Strategy find mass of each component in unit
volume
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Topics

• How do things dissolve ?
• Microscopic details of dissolution
• Why do things dissolve ?
• Thermodynamics of dissolution
• How do we quantify solutions ?
• Measures of concentration
• Solubility

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Three steps for dissolving

• Expansion of the solute lattice
• Expansion of the solvent structure
• cavitation
• Mixing of the expanded solute and solvent
• solvation of individual solvent units

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Steps in Solution Formation

• Step 1 - Expanding the solute
• Step 2 - Expanding the solvent
• Step 3 - Allowing the solute and solvent to
  interact to form a solution
• DHsoln DHstep 1 DHstep 2 DHstep 3

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Steps in Solution Formation

• Step 1 - Expanding the solute (endothermic)
• Step 2 - Expanding the solvent (endothermic)
• Step 3 - Allowing the solute and solvent to
  interact to form a solution (exothermic)
• DHsoln DHstep 1 DHstep 2 DHstep 3

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Energetics of dissolution
Expanded solute expanded solvent
Cavitation energy
Energy of Mixing
Expanded solute solvent
Lattice energy
Solution
Separated solute and solvent
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Energy terms for different solvent/solute
interactions (Table 11.3)
DHsoln
Solvent
Solute
DH1
DH2
DH3
polar
polar
large
large
large, lt0
small
polar
nonpolar
small
large
small
large, gt0
nonpolar
polar
large
small
small
large, gt0
nonpolar
nonpolar
small
small
small
small
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Energy of Mixing ?

• Entropy of mixing
• Natures prefers disorder
• Does NOT depend on chemical characteristics of
  the solute and solvent
• Enthalpy of mixing
• intermolecular forces/interactions
• stronger interactions lead to greater
  stabilization

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Aqueous Solution of Ionic Solid

• Lattice energy of ionic solids is large
• Cavitation energy of polar solvents is derived
  from dipolar interactions
• Dipolar solvent --- ions (solute) interactions
  result in a large, exothermic mixing term
• Result Often spontaneous, but can be exothermic
  or endothemic

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Water is a good solvent for ionic solids

• Polar water molecules have a strong attraction
  for small ions
• Smaller the ion, greater the exothermicity in
  water
• Water molecules can form Hydrogen bonds with many
  polar solutes

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Chemical Structure

• The energy cost of expanding the solute lattice
  and disrupting the solvent structure (cavitation
  energy) must be regained by solvation
• Solvation energy is a consequence of
  intermolecular forces dipolar interactions,
  hydrogen bonding and hydrophobic interactions

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Solubility

• Solubility is the upper limit on the amount of
  solute that can go into a solution
• A solute may have infinite solubility in a given
  solvent
• When a solute is present at the limit of
  solubility, the solution is called saturated

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Factors that affect Solubility

• Chemical Structure of Solute/Solvent
• Amount of solute present
• Temperature
• Pressure

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Pressure

• Largest effects on the solubility of gases.
• Higher pressure leads to increased solubility, as
  long as the molecules do not react with the
  solvent

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Properties of Solutions

• Vapor Pressure
• Ideal and non-ideal solutions
• Raoults Law and Henrys Law
• Colligative Properties
• Vapor Pressure Lowering
• Freezing point depression (cryoscopy)
• Boiling point elevation (ebullioscopy)
• Osmotic Pressure (Osmosis)

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Vapor Pressure

• In an isolated one-component system, it is the
  pressure exerted by the gas in thermodynamic
  equilibrium with the liquid
• In a multi-component system, it is the partial
  pressure of the gas in equilibrium with the liquid

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Liquid-Vapor Equilibrium
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Vapor Pressure
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What is Partial Pressure?

• Fraction of the total Pressure exerted by one
  (gaseous) component
• Ptotal P1 P2 Pn
• P1 c1Ptotal
• What is the partial pressure of O2 in air?

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Henrys Law
The amount of a gas dissolved in a solution is
directly proportional to the pressure of the gas
above the solution.

• P kC
• P partial pressure of gaseous solute above the
  solution
• C molar concentration of dissolved gas
• k a constant for the given solute/solvent

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Example CO2 Dissolved in Soda
In bottle PCO2 5.0 atm In atmosphere PCO2
4.0 10 - 4 atm kCO2 32 L atm/mol
In bottle
In atmosphere
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Temperature

• Increasing temperature often increases
  solubility, not always.
• Thermal energy can help in expanding the solute
  lattice and cavitation
• Increasing temperature commonly decreases
  solubility of gases

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Raoults Law
The presence of a nonvolatile solute lowers the
vapor pressure of a solvent.

• Psoln csolvent Psolvent
• Psoln vapor pressure of the solution
• csolvent mole fraction of the solvent
• Psolvent vapor pressure of the pure solvent

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Vapor Pressure Lowering

• The vapor pressure of a solution is proportional
  to the mole fraction of the solvent if
• the solute is nonvolatile and nonreactive
• the solvent and solute do not have strong
  interactions

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Vapor Pressure Lowering
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Ideal Solutions

• A solution is IDEAL if its components obey
  Raoults Law
• Ptotal xaPa0 xbPb0

Solutions tend to be ideal when

• DHsolution is close to zero
• Solute and solvent molecules are similar in size
  and polarity
• Vsolution Vsolute Vsolvent (for liquids)

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Vapor Pressure of Ideal Solution (AB)
Ptotal
PAo
PBo
PA xAPAo
PB xBPBo
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Non-ideal Solutions

• In a NON-IDEAL solution, if the solute-solvent
  attractions are stronger than the solvent-solvent
  ones, the vapor pressure of the solution will be
  lower than predicted by Raoults Law
• Negative deviations from ideality.
• In a NON-IDEAL solution, if the solvent-solvent
  attractions are stronger than the solvent-solute
  ones, the vapor pressure of the solution will be
  higher.
• Positive deviations from ideality

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Colligative Properties

• Depend only on the number, not on the identity,
  of the solute particles in an ideal solution.
• Boiling point elevation
• Freezing point depression
• Osmotic pressure

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P-T Phase Diagram
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Phase diagram of a pure substance
P
solid
liquid
gas
T
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solid
vapor
liquid
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Boiling Point Elevation

• A nonvolatile solute elevates the boiling point
  of the solvent.
• DT Kbmsolute
• Kb molal boiling point elevation constant
• m molality of the solute

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Freezing Point Depression

• A nonvolatile solute depresses the freezing point
  of the solvent.
• DT Kfmsolute
• Kf molal freezing point depression constant
• m molality of the solute

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Freezing Point Depression
Example Problem

• The molecular weight of glucose is 180.0 g/mol.
  What is the freezing point of a solution of 150
  .0 g of water and 18.0 g of glucose ?
• DT Kf m
• Kf of water 1.86 C kg/mol

m
(18.0/180)/0.150 mol/kg 0.667
mol/kg
solute
o
o
(1.86)(0.667) C 1.24
C
T
D
o
o
- 1.24 C
(0 - 1.24) C
Freezing Point
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Boiling Point Elevation
Example Problem

• A solution of 150 .0 g of water and 18 g of
  glucose has a boiling point of 100.34 oC. What is
  the molecular weight of glucose?
• DT Kb m
• Kb of water 0.51 o C kg/mol

(100.34 - 100.0)/0.51 mol/kg 0.67
mol/kg
m
solute
18 / 0.1500 g/kg
120 g/kg
(120)/(0.67) g/mol 180 g/mol
Molecular Weight
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Osmotic Pressure
Pressure P
Pressure PP
semipermeable membrane
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Osmotic Pressure

• Osmosis The flow of solvent into the solution
  through the semipermeable membrane.
• Osmotic Pressure External pressure required to
  balance flow of pure solvent through a
  semipermeable membrane separating a solution from
  pure solvent

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Osmotic Pressure

• p RT Msolute
• p Osmotic Pressure
• R Gas Constant
• T Absolute Temperature
• Msolute Molarity
• Semi-permeable membrane allows bi-directional
  flow of solvent only

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Isotonic solutions
Solvent flow will rupture cell
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Applications of Osmosis

• blood plasma
• dialysis
• desalination (reverse osmosis)
• determining polymer molecular weights

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Osmotic Pressure

• The molecular weight of glucose is 180.0 g/mol.
  What is the osmotic pressure of a 150 .0 ml
  solution of water containing 1.80 g of glucose at
  20 degrees Celsius?
• p RT Msolute

Gas constant 0.08206 L atm/K mol
Msolute (1.80/180)/0.150 mol/L
0.0667 mol/L
p (0.08206)(27320)(0.0667) atm 1.6 atm
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vant Hoff factor

• i is apparent number of particles relative to
  the number if no dissociation occurs
• i may be fractional because of incomplete ionic
  dissociation (ion pairing)

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van't Hoff factor
Example Problem
The molecular weight of rock salt (NaCl) is 58.44
g/mol. The osmotic pressure of a 150 .0 ml
solution of water containing 0.080 g of salt was
found to be 0.40 atm at 298 K. What percentage
of the salt is dissociated?
p i RTMsolute
R 0.08206 L atm/K mol
MNaCl (0.080/58.44)/0.150 mol/L
0.00912 mol/L
p0 (0.08206)(298)(0.00912) atm 0.223
atm
pobserved
(0.40)/(0.223) 1.8
i

p0
100(iobserved - 1) / (itheoretical -1) 80
Percent Dissociated
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Osmotic Pressure - Electrolytes

• p i RT Msolute
• p Osmotic Pressure
• R Gas Constant
• T Absolute Temperature
• Msolute Molarity
• i vant Hoff factor

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Summary of Chapter 11

• Microscopic mechanism of solution (energetics)
• Physical factors affecting solubility
• Temperature
• Pressure (Henrys law)
• Ideal and nonideal solutions
• Raoults law
• Colligative properties (nonelectrolytes)
• boiling point elevation
• freezing point depression
• osmotic pressure
• electrolytes and vant Hoff factor

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• Which of the species below would you expect to
  show the least hydrogen bonding
• (a) NH3
• (b) H2O
• (c) HF
• (d) CH4
• (e) all the same
• On a relative basis, the weaker the
  intermolecular forces in a substance
• (a) Greater its heat of vaporization
• (b) More it deviates from ideal gas behavior
• (C) The greater its vapor pressure at a
  particular temperature
• (d) The higher its melting point
• (e) None of the above