Chapter 12: Physical Properties of Solutions Solutions
Chapter 12: Physical Properties of Solutions
Solutions • The important idea is that the mixing is at the molecular (or ionic or atomic) level • Examples sugar, salt in water ethanol, O2 in water Ag/Hg amalgam O2 /C2 H2 (oxygen/acetylene)
1
Mixtures that are not Solutions • Oil & water shaken together (e.g., salad dressing) (Solutions do not separate) • Baking powder • Milk (Liquid solutions are clear)
Solvent/Solute • Solvent is component present in greater amount • Examples sugar, salt, etc. in water CO2 in water • (Sometimes a distinction between solvent and solute is not meaningful)
Solubility • The maximum amount of solute that a given amount of solvent can hold at a given temperature e.g., the solubility of alanine in H2 O is 167 g alanine per 1000 g H2 O at 25° C. • Solubility varies with T. Solubility usually increases with T but there are exceptions (like CaSO4 )
2
Saturation • Solutions that have as much solute as possible are saturated. • Solutions that could dissolve more solute are unsaturated. • Sometimes a supersaturated solution can be formed (usually by careful cooling). • Solute will separate from supersaturated solution if the solution is disturbed.
Dynamic Equilibrium • If both solute and solvent are present then solute is both entering and leaving the solution at all times. • (This fact can be demonstrated by using radioactive isotopes)
3
When Do Solutions Form? • It always costs energy to separate solute molecules/ions/atoms. • It always costs energy to separate solvent molecules (or atoms) • The disorder associated with forming a solution is always favorable.
When Do Solutions Form? (II) • The interaction between solvent and solute and solvent may be very favorable, somewhat favorable, or slightly unfavorable. • Solutions form when the energy advantage of forming the solution outweighs the energy disadvantage.
4
Basic Solubility Rule • Like dissolves like. Polar molecules (and ionic solutes) dissolve best in polar solvents (like water). Nonpolar molecules dissolve best in nonpolar solvents (hence, “dry” cleaning).
Salts are More Soluble in Water than in Other Solvents • Water molecules interact strongly with ions Cations interact with the O atoms Anions interact with the H atoms • The smaller the charges on the ions, the greater the solubility MgS is much less soluble than NaCl CaSO4 is less soluble than Ca(NO3)2
Some Molecules that are Soluble in Water H
H H
H H C H O H
H
C HH
O H
C
C
O
H H
C H
H
H H H H C C H C O H HH
H
H
O
O C
H C
H
H
5
Carbohydrates • Sugars dissolve in water because their many -OH groups form H-bonds with the HOH solvent molecules.
Some Nonpolar Solvents H
Cl
H
H
H
H H
Cl Cl
Cl
C H H
O C
O
Some Molecules that are Soluble in Nonpolar Solvents Cl Cl Br
Cl H
Br Cl
Cl
OH
6
Solubility Units: % by Mass (% by mass) ? 100
(masssolute) (masssolution)
• NO information about numbers of moles
Practice • A sample of 6.44 g of naphthalene (C10H8) is dissolved in 80.1 g benzene (C6H6). Calculate the percent by mass of naphthalene in this solution.
Solubility Units: Mole Fraction Xi ?
ni n tot
• Must know number of moles • Used in Raoult’s Law (vapor pressure) calculations
7
Practice • What is the mole fraction of oxygen in air composed of 79% nitrogen, 20% oxygen, and 1% carbon dioxide?
Solubility Units: Molality m?
moles solute kg solvent
• Used for calculations of colligative properties • Easily confused with molarity (M)
Practice • What is the molality of a solution containing 7.78 g of urea [(NH2)2CO] in 203 g of water?
8
Solubility Units: Molarity M?
moles solute Lsolution
• Used in stoichiometry problems involving solutions (volumetric problems) • Used in dilution problems • Easily confused with molality (m)
Conversions of Concentration Units • Xi, m, and % by mass can be interconverted if the molar masses are known. • Conversions to and from molarity require the density of the solution
Practice • Calculate the molality of a 5.86 M ethanol (C2H5OH) solution whose density is 0.927 g/mL. • Calculate the molality of a 44.6 % by mass aqueous solution of sodium chloride.
9
M vs. m in Dilute Solutions in Water • The density of most dilute water solutions is very nearly 1.00 g/mL, so 1 L of solution contains very nearly 1.00 kg of water. • The numerical values of M and m are nearly the same, but the units differ. • This relationship works for water only.
Effect of T on Solubility • Solubility of gases in liquids always decreases with T (O2, CO2 in water) • Solubility of solids, liquids in liquids usually increases with T (but there are exceptions, like CaSO4)
Which is why warm water is bad for fish -
10
Also, CaSO 4
Henry’s Law • Solubility of a gas in a liquid is proportional to the pressure of the gas above the liquid. c=kP Chang gives c in mol/L so k has units of mol/(L-atm). (It is more common to write m = k P)
11
Henry’s Law, con’t. • If more than one gas is present P is the partial pressure of the gas that is dissolved in the solution. for O2 in water open to the atmosphere at sea level the equation is c = k (0.22 atm) • The partial pressures of other gases don’t matter!
Practice • Calculate the molar concentration of oxygen in water at 25oC for a partial pressure of 0.22 atm. The Henry’s law constant for oxygen is 1.3 x 10-3 mol/L atm.
Vapor Pressure
• The pressure of the gas that is in equilibrium with a liquid or a solution H2O at 100° C: Pvap = 760 torr H2O at 25° C: Pvap = 24 torr
12
Raoult’s Law (Ideal Solutions) • Vapor pressure is proportional to mole fraction Pvap,i = Xi Pvap,i° where Pvap,i° is the vapor pressure of the pure liquid
Raoult’s Law, con’t.
• Raoult’s Law must be applied to each substance present. • If a solute is nonvolatile (sugar, NaCl) then Pvap,io = 0 for that solute.
13
P
P
benzene
toluene
0.2 0.4 0.6 0.8 Xi
P
0.2 0.4 0.6 0.8 Xi
P benzene
toluene
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
Xi
Xbenz + Xtol = 1
P toluene 0.8 0.6 0.4 0.2
P
P benzene
toluene
0.2 0.4 0.6 0.8
0.8 0.6 0.4 0.2
P benz + P tol = P total total P
14
Non-Ideal Solutions
• Most solutions are not ideal. • The pressures may be larger or smaller than those calculated from Raoult’s Law.
Practice • Calculate the vapor pressure of a solution made by dissolving 82.4 g urea [(NH2)2CO] in 212 mL of water at 35oC. What is the vapor pressure lowering?
15
Colligative Properties • Depend on identity of solvent molality of solute ionization (or, dissociation) of solute • Same for all nonelectrolytes (sugar, ethanol); Same for all 1:1 electrolytes (NaCl, KNO3); etc.
Colligative Properties, con’t.
• • • •
Vapor-Pressure Lowering Boiling-Point Elevation Freezing-Point Depression Osmotic Pressure
• Start with nonelectrolytes because the equations are simpler -
16
Vapor-Pressure Lowering (only one solute) • From Raoult’s Law Psolvent = Xsolvent P solvent° Psolvent = (1-Xsolute ) Psolvent° Xsolute Psolvent° = Psolvent° - Psolvent ? Psolvent = Xsolute Psolvent °
P
P
benzene 0.2 0.4 0.6 0.8 Xi
toluene 0.2 0.4 0.6 0.8 Xi
17
Boiling-Point Elevation (solute must be nonvolatile) • At the boiling point Psolv = Patm • Adding solute lowers Psolv • The temperature at which Psolv = Patm is higher than for the pure solvent • ? T = Kb m, where m is the molality
Freezing-Point Depression
• ? T = -Kf m, where m is the molality • Kf is always larger than Kb for the same solvent (water: Kf = 1.86 °/m; Kb = 0.52 °/m)
Practice • Calculate the boiling and freezing point of a solution containing 478 g of antifreeze [CH2(OH)CH2 (OH)] and 3202 g water.
18
Osmotic Pressure • Osmosis is the selective passage of solvent molecules through a porous membrane from a dilute solution to a more concentrated one. • Solvent goes (if it can find a way) from more dilute to more concentrated solutions. • Solvent transfer can be stopped (or even reversed) if the pressure difference is great enough.
Definitions • Isotonic solution: two solutions of equal concentration, therefore equal osmotic pressure. • Hypertonic solution: two solutions of unequal concentration, more concentrated one. • Hypotonic solution: two solutions of unequal concentration, less concentrated one
19
cell in isotonic sol’n
cell in distilled water
cell in salt water
20
Osmotic Pressure, con’t.
• ? = MRT, where M is molarity • (The apparent similarity to the ideal-gas equation is not really significant.) • The effect is HUGE. ? for M = 0.1 M at 295 K is 2.4 atm, which is over 80 ft of water!
Practice • What is the osmotic pressure (inatm) of a 0.884 M urea [(NH2)2CO] solution at 16oC? • A solution of 0.85 g of an organic compound in 100.0g of benzene has a freezing point of 5.16oC. Benzene freezes at 5.5oC, with Kf = 5.12oC/m
Van’ Hoff Factor i (Electrolyte Solutions) • What matters for colligative properties is the particle molality. • For dilute NaCl(aq), m´ = 2m (i = 2) For dilute CaCl2(aq), m´ = 3m (i = 3) For dilute CaSO4(aq), m´ = 2m (i = 2)
21
Van’t Hoff Factor, con’t. • All expressions for colligative properties must include the factor i ? ? Psolvent = i Xsolute Psolvent ? ? T = i Kb m ? ? T = - i Kf m ? ? = i MRT
Ideality of Electrolyte Solutions
• In practice the van’t Hoff Factor i is almost never as large as expected • The difference between expected and observed values is smallest for very dilute solutions and larger for more concentrated solutions
Practice • List, from greatest to least, the relative order of freezing point depression for 1M aqueous solutions of the following: NaCl, Ca(NO3)2, sucrose
22
Colloids • A colloid is a dispersion of particles of one substance throughout a dispersing medium made of another substance. • Colloid particles range from 1 x 103 pm to 1 x 10 6 pm. • Hydrophillic Colloids – in water these could be proteins
• Hydrophobic Colloids – In water these could be oil droplets
23
Solutions • The important idea is that the mixing is at the molecular (or ionic or atomic) level • Examples sugar, salt in water ethanol, O2 in water Ag/Hg amalgam O2 /C2 H2 (oxygen/acetylene)
1
Mixtures that are not Solutions • Oil & water shaken together (e.g., salad dressing) (Solutions do not separate) • Baking powder • Milk (Liquid solutions are clear)
Solvent/Solute • Solvent is component present in greater amount • Examples sugar, salt, etc. in water CO2 in water • (Sometimes a distinction between solvent and solute is not meaningful)
Solubility • The maximum amount of solute that a given amount of solvent can hold at a given temperature e.g., the solubility of alanine in H2 O is 167 g alanine per 1000 g H2 O at 25° C. • Solubility varies with T. Solubility usually increases with T but there are exceptions (like CaSO4 )
2
Saturation • Solutions that have as much solute as possible are saturated. • Solutions that could dissolve more solute are unsaturated. • Sometimes a supersaturated solution can be formed (usually by careful cooling). • Solute will separate from supersaturated solution if the solution is disturbed.
Dynamic Equilibrium • If both solute and solvent are present then solute is both entering and leaving the solution at all times. • (This fact can be demonstrated by using radioactive isotopes)
3
When Do Solutions Form? • It always costs energy to separate solute molecules/ions/atoms. • It always costs energy to separate solvent molecules (or atoms) • The disorder associated with forming a solution is always favorable.
When Do Solutions Form? (II) • The interaction between solvent and solute and solvent may be very favorable, somewhat favorable, or slightly unfavorable. • Solutions form when the energy advantage of forming the solution outweighs the energy disadvantage.
4
Basic Solubility Rule • Like dissolves like. Polar molecules (and ionic solutes) dissolve best in polar solvents (like water). Nonpolar molecules dissolve best in nonpolar solvents (hence, “dry” cleaning).
Salts are More Soluble in Water than in Other Solvents • Water molecules interact strongly with ions Cations interact with the O atoms Anions interact with the H atoms • The smaller the charges on the ions, the greater the solubility MgS is much less soluble than NaCl CaSO4 is less soluble than Ca(NO3)2
Some Molecules that are Soluble in Water H
H H
H H C H O H
H
C HH
O H
C
C
O
H H
C H
H
H H H H C C H C O H HH
H
H
O
O C
H C
H
H
5
Carbohydrates • Sugars dissolve in water because their many -OH groups form H-bonds with the HOH solvent molecules.
Some Nonpolar Solvents H
Cl
H
H
H
H H
Cl Cl
Cl
C H H
O C
O
Some Molecules that are Soluble in Nonpolar Solvents Cl Cl Br
Cl H
Br Cl
Cl
OH
6
Solubility Units: % by Mass (% by mass) ? 100
(masssolute) (masssolution)
• NO information about numbers of moles
Practice • A sample of 6.44 g of naphthalene (C10H8) is dissolved in 80.1 g benzene (C6H6). Calculate the percent by mass of naphthalene in this solution.
Solubility Units: Mole Fraction Xi ?
ni n tot
• Must know number of moles • Used in Raoult’s Law (vapor pressure) calculations
7
Practice • What is the mole fraction of oxygen in air composed of 79% nitrogen, 20% oxygen, and 1% carbon dioxide?
Solubility Units: Molality m?
moles solute kg solvent
• Used for calculations of colligative properties • Easily confused with molarity (M)
Practice • What is the molality of a solution containing 7.78 g of urea [(NH2)2CO] in 203 g of water?
8
Solubility Units: Molarity M?
moles solute Lsolution
• Used in stoichiometry problems involving solutions (volumetric problems) • Used in dilution problems • Easily confused with molality (m)
Conversions of Concentration Units • Xi, m, and % by mass can be interconverted if the molar masses are known. • Conversions to and from molarity require the density of the solution
Practice • Calculate the molality of a 5.86 M ethanol (C2H5OH) solution whose density is 0.927 g/mL. • Calculate the molality of a 44.6 % by mass aqueous solution of sodium chloride.
9
M vs. m in Dilute Solutions in Water • The density of most dilute water solutions is very nearly 1.00 g/mL, so 1 L of solution contains very nearly 1.00 kg of water. • The numerical values of M and m are nearly the same, but the units differ. • This relationship works for water only.
Effect of T on Solubility • Solubility of gases in liquids always decreases with T (O2, CO2 in water) • Solubility of solids, liquids in liquids usually increases with T (but there are exceptions, like CaSO4)
Which is why warm water is bad for fish -
10
Also, CaSO 4
Henry’s Law • Solubility of a gas in a liquid is proportional to the pressure of the gas above the liquid. c=kP Chang gives c in mol/L so k has units of mol/(L-atm). (It is more common to write m = k P)
11
Henry’s Law, con’t. • If more than one gas is present P is the partial pressure of the gas that is dissolved in the solution. for O2 in water open to the atmosphere at sea level the equation is c = k (0.22 atm) • The partial pressures of other gases don’t matter!
Practice • Calculate the molar concentration of oxygen in water at 25oC for a partial pressure of 0.22 atm. The Henry’s law constant for oxygen is 1.3 x 10-3 mol/L atm.
Vapor Pressure
• The pressure of the gas that is in equilibrium with a liquid or a solution H2O at 100° C: Pvap = 760 torr H2O at 25° C: Pvap = 24 torr
12
Raoult’s Law (Ideal Solutions) • Vapor pressure is proportional to mole fraction Pvap,i = Xi Pvap,i° where Pvap,i° is the vapor pressure of the pure liquid
Raoult’s Law, con’t.
• Raoult’s Law must be applied to each substance present. • If a solute is nonvolatile (sugar, NaCl) then Pvap,io = 0 for that solute.
13
P
P
benzene
toluene
0.2 0.4 0.6 0.8 Xi
P
0.2 0.4 0.6 0.8 Xi
P benzene
toluene
0.2 0.4 0.6 0.8
0.2 0.4 0.6 0.8
Xi
Xbenz + Xtol = 1
P toluene 0.8 0.6 0.4 0.2
P
P benzene
toluene
0.2 0.4 0.6 0.8
0.8 0.6 0.4 0.2
P benz + P tol = P total total P
14
Non-Ideal Solutions
• Most solutions are not ideal. • The pressures may be larger or smaller than those calculated from Raoult’s Law.
Practice • Calculate the vapor pressure of a solution made by dissolving 82.4 g urea [(NH2)2CO] in 212 mL of water at 35oC. What is the vapor pressure lowering?
15
Colligative Properties • Depend on identity of solvent molality of solute ionization (or, dissociation) of solute • Same for all nonelectrolytes (sugar, ethanol); Same for all 1:1 electrolytes (NaCl, KNO3); etc.
Colligative Properties, con’t.
• • • •
Vapor-Pressure Lowering Boiling-Point Elevation Freezing-Point Depression Osmotic Pressure
• Start with nonelectrolytes because the equations are simpler -
16
Vapor-Pressure Lowering (only one solute) • From Raoult’s Law Psolvent = Xsolvent P solvent° Psolvent = (1-Xsolute ) Psolvent° Xsolute Psolvent° = Psolvent° - Psolvent ? Psolvent = Xsolute Psolvent °
P
P
benzene 0.2 0.4 0.6 0.8 Xi
toluene 0.2 0.4 0.6 0.8 Xi
17
Boiling-Point Elevation (solute must be nonvolatile) • At the boiling point Psolv = Patm • Adding solute lowers Psolv • The temperature at which Psolv = Patm is higher than for the pure solvent • ? T = Kb m, where m is the molality
Freezing-Point Depression
• ? T = -Kf m, where m is the molality • Kf is always larger than Kb for the same solvent (water: Kf = 1.86 °/m; Kb = 0.52 °/m)
Practice • Calculate the boiling and freezing point of a solution containing 478 g of antifreeze [CH2(OH)CH2 (OH)] and 3202 g water.
18
Osmotic Pressure • Osmosis is the selective passage of solvent molecules through a porous membrane from a dilute solution to a more concentrated one. • Solvent goes (if it can find a way) from more dilute to more concentrated solutions. • Solvent transfer can be stopped (or even reversed) if the pressure difference is great enough.
Definitions • Isotonic solution: two solutions of equal concentration, therefore equal osmotic pressure. • Hypertonic solution: two solutions of unequal concentration, more concentrated one. • Hypotonic solution: two solutions of unequal concentration, less concentrated one
19
cell in isotonic sol’n
cell in distilled water
cell in salt water
20
Osmotic Pressure, con’t.
• ? = MRT, where M is molarity • (The apparent similarity to the ideal-gas equation is not really significant.) • The effect is HUGE. ? for M = 0.1 M at 295 K is 2.4 atm, which is over 80 ft of water!
Practice • What is the osmotic pressure (inatm) of a 0.884 M urea [(NH2)2CO] solution at 16oC? • A solution of 0.85 g of an organic compound in 100.0g of benzene has a freezing point of 5.16oC. Benzene freezes at 5.5oC, with Kf = 5.12oC/m
Van’ Hoff Factor i (Electrolyte Solutions) • What matters for colligative properties is the particle molality. • For dilute NaCl(aq), m´ = 2m (i = 2) For dilute CaCl2(aq), m´ = 3m (i = 3) For dilute CaSO4(aq), m´ = 2m (i = 2)
21
Van’t Hoff Factor, con’t. • All expressions for colligative properties must include the factor i ? ? Psolvent = i Xsolute Psolvent ? ? T = i Kb m ? ? T = - i Kf m ? ? = i MRT
Ideality of Electrolyte Solutions
• In practice the van’t Hoff Factor i is almost never as large as expected • The difference between expected and observed values is smallest for very dilute solutions and larger for more concentrated solutions
Practice • List, from greatest to least, the relative order of freezing point depression for 1M aqueous solutions of the following: NaCl, Ca(NO3)2, sucrose
22
Colloids • A colloid is a dispersion of particles of one substance throughout a dispersing medium made of another substance. • Colloid particles range from 1 x 103 pm to 1 x 10 6 pm. • Hydrophillic Colloids – in water these could be proteins
• Hydrophobic Colloids – In water these could be oil droplets
23
