Chapter 10 Solutions
Solutions
A solution is a homogenous mixture of 2 or more
substances
Chapter 14
The solute is (are) the substance(s) present in the smaller
amount(s)
The solvent is the substance present in the larger amount
Deicing of airplanes is
based on freezing point
depression.
air
seltzer water
H2 in Pd
alcohol/H2O
salt water
brass (Cu/Zn)
solder (Sn/Pb)
1
A saturated solution contains the maximum amount of a solute
that will dissolve in a given solvent at a specific temperature.
An unsaturated solution contains less solute than the solvent
has the capacity to dissolve at a specific temperature.
2
DHsoln, the heat of solution, is the sum of three processes:
•
•
•
solvent-solvent interaction
solute-solute interaction
solvent-solute interaction
A supersaturated solution contains more solute than is
present in a saturated solution at a specific temperature.
Sodium acetate crystals rapidly form when a seed crystal is
added to a supersaturated solution of sodium acetate.
DHsoln = DH1 + DH2 + DH3
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4
1
Chapter 10 Solutions
Q. For NaCl(s), D Hsoln >0; so why does it dissolve?
How are DHsoln and Solubility related?
Estimated DHsoln
(kJ/mol)
Solubility in H2O
18oC (g/100 mL)
AgCl
+61
0.000009
LiF
+32
0.3
NaCl
+26
35.7
KF
+2
92.3
RbF
-3
131.0
In general, for a soluble salt DHsoln < 0 or  0 (only slightly endothermic)
Rationalize solubilities:
Nitrates have big, singly charged anions, so low lattice enthalpy;
hydration enthalpy is large due to H-bonding with H2O, so very soluble.
A. Processes naturally run in the direction that leads to the
most probable state (greatest entropy).
Carbonates are also large anions, but doubly charged, so higher lattice
enthalpy than nitrates and less soluble.
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6
Concentration Units, cont’d
Concentration Units
The concentration of a solution is the amount of solute
present in a given quantity of solvent or solution.
Mole Fraction (X)
moles of A
XA = sum of moles of all components
Percent by Mass
% by mass =
mass of solute
x 100%
mass of solute + mass of solvent
=
mass of solute
Xsolute =
x 100%
mol solute
mol solute + mol solvent
mass of solution
Parts per Million (ppm)
mass of solute
ppm =
mass of solution
A solution of 5.72 g Cu(II) sulfate in 0.125L water has d = 1.00 g/mL;
calculate the mole fraction of copper ions in the solution. (CuSO4 molar
mass = 160 g/mol)
x 106
Q: A 2.5 g sample of groundwater contains 5.4 g of Zn2+. What is Zn2+ conc in ppm?
A = 0.00512
A: 2.2 ppm
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8
2
Chapter 10 Solutions
Concentration Units cont’d
What is the molality of a 5.86 M ethanol (C2H5OH, 46.1 g/mol)
solution (in H2O) whose density is 0.927 g/mL?
Molarity (M)
m
moles of solute
M =
liters of solution
Need to know moles, mass;
given moles and volume
Assume 1 L of solution:
1 L  5.86 mol ethanol/L  46.1 g/mol = 270g ethanol
1 L  0.927g of soln/mL 1000 mL/L = 927g soln
Molality (m)
m =
moles of solute
= mass of solvent (kg)
moles of solute
moles of solute
kg of solvent
m =
Q. Why do we need molality?
=
A. Molarity varies with temperature, molality does not
=
mass of solvent (kg)
5.86 moles C2H5OH
927 g – 270 g
=
5.86 moles C2H5OH
mass of soln – mass of solute
5.86 moles C2H5OH
0.657 kg solvent
= 8.92 m
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Temperature and Solubility of Solids
10
Factors Affecting Gas Solubility
For most solids, solubility increases with
increasing temperature; DHsoln >0
KCl(s) + energy  KCl(aq); DHsoln= 17 kJ/mol
But there are many exceptions
LiCl(s)  LiCl(aq) + energy; DHsoln= -37 kJ/mol
According to le Chatelier’s principle, expect
solubility to decrease with increase in
temperature
Solubility decreases with temperature
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Carbonated beverages are bottled under CO2
pressure. When the bottle is opened, the
pressure is released and bubbles of CO2 form
and rise to the surface.
What factors affect how much gas dissolves in
a liquid?
Sg = kH  Pg
where Sg = solubility of gas, M
Pg = pressure of gas, atm
kH = Henry’s Law constant, mol/L•atm;
depends on solvent, gas, temp
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3
Chapter 10 Solutions
Pressure and Solubility of Gases
The solubility of a gas in a liquid is proportional to the pressure of the gas
over the solution (Henry’s law).
Gas Solubility Varies with Partial Pressure
Solubility of gases in water at 20oC
Sg = k H Pg
Sg = kHPg
kH depends on gas,
solvent, and temperature
Push in piston
New equilib
established
P increases
At equilibrium:
rate leaving=rate entering soln
Sg increases
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14
Le Chatelier’s principle explains how temperature
affects gas solubility
Temperature and Gas Solubility
Solubility of gases usually
decreases with increasing
temperature
Gas + solvent(l)
Saturated solution + heat
Equilibrium shifts left
How do we rationalize this?
For most soluble gases, DHsoln<0
Le Chatelier’s principle: if a change is imposed on a system at
equilibrium, the position of the equilibrium will shift in a direction that
tends to reduce that change
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4
Chapter 10 Solutions
Chemistry In Action: The Killer Lake
Colligative Properties of Nonelectrolyte Solutions
Colligative properties are properties that depend only on the number
of solute particles in solution and not on the nature of the particles.
In an ideal solution, the properties depend only on the concentration of
solute (not identity of solute or solvent; IMFs all identical).
8/21/86
CO2 Cloud Released
1700 Casualties
Vapor-Pressure Lowering
What shifted equilibrium?
•
earthquake
•
landslide
•
strong winds
Lake Nyos, West Africa
P1 = X1 P 10
Boiling-Point Elevation
DTb = Kb m
Freezing-Point Depression
DTf = Kf m
Osmotic Pressure (p)
p = MRT
Why nonelectrolyte?
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Effect of nonvolatile solute on vapor pressure
18
Why does a nonvolatile solute reduce vapor
pressure?
A pure solvent tends to form an
even more random vapor.
Vaporization continues until
equilibrium is reached.
19
When a nonvolatile solute is present, the
liquid phase has a greater randomness than
pure solvent, and therefore a smaller
tendency to form the vapor. So the vapor
pressure of the solution is less than the pure
liquid.
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5
Chapter 10 Solutions
Vapor-Pressure Lowering – Raoult’s Law
A beaker of pure water and a beaker of concentrated sugar
solution are placed in a small closed system. What happens
over time? hint: compare the vp of the two liquids
If the solute is non-volatile (no measurable vapor
pressure), the VP of its solution is always less than that of
the pure solvent.
P°
o
Psolv = Xsolv Psolv
o = vapor pressure of pure solvent
Psolv
Xsolv = mole fraction of the solvent
pure water
An ideal solution obeys Raoult’s Law
concentrated
sugar
solution
Only the solvent contributes to VP
since solute is nonvolatile
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22
Mixture of 2 volatile liquids (still Raoult’s law)
Boiling-Point Elevation: a nonvolatile solute raises
the bp of water
Vapor Pressure
T bo is the boiling point of pure water
PB
°
Nonvolatile solute lowers VP at each T
T
b
is the boiling point of solution
PA°
DTb = Tb – T bo
DTb = Kb m
Boiling
point of
solution
Tb
xA = 0
XB = 1
m is the molality of the solution
Kb is the molal boiling-point
elevation constant (0C/m);
depends on solvent, not
solute
Liquid has equal
and
the vapor contains more
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Which is more volatile?
is more volatile
Mole fraction
xA = 1
XB = 0
;
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6
Chapter 10 Solutions
Fractional Distillation Apparatus
Fractional distillation separates crude oil into fractions
Gases (1-4 carbons)
Fractional distillation separates the liquid
components of a mixture based on their
boiling points: the most volatile component
is collected first.
Gasoline (5-13 carbons)
Kerosene (12-16 carbons)
Fuel oil (15-18 carbons)
Enriched in more
volatile component
Lube oil + wax (16-20
carbons)
Enriched in less
volatile component(s)
>370°C
Effect of Solute on Freezing Point
Residue (>20 carbons)
Freezing Point Depression
IMF explanation
As solution conc
increases, FP
decreases
Pure ice
Adding antifreeze to water
prevents the water from
freezing.
When a solution of purple dye in
water is immersed in a cold bath,
pure ice forms along the walls.
The dye solution has a lower and
lower FP and concentrates in the
center.
Ice in equilibrium with water.
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The presence of a solute lowers
the rate at which molecules in the
liquid return to the solid state.
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7
Chapter 10 Solutions
Freezing Point Depression
Freezing-Point Depression of water
Entropy Explanation
A pure solid has a high degree of
order, whereas a liquid is disordered.
The solid has a tendency to form the
liquid and does so when the
temperature reaches the melting
point.
T f o is the freezing point of
the pure water
When a solute is present in the
liquid, the solution has a higher
degree of disorder. Therefore, the
solid has a stronger tendency to
form liquid, and freezes at a lower
temperature than the pure liquid.
Tf is the freezing point of
the solution
o
DTf = T f – Tf
DTf = Kf m
m is the molality of the solution
Kf is the molal freezing-point
depression constant (0C/m);
depends on solvent, not
solute
Tf°
Tf
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Kf and Kb depend on the solvent, not solute
30
What is the freezing point of a solution containing 478 g of
ethylene glycol (antifreeze) in 3202 g of water? The molar
mass of ethylene glycol is 62.01 g.
DTf = Kf m
Kf water = 1.86 0C/m
1 mol
m =
moles of solute
mass of solvent (kg)
478 g x
=
62.01 g
= 2.41 m
3.202 kg solvent
DTf = Kf m = 1.86 0C/m  2.41 m = 4.48 0C
0
DTf = T f – Tf
0
Tf = T f – DTf
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Do #56b
= 0.00 0C – 4.48 0C = -4.48 0C
32
8
Chapter 10 Solutions
Osmosis
Osmosis is the selective passage of solvent molecules through
a porous membrane from a dilute solution to a more
concentrated one.
Carrot
placed in
concentrated
NaCl(aq)
33
Red blood cells in three stages of osmosis
isotonic
solution
hypotonic
solution
34
Osmotic Pressure (p)
hypertonic
solution
Iinitially: a water solution (with a
nonvolatile solute) and pure water,
separated by a semipermeable
membrane through which only water
molecules can pass.
35
The system at equilibrium, where
the rate of solvent transfer is the
same in both directions
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9
Chapter 10 Solutions
The Osmotic Pressure is the pressure required
to stop osmosis
nRT
Osmotic pressure: = V
a) Osmotic pressure is quite large, even for a dilute solution:
e.g. 0.10 M solution at 25oC
 = (0.10 mol/L)(0.0821 Latm/mol K)(298K) = 2.4 atm
b) Reverse osmosis can be used to desalinate seawater
 = MRT = n RT
V
where  is osmotic pressure in atm,
M is molarity, R is the gas law
constant, T = Kelvin temperature.
Note similarity to gas law.
37
Dialysis membrane allows passage of solvent
and small solute molecules/ions
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Colligative Properties of Electrolyte Solutions
In kidney dialysis, the dialyzing solution contains the same concentrations
of ions and small molecules as blood but has none of the waste products
normally removed by the kidneys, so waste molecules migrate into
dialyzing solution.
0.1 m NaCl solution
0.1 m Na+ ions + 0.1 m Cl- ions
Since colligative properties depend on the number of solute
particles in solution, must take into account the number of ions
formed when an ionic compound dissociates.
0.1 m NaCl solution
0.2 m ions in solution
DT = i kf  m where i is the van’t Hoff i factor; it is determined
experimentally
Solute
i should be
nonelectrolytes
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1
NaCl
2
CaCl2
3
FeCl3
4
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10
Chapter 10 Solutions
Salts do not completely dissociate
van’t Hoff factor (i)
=
actual # of particles in soln after dissocn
# of formula units initially dissolved in soln
0.10 m
0.01 m
Limiting
Value
Sucrose
1.00
1.00
1.00
NaCl
1.87
1.94
2.00
K2SO4
2.32
2.70
3.00
MgSO4
1.21
1.53
2.00
Electrolyte
In an aqueous solution, ions
aggregate, forming ion pairs
that behave as a unit.
Describe the trends observed.
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