Chapter 13
Physical Properties of Solution
Dr. Nabil EL-Halabi
Types of Solutions:
We can distinguish six types of solutions, depending on the original states (solid, liquid or gas) of
the solution component (Table 13.1).
A saturated solution: A solution that contains the maximum amount of a solute that will dissolve in
a given solvent, at a specific temperature.
An unsaturated solution: A solution that contains less solute than the solvent has the capacity to
dissolve.
A supersaturated solution: A solution that contains more solute than is present in a saturated
solution.
Supersaturated solutions are not very stable. In time, some of the solute will come out of a
supersaturated solutions as crystals.
Crystallization: The process in which dissolved solute comes out of solution and forms crystals.
A Molecular View of the Solution Process:
When the solute dissolves in the solvent, particles of the solute disperse throughout the solvent. The
ease with which a solute particle replaces a solvent molecule depends on the strength of:
1- solvent - solvent interaction.
2- solute - solute interaction.
3- solvent - solute interaction.
For simplicity, the solution process taking place in three steps (Figure 13.2).
Step 1: is the separation of solvent molecules. H1 (energy needed to break the attractive forces).
Step 2: is the separation of solute molecules. H2 (energy needed to break the attractive forces).
Step 3: is the mixing of the solvent and solute molecules. H3 (may be exothermic or endothermic).
The heat of solution Hsoln is given by:
Hsoln = H1 + H2 + H3
If the solvent - solute attraction is stronger than solvent – solvent attraction and solute - solute
attraction, the solution process is favorable; that is, it is exothermic (Hsoln < 0).
If the solvent - solute attraction is weaker than solvent – solvent attraction and solute - solute
attraction, the solution process is endothermic (Hsoln > 0).
The solution process is governed by two factors:
1- Energy, which determines whether a solution process is exothermic or endothermic.
2- An inherent tendency toward disorder in all natural events.
The solution process is accompanied by an increase in disorder or randomness. It is the increase in
disorder of the system that favors the solubility of any substance, even if the solution process is
endothermic.
Solubility: is a measure of the amount of a solute that will dissolve in a solvent at a specific
temperature.
“like dissolves like”
Two substances with similar intermolecular forces are likely to be soluble in each other.
1- Non-polar molecules are soluble in non-polar solvents, CCl4 in C6H6.
2- Polar molecules are soluble in polar solvents, C2H5OH in H2O.
3- Ionic compounds are more soluble in polar solvents, NaCl in H2O or NH3(l).
When two liquids are completely soluble in each other in all proportions, they said to be miscible.
(as C2H5OH in H2O) because of their ability to form H bonds.
Solvation: is the process in which an ion or a molecule is surrounded by solvent molecules
arranged in a specific manner. When the solvent is water the process is called hydration.
Usually, the intermolecular interaction between ions and nonpolar compounds is ion - induced
dipole interaction, which is much weaker than ion - dipole interaction. Consequently, ionic
compounds usually have extremely low solubility in nonpolar solvents.
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Concentration Units:
The concentration of a solution: is the amount of solute present in a given amount of solution.
Percent by mass (percent by weight or weight percent).
% by mass = mass of solute / (mass of solute + mass of solvent) * 100%
= mass of solute / mass of soln * 100%
Molarity (M)
Molarity = moles of solute / liters of soln
(mol/L)
Molality (m): is the number of moles of solute dissolved in kg (1000 g) of solvent.
Molality = moles of solute / mass of solvent (kg)
The advantage of molarity is that it is easier to measure the volume of a solution, using precisely
calibrated volumetric flasks, than to weigh the solvent. For this reason, molarity is often preferred
over molality.
Molality is independent of temperature, and the same is percent by mass.
Effect of Temperature on Solubility
Solid Solubility and Temperature:
In most cases, the solubility of a solid substance increases with temperature.
The solution process of CaCl2 is exothermic and that of NH4NO3 is endothermic, but the solubility
of both compounds increases with increasing temperature. In general, the effect of temperature on
solubility is best determined experimentally.
Gas Solubility and Temperature:
The solubility of gases in water usually decreases with increasing temperature.
As the temperature rises, the dissolved air molecules begin to “boil up” of the solution before the
water itself boils.
The reduced solubility of molecular oxygen is hot water has a direct bearing on thermal pollution,
that is, the heating of the environment – usually waterways – to temperatures that are harmful to its
living inhabitants.
Effect of Pressure on the Solubility of Gases
Henry,s law: The solubility of a gas in a liquid is proportional to the pressure of the gas over the
solution
CαP
C = kP
C is the molar concentration (moles per liter) of the dissolved gas.
P is the pressure (in atm) of the gas over the solution.
k is a constant (mol/L atm) that depends only on temperature.
When the partial pressure of the gas over the solution increases, the concentration of the dissolved
gas also increases according to the equation.
Suppose we have a gas in dynamic equilibrium with a solution, the number of gas molecules
entering the solution is equal to the number of dissolved molecules moving into the gas phase.
When the partial pressure is increased, more molecules dissolve in the liquid because more
molecules are striking the surface of the liquid.
A practical demonstration of Henry,s law is the effervescence of a soft drink when the cap of the
bottle is removed. (The amount of CO2 dissolved in the soft drink is many times the amount that
would dissolve under normal atmospheric conditions. When the cap is removed, the excess CO2
comes out of solution, causing the effervescence).
Most gases obey Henry,s law, but there are some exceptions, that if the dissolved gas reacts with
water, higher solubilities can result.
NH3 + H2O  NH4+ + OH2
Colligative Properties: Properties of solutions that depend on the number of solute particles (atoms,
molecules, ions) and not on the nature of the solute.
The Colligative Properties are:
1- Vapor pressure lowering.
2- Boiling point elevation.
3- Freezing point depression.
4- Osmotic pressure.
1- Vapor pressure lowering:
The vapor pressure of a solution is affected by the presence of a solute.
If a solute is nonvolatile (that is, it does not have a measurable vapor pressure), the vapor pressure
of its solution is less than that of pure solvent.
Raoult,s Law: The partial pressure of a solvent over a solution,
P1 is given by the vapor pressure of the pure solvent, P1o, times
the mole fraction of the solvent in the solution, X1:
P1 = X1P1o
If the solution contains only one solute:
X1 = 1 – X2 , in which X2 is the mole fraction of the solute.
P1 = (1 – X2 )P1o
o
P1 - P1 = P = X2P1o
The decrease in vapor pressure, P, is directly proportional to
the mole fraction of the solute present.Vaporization increase
the disorder of a system, Because a solution is more disorder
than a pure solvent, thus solvent molecules have a less tendency to leave a solution than to leave the
pure solvent to become vapor, and the vapor pressure of a solution is less than that of the solvent.
If both components of a solution are volatile (that is, it does not have a measurable vapor pressure),
The total pressure is given by Dalton,s Law:
PA = XA PAo
PT = PA + PB
PB = XB PBo
PT = XA PAo + XB PBo
PA and PB are the partial pressures over the solution for components A and B; PAo and PBo are the
vapor pressures of the pure substances; and XA and XB are their mole fractions.
Ideal solution: any solution that obeys Raoult,s Law. One characteristic of an ideal solution is that
Hsoln, is always zero.
2- Boiling point elevation:
Because the presence a nonvolatile solute lowers the vapor pressure of a solution, it must also affect
the boiling point of the solution. Because at any temperature the vapor pressure of the solution is
lower than that of the pure solvent, the liquid – vapor curve for the solution lies below that for the
pure solvent (figure 13.7).
The boiling point elevation, Tb = Tb - Tbo
Tb = boiling point of the solution.
Tbo= boiling point of the pure solvent.
Because Tb is proportional to the vapor pressure lowering, it is also proportional to the
concentration (molality) of the solution. That is,
Tb = Kbm
m is molality, and Kb is the molal boiling - point elevation constant.
Note: we can not express the concentration units in molarity because it changes with temperature.
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3- Freezing point depression:
Since the new triple point lies to the left of that for the pure solvent (figure 13.7), the freezing point
of the solution is lower than freezing point of the solvent.
The freezing point depression, Tf = Tfo – Tf Tf = freezing point of the solution.
Tbo= freezing point of the pure solvent.
Tf = Kfm
m is molality, and Kf is the molal freezing - point depression constant.
Because a solution has greater disorder than the solvent, more energy needs to be removed from it
to create order than in the case of a pure solvent. Therefore, the solution has a lower freezing point
than the solvent. Note that when a solution freezes, the solid that separates is the solvent
component.
4- Osmotic pressure:
Osmoses: The net movement of solvent molecules through a semipermeable membrane from a pure
solvent or from a dilute solution to a more concentrated solution.
A semipermeable membrane: allows solvent molecules to pass through but blocks the passage of
solute molecules.
The Osmotic pressure (: the pressure required to stop osmosis.
MRT
M = molarity, R = the gas constant (0.0821L.atm/K.mol), T = absolute temperature.
Because the vapor pressure of pure water is higher than that of a solution, there is a net transfer of
water molecules from the left beaker to the right one. (figure. 13.9)
We know that all colligative properties depend only on the number of particles in solution.
If two solutions are of equal concentration and, hence, of the same osmotic pressure, they are said to
be isotonic.
If two solutions are of unequal osmotic pressure, the more concentrated solution is said to be
hypertonic and the more dilute solution is described as hypotonic (Figure 13.10).
Using Colligative Properties to Determine Molar Mass:
Theoritically, any of the four colligative properties are suitable for this purpose. In practice,
however, only freezing point depression and osmotic pressure are used because the show the most
pronounced changes.
A pressure such as 10.0 mmHg in example 13.10 can be measured easily and accurately. For this
reason, osmotic pressure measurements can be used to determine the molar masses of large
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molecules, such as proteins, but in using freezing point depression technique, the depression of the
temperature is too small to be measured accurately.
The freezing point depression technique is more suitable for determining the molar mass of smaller
and more soluble molecules, those having molar masses of 500g or less, because the freezing point
depression of their solutions are much greater.
Colligative Properties of Electrolytes:
For ionic solutions we must take into account the number of ions present.
i = Vant,s Hoff factor or the number of ions present
i = a ctual no. of particles in soln. After dissociation / no. of formula units initially dissolved in soln
Tf = iKfm
Tb = iKbm
 = iMRT
i should be 1 for nonelectrolytes, 2 for strong electrolyte such as NaCl and KNO3, 3 for strong
electrolyte such as Na2SO4 and MgCl2.
Ion pair: a cation and an anion held together by electrostatic forces.
The formation of an ion pair reduces the number of particles in solution by one, casing a reduction
in colligative properties (figure 13.11), The measured valeues of i in (Table 13.3) are sometimes
less than the calculated ones because of ion pair formation.
Selected Problems: 7 – 10, 13, 14, 16, 17, 18, 20, 21, 22, 25, 26, 33 – 36, 49, 50, 51, 52, 57, 62, 64,
71, 73, 75, 79, 80.
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