11 solutions

AP* Chemistry
PROPERTIES OF SOLUTIONS

IMPORTANT TERMS
Solution—a homogeneous mixture of two or more substances in a single phase.
Does not have to involve liquids. Air is a solution of nitrogen, oxygen, carbon dioxide etc.;
solder is a solution of lead, tin etc.

solute—component in lesser concentration;
dissolvee
solvent—component in greater
concentration; dissolver

solubility—maximum amount of material that
will dissolve in a given amount of solvent at a
given temperature to produce a stable solution.
In other words, the solution is saturated.
Study the solubility rules!!

molar solubility—the number of moles of solute that dissolves in exactly 1.0 L of solvent,
expressed in units of molarity, M or the use of square brackets.

Saturated solution— a solution containing the maximum
amount of solute that will dissolve under a given set of
pressure and temperature conditions. Saturated solutions are
at dynamic equilibrium with any excess undissolved solute
present. Solute particles dissolve and recrystallize at equal
rates.
Unsaturated solution— a solution containing less than the
maximum amount of solute that will dissolve under a given
set of conditions. (more solute can dissolve)

Supersaturated solution—oxymoron—a solution that has
been prepared at an elevated temperature and then slowly
cooled. It contains more than the usual maximum amount of
solution dissolved. A supersaturated solution is very
unstable and agitation (stirring, pouring, etc.) or the
addition of a “seed crystal’ will cause all excess solute
to crystallize out of solution leaving the remaining
solvent saturated. (rock candy is made this way as are
those liquid hand warmer packets of sodium acetate
solution, pictured at left, folks use hunting, at football
games, skiing, etc.)

*AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.
© 2008 by René McCormick. All rights reserved.

miscible—When two or more liquids mix (ex. Water and food coloring)

immiscible—When two or more liquids DON’T mix.—they usually layer if allowed to set
for a while. (ex. Water and oil)

Concentration Units
Molarity (M) = # of moles of solute per liter of solution; IS temperature dependent.
The liquid solvent can expand and contract with changes in temperature. Thus, not a constant
ratio of solute:solvent particles. Most molar solutions are made at 25° C so this point is subtle
and picky, but important none the less!!

moles of solute
M =
liters of solution

Mass percent (weight percent) = percent by mass of the solute in the solution

grams of solute
Mass percent = × 100%
grams of solution

Mole fraction (χ) = ratio of the number of moles of a given component to the total number
of moles of present.

na
Mole fractiona = χa Mole Fraction a = χ a =
na + nb +

Molality (m) = # of moles of solute per kilogram of solvent; NOT temperature dependent.
Represents a ratio of solute:solvent molecules at all times.

moles of solute
m =
kilograms of solvent

Properties of Solutions 2

Exercise 1 Various Methods for Describing Solution Composition

A solution is prepared by mixing 1.00g ethanol (C2H5OH) with 100.0g water to give a final volume
of 101 mL. Calculate the molarity, mass percent, mole fraction, and molality of ethanol in this
solution.

molarity = 0.215 M
mass percent = 0.990% C2H5OH
mole fraction = 0.00389
molality = 0.217 m

Exercise 2 Calculating Various Methods of Solution Composition
from the Molarity

The electrolyte in automobile lead storage batteries is a 3.75 M sulfuric acid solution that has a
density of 1.230 g/mL. Calculate the mass percent, molality, and normality of the sulfuric acid.

mass percent = 29.9% H2SO4
molality = 4.35 m
normality is 7.50 N

THE SOLUTION PROCESS

Energies involved in solution formation
When a solute is dissolved in a solvent, the attractive forces between solute and solvent
particles are great enough to overcome the attractive forces within the pure solvent and
within the pure solute. The solute becomes solvated (usually by dipole—dipole or
ion—dipole forces). When the solvent is water the solute is hydrated.

Substances with similar types of intermolecular forces dissolve in each other. “Like
dissolves like.”
• Polar solvents dissolve polar or ionic solutes.
• Nonpolar solvents dissolve nonpolar solutes.


Water dissolves many salts because the stronger ion—dipole attractions water forms with
the ions of the salt are very similar to the strong attractions between the ions themselves.
The same salts are insoluble in hexane (C6H14) because the weaker London dispersion
forces their ions could form with this nonpolar solvent are much weaker than the
attraction between the ions of the salt.
Oil does not dissolve in water. Oil is immiscible in water due to the fact that any weak
dipole-induced dipole attractions that form between oil and water cannot overcome the
stronger dipole-dipole hydrogen bonding that water molecules have for each other.

Solubilities of alcohols in water: As the hydrocarbon portion of the alcohol increases in
length, the alcohol becomes less soluble. (More of the molecule is nonpolar; the dipole
moment is diminished.)
Solubilities of alcohol in nonpolar solvents: As the hydrocarbon portion of the alcohol
increases in length, the alcohol becomes more soluble in a nonpolar solvent such as
hexane.

Enthalpy of solution (ΔHsoln) = the enthalpy change associated with the formation of a
solution (just the sum of all of the steps involved!)

3 steps: ΔHsoln = ΔH1 + ΔH2 + ΔH3

ΔHsoln can be positive (endothermic) or negative (exothermic).

Step 1 (ΔH1)
Separating the solute into individual components of the solute (expanding the solute).
This requires E be added to the system, therefore endothermic. The magnitude of the
value is high in ionic and polar solutes, low in nonpolar solutes.
ΔHsolute = −ΔHlattice energy

Step 2(ΔH2)
Overcoming IMFs in solvent to make room for the solute (expanding the solvent).
Requires that E be added to the system, therefore endothermic. The magnitude of the
value is high in polar solvents, low in nonpolar solvents.


Step 3 (ΔH3)
Interaction of solute and solvent to form the solution. Energy must be released here, else
the solution would never form since nature always tends toward a lower energy state,
therefore exothermic. The magnitude of this value is high in polar solute—polar solvent
interactions, low in other types of interactions.

ΔH2 + ΔH3 = enthalpy of hydration (ΔHhyd)

Enthalpy of hydration is more negative for small ions and highly charged ions.

• Some heats of solution are positive (endothermic). The reason that the solute
dissolves is that the solution process greatly increases the entropy (disorder) which
overrides the cost of the small positive heat of solution. This makes the process
spontaneous. The solution process involves two factors; the change in heat and the
change in entropy, and the relative magnitude of these two factors determine whether
a solute dissolves in a solvent.

• Hot and cold packs:
These often consist of a heavy outer pouch containing water and a thin inner pouch
containing a salt. A squeeze on the outer pouch breaks the inner pouch and the salt
dissolves. Some hot packs use anhydrous CaCl2 (ΔHsoln = −82.8 kJ/mol) whereas
many cold packs use NH4NO3 (ΔHsoln = +25.7 kJ/mol). We discussed other hot packs
earlier that function on the principle of a supersaturated solution crystallizing,
releasing the heat of crystallization. Other hot packs contain iron filings and the
process of rusting is sped up thus, producing heat energy.

Exercise 3 Differentiating Solvent Properties

Decide whether liquid hexane (C6H14) or liquid methanol (CH3OH) is the more appropriate solvent
for the substances grease (C20H42) and potassium iodide (KI).

hexane → grease
methanol → KI


FACTORS AFFECTING SOLUBILITY

Molecular Structure:

Fat soluble vitamins, (A,D,E,K) –nonpolar (can be stored in fatty body tissues)
Water soluble vitamins, (B&C) –polar (are not stored, wash away and must be consumed
regularly)
Hydrophobic— water fearing (nonpolar)
Hydrophilic – water loving (polar)

The Effect of Increasing Pressure

The solubility of a gas increases with
increasing pressure. Increasing
pressure has very little effect on the
solubility of liquids and solids.
(carbonated beverages must be
bottled at high pressures to ensure a
high concentration of carbon dioxide
in the liquid)

Henry’s Law— the amount of a gas dissolved in a solution is directly proportional to the
pressure of the gas above the solution. Henry’s Law is obeyed best for dilute solutions of
gases that don’t dissociate or react with the solvent.

Henry’s Law: C = kP

P = partial pressure of the gaseous solute above the solution
k = constant (depends on the solution)
C = concentration of dissolved gas


Exercise 4 Calculations Using Henry’s Law

A certain soft drink is bottled so that a bottle at 25°C contains CO2 gas at a pressure of 5.0 atm over the liquid.
Assuming that the partial pressure of CO2 in the atmosphere is 4.0 × 10−4 atm, calculate the equilibrium
concentrations of CO2 in the soda both before and after the bottle is opened. The Henry’s law constant for
CO2 in aqueous solution is 0.031 mol/L • atm at 25°C.

before = 0.16 mol/L
after = 1.2 × 10—5 mol/L

The Effect of Increasing Temperature

The amount of solute that will dissolve usually increases with increasing temperature
since most solution formation is endothermic. Solubility generally increases with
temperature if the solution process is endothermic (ΔHsoln > 0). Solubility generally
decreases with temperature if the solution process is exothermic (ΔHsoln < 0). Potassium
hydroxide, sodium hydroxide and sodium sulfate are three compounds that become less
soluble as the temperature rises. This can be explained by LeChatelier’s Principle.

Remember, the dissolving of a solid occurs
more rapidly with an increase in temperature,
but the amount of solid may increase or
decrease with an increase in temperature. It
is very difficult to predict what this solubility
may be—experimental evidence is the only
sure way.

The solubility of a gas in water always
decreases with increasing temperature.

There are all types of environmental issues
involved with the solubility of a gas at higher
temperatures. Thermal pollution – water
being returned to its natural source at a higher
ambient temperature has killed much wildlife
as less oxygen is dissolved in the water.
Boiler scale is another problem. This is
where a coating builds up on the walls of
containers such as industrial boilers and pipes
causing inefficient heat transfer and blockage.


COLLIGATIVE PROPERTIES

Colligative Properties— properties that depend on the number of dissolved particles; not on the
identity of the particle. Intermolecular forces of the solvent are interrupted when the solute is added.
This changes the properties of the solvent. These properties include: vapor pressure lowering,
boiling-point elevation, freezing-point depression, and osmotic pressure.

Vapor Pressure Lowering— The presence of a
nonvolatile solute lowers the vapor pressure of a
solvent. This is because the dissolved nonvolatile
solute decreases the number of solvent molecules
per unit volume. (Nonvolatile solute dilutes the
solution and interferes with the IMFs of the solvent).
There are fewer solvent molecules on the surface to
escape. This can be mathematically expressed by

Raoult’s Law: Psolution = (χsolvent) (Posolvent)
Psolution = observed vapor pressure of the solvent in the solution
χsolvent = mole fraction of solvent
Posolvent = vapor pressure of the pure solvent
i = van’t Hoff factor (moles of electrolyte must be multiplied by this)
number of moles particles in solution/number of moles particles dissolved

The vapor pressure of a solution is directly proportional to the mole fraction of solvent
present. If the solute ionizes the number of ions further affects (lowers) the vapor
pressure. The moles of solute must be multiplied by the number of ions the given solute
breaks into. For instance, if we had 1 mole of NaCl as the solute, we would use 2 moles
of particles for our mole fraction calculations, AlCl3 would yield a van’t Hoff factor
of 4 and so on.
For nonelectrolytes, i = 1. For electrolytes, i = the number of particles formed when one
formula unit of the solute dissolves in the solvent.
The experimental value of i is often less than the expected value of i because of a
phenomenon called “ion pairing”. Especially in concentrated solutions, oppositely
charged ions can pair up and thus, we have fewer particles than expected. Conversely,
nonelectrolytes may also pair up forming dimers (2 units bound together).

An ideal solution is a solution that obeys Raoult’s Law. There is no such thing. In very
dilute solutions, Raoult’s Law works fairly well. Solutions are most ideal when the
solute and the solvent are very similar. If hydrogen bonding occurs between solute and
solvent, vapor pressure is less than expected. We call this a negative deviation from
Raoult’s law. This can often be predicted when the enthalpy of solution formation is
large and negative (highly exothermic)
• A great example of this negative deviation is acetone and
water.

EXAMPLE: Calculate the vapor pressure caused by the addition of 100.g of sucrose,
C12H22O11, to 1000.g of water if the vapor pressure of the pure water at 25oC is 23.8 torr.

1 mol sucrose
100 g sucrose × = 0.292 mol
342.0 g sucrose

1 mole water
1000 g water × = 55.6 mol water
18.0 g water

55.6
χ water = = 0.995
0.292 + 55.6

Psoln = 0.995 × 23.8 = 23.7 torr

Exercise 5 Calculating the Vapor Pressure of a Solution

Calculate the expected vapor pressure at 25°C for a solution prepared by dissolving 158.0 g of
common table sugar (sucrose, molar mass = 342.3 g/mol) in 643.5 cm3 of water. At 25°C, the
density of water is 0.9971 g/cm3 and the vapor pressure is 23.76 torr.

= 23.46 torr


Exercise 6 Calculating the Vapor Pressure of a Solution Containing Ionic Solute

Predict the vapor pressure of a solution prepared by mixing 35.0 g solid Na2SO4
(molar mass = 142 g/mol) with 175 g water at 25°C. The vapor pressure of pure water at 25°C is
23.76 torr.

= 22.1 torr
We can determine the molecular mass of a solute by using the vapor pressure of a
solution if the mass of the solute is known.
P
χ solvent = oso ln
Psolvent
nsolvent
χ solvent =
nsolvent + nx
g
solve for nx and remember, = MM
mol

Solutions in which both solute and solvent are liquid and the liquids are volatile do not
behave ideally. Both solute and solvent contribute to the vapor pressure. If the solute is
more volatile than the solvent, the vapor pressure of the solution is higher than the vapor
pressure of the solvent. In this case, the molecules have a higher tendency to escape than
expected. We call this a positive deviation from Raoult’s law. The enthalpy of solution
for this type of deviation is positive. (endothermic)


Ptotal = PA + PB = χ A PA + χ B PB0 (same as Dalton’s Law)
0

Exercise 7 Calculating the VP of a Solution Containing Two Liquids

A solution is prepared by mixing 5.81 g acetone (C3H6O, molar mass = 58.1 g/mol) and 11.9 g
chloroform (HCCl3, molar mass = 119.4 g/mol). At 35°C, this solution has a total vapor pressure of
260. torr. Is this an ideal solution? The vapor pressures of pure acetone and pure chloroform at
35°C are 345 and 293 torr, respectively.

Not an ideal solution

Boiling-point Elevation— Because vapor pressure is lowered by the addition of a
nonvolatile solute, more E must be added to the system to achieve a vapor pressure equal to
the atmospheric pressure (definition of normal BP), so the boiling point is increased.

Boiling Point Elevation: ΔTb = Kb × m × i

Kb = molal boiling-point elevation constant (for water = 0.51°C kg/mol)
i = van’t Hoff factor
m = concentration in molality
ΔT = change in temperature

Freezing-point Depression— Because vapor pressure is lowered by the addition of a
nonvolatile solute, less E must be added to the system to achieve a temperature at which the
vapor pressure of the solid and the liquid are equal (definition of FP or MP). If the vapor
pressure of the liquid is lowered, the freezing point decreases. This is why NaCl and CaCl2
are used on icy roads and sidewalks to keep them from freezing in really cold weather.


WHY IS A SOLUTION’S FREEZING POINT DEPRESSED? Molecules cluster in order to freeze.
They must be attracted to one another and have a spot in which to cluster. Solute molecules
get in the way! The more ions in solution, the greater the effect on the freezing point and the
boiling point. A solution does not have a sharply defined freezing point, a solvent does.
Useful for separation purposes in fractional crystallization.

Freezing Point Depression: ΔT = Kf × m × i

Kf = molal freezing-point depression constant (for water = 1.86 °C kg/mol)
add 6 qts. of antifreeze to 12 qts. cooling system in order to lower the FP to −34°F and
raise the BP to +226° F

Determining the molar mass (MM) of a solute using freezing-point depression or
boiling-point elevation
solute concentration must be low (0.10m)
disadvantage—compound must be nonvolatile and stable at the boiling point.
still used widely
remember that the units you seek are grams/mole!

EXAMPLE: Calculate the freezing point and boiling point of a solution of 100. g ethylene
glycol (C2H6O2) in 900. g of water.


Exercise 8 Calculating the Molar Mass by Boiling-Point Elevation

A solution was prepared by dissolving 18.00 g glucose in 150.0 g water. The resulting solution was
found to have a boiling point of 100.34°C. Calculate the molar mass of glucose. Glucose is a
molecular solid that is present as individual molecules in solution.

= 180 g/mol

Exercise 9 Freezing-point Depression

What mass of ethylene glycol (C2H6O2, molar mass = 62.1 g/mol), the main component of
antifreeze, must be added to 10.0 L water to produce a solution for use in a car’s radiator that freezes
at −10.0°F (−23.3°C)? Assume the density of water is exactly 1.00 g/mL.

= 7.76 × 103 g (or 7.76 kg)


Exercise 10 Determining Molar Mass by Freezing-Point Depression

A chemist is trying to identify a human hormone, which controls metabolism, by determining its
molar mass. A sample weighing 0.546 g was dissolved in 15.0 g benzene, and the freezing-point
depression was determined to be 0.240°C. Calculate the molar mass of the hormone.

= 776 g/mol

Osmotic Pressure: a special use of PV=nRT

Semipermeable or selectively permeable membrane –
membrane which allows solvent but not solute molecules to
pass through (small molecules can pass but large ones cannot)

Osmosis—a special case of diffusion; water travels along a
concentration gradient.
• Osmosis occurs when water molecules move through a
semipermeable membrane from a region of lower solute
concentration to a region of higher solute concentration.
Is driven by the need nature has to establish an equilibrium.

Osmotic pressure—(π) – the pressure that must be
applied to a solution to prevent the net movement
of water from solvent to solution (osmosis).
The osmotic pressure of a solution is proportional
to the number of solute particles in a given volume
of solution, that is, to the molarity. The equation is
similar to the ideal gas law since both relate the
pressure of a system to its concentration and
temperature.

⎛n⎞
Osmotic Pressure: π = MRTi or π = ⎜ ⎟ RTi
⎝V ⎠
π = osmotic pressure in atm
M = molarity of the solution
R = 0.08206 L• atm/mol•K
T= temperature in Kelvin
i = van’t Hoff factor


The use of osmotic pressure calculations for determining the molecular mass of an
unknown substance is more accurate than the use of freezing-point depression or
boiling point elevation data because a small concentration of solute produces a relatively
large osmotic pressure.
Ideal for measuring molar masses of large molecules of biological importance.

EXAMPLE: The concentration of hemoglobin in blood is roughly 15.0g/100.mL of solution.
Assume that a solution contains 15.0g of hemoglobin dissolved in water to make 100.mL of solution
and that the osmotic pressure of this solution is found to be 0.0500 atm at 25oC. What is the
molecular mass of hemoglobin? (The osmotic pressure of a 1 m solution at 25oC is 24.45 atm)

⎛ 15 ⎞
⎜ ⎟ (0.08206)(298) g
π=
nRT
or MM =
dRT
; so, MM = ⎝ 0.1 ⎠ = 73, 400
V π 0.050 mol

Exercise 11 Determining Molar Mass from Osmotic Pressure

To determine the molar mass of a certain protein, 1.00 × 10−3 g of it was dissolved in enough water
to make 1.00 mL of solution. The osmotic pressure of this solution was found to be 1.12 torr at
25.0°C. Calculate the molar mass of the protein.

= 1.66 × 104 g/mol

Exercise 12 Isotonic Solutions

What concentration of sodium chloride in water is needed to produce an aqueous solution isotonic
with blood (π = 7.70 atm at 25°C)?

= 0.158 M


Exercise 13 Osmotic Pressure

The observed osmotic pressure for a 0.10 M solution of Fe(NH4)2(SO4)2 at 25°C is 10.8 atm.
Compare the expected and experimental values for i.

expected = 5
experimental = 4.4

Applications of Osmosis:
Dialysis— a phenomenon in which a semipermeable
membrane allows transfer of both solvent molecules and
small solute molecules and ions.

occurs in walls of most plant and animal cells
kidney dialysis is one of most important applications –
waste molecules move into the “wash” solution and filter
the blood.

• isotonic solution –solutions that have the same osmotic pressure (Ex. IV fluids)
• hypertonic— solution has higher osmotic pressure (cells bathed in a hypertonic
solution would shrivel–crenation) Treating the surface of food with salt causes this
to happen to bacteria, thus protecting or preserving the food.
• hypotonic – solution has lower osmotic pressure (cells bathed in a hypotonic solution
would burst—hemolysis)

• reverse osmosis— the process occurring when the high
external pressure on a solution causes a net flow of solvent
through a semipermeable membrane from the solution to the
solvent

• used in desalination (the membrane here acts as a “molecular
filter” to remove solute particles) The need for this process will
probably increase as the need for drinkable water increases.


Colloids— (also called colloidal dispersions)
Thomas Graham, 1860—albumin, starch, gelatin and glue diffuse only very slowly and
could not be crystallized. He called these substances colloids.
a suspension of tiny particles in some medium
The dispersed colloidal particles are larger than a simple molecule but small enough to
remain distributed and not settle out.
A colloidal particle has a diameter between 1 and 1000 nm and may contain many atoms,
ions, or molecules.
Because of their small particle size, colloids have an enormous total surface area.
The particles stay suspended because of electrostatic repulsion.
hydrophobic/hydrophilic ends
Coagulation, destruction of a colloid, occurs by heating
(particles collide so hard that they stick together) or by the
addition of an electrolyte (neutralizes ion layers). This process
is important in removal of soot from smoke so that air quality
has improved somewhat in industrialized cities.
Tyndall effect— the scattering of light by particles
• Used to distinguish between a suspension and a true
solution. A true solution has particles that are too small to
scatter light.
Brownian motion— a characteristic movement in which the
particles change speed and direction erratically (solvent molecules collide with the
colloidal particles).
• Suspensions are temporary solutions. They will settle eventually—colloids will not
do this.
• Solutions are permanent. Particles are really small. Colloids lie in between solutions
and suspensions!

Examples of Some Common Colloids:
• Foam— colloidal dispersion of a gas dispersed in a liquid or solid (ex. Whipped
cream and marshmallows)
• Aerosol— colloidal dispersion of a liquid or solid dispersed in a gas (ex. Fog and
smoke)
• Emulsion— colloidal dispersion of a liquid dispersed in a solid or liquid (ex. Butter
and milk)
• Sol— colloidal dispersion of a solid dispersed in a liquid or solid (ex. Paint or ruby)


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