1) An ideal solution follows Raoult's law, which states that the vapor pressure of a solvent is directly proportional to its mole fraction in the solution. Real solutions behave ideally only at very low concentrations as the vapor pressure lowering depends on the sum of all solute mole fractions. 2) There are four colligative properties of solutions that depend only on the number of solute particles and not their identity: vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure. 3) The freezing point of a solution is lower than that of the pure solvent based on principles of thermodynamics. For very dilute solutions, the freezing point depression is directly proportional to the molality

1. Solutions
• The Ideal Solution and Colligative Properties .

2. Definitions of Ideal solution
Similar to ideal gas law (limiting law) at low pressure gases behaves
ideally. Solution with low concentrations behave ideal.

3. D E F I N IT I O N O F T H E I D EA L S O L U TI O N

4. Raoult's law. It states that the vapor
pressure of the solvent over a
solution is equal to the vapor
pressure of the pure solvent
multiplied by the mole fraction of the
solvent in the solution.
Raoult's law is another example of a limiting law.
Real solutions follow Raoult's law more closely as the solution becomes more dilute.
The ideal solution is defined as one that follows Raoult's law over the entire range of
concentrations. The vapor pressure of the solvent over an ideal solution of an involatile
solute is shown in Fig. 13.3. All real solutions behave ideally as the concentration of the
solutes approaches zero

5. In a solution containing several involatile solutes, the vapor pressure lowering depends
on
the sum of the mole fractions of the various solutes.
In a gas mixture, the ratio of the partial
pressure of the water vapor to the vapor
pressure of pure water at the same
temperature is called the relative
humidity. When multiplied by 100, it is
the percent relative humidity. Thus

6. A N A LYTI CA L F O R M O F T H E C H E M I CA L P O T E N T i A L I N I D EA L L I Q U I D S O L U TI O
N S
If the solution is in equilibrium with vapor, the requirement of the second law is that the chemical potential of
the solvent have the same value in the solution as in the vapor, or
Assume that the vapor is ideal gas so that

7. T H E G I B B S-D U H E M E Q U AT I O N

9. C O l U G AT I V E P R O P E RT I E S
Since the second term in Eq. (13.5) i s negative, the chemical potential o f the solvent in
solution is less than the chemical potential of the pure solvent by an amount - R T In x.
(1)
These properties are :
the vapor pressure lowering
(2) the freezing-point depression ;
(3) the boiling-point elevation
(4) the osmotic pressure.
Since these properties are all bound together through their common origin, they are called
colligative properties (colligative : from Latin : co-, together, ligare, to bind).
They do not depend on the nature of the solute present but only on the number of solute
molecules relative to the total number of molecules present.

10. the solid lines refer to the pure solvent. Since the solute is
involatile, it does not appear in the gas phase, so the curve
for the gas is the same as for the pure gas
liq
gas

11. T H E F R E E Z I N G - P O I NT D E P R ES S I O N
Consider a solution that is in equilibrium with pure solid solvent.

14. The relation between freezing point and composition of a solution can be simplified considerably if the solution
is dilute.
m = m2 + m3 + ... . The mass of solvent is nM then m2 = n2/nM; m3 = n3 /nM, .......

15. If the solution is very dilute in all solutes, then m approaches zero and T approaches To T0

19. Solubility
Suppose we consider the equilibrium between solute in solution and pure solid solute. In
this condition the solution is saturated with respect to the solute. The equilibrium
condition is that the of the solute must be the same everywhere, that is

20. Either Eq. (13.25) or Eq. (13.26) is an expression of the ideal law of solubility. According
to this law, the solubility of a substance is the same in all solvents with which it forms
an ideal solution and The solubility of a substance in an ideal solution depends on the
properties of that substance only.

21. Figure 13.5 shows the variation of the solubility, x, as a function of temperature for two
substances with the same entropy of fusion but different melting points

22. The ideal law of solubility is frequently in error if the temperature of interest is far below the melting
point of the solid

23. The law is never accurate for solutions of ionic materials
in water, since the saturated solutions of these
materials are far from being ideal and are far below
their melting points. As the table of solubilities of
naphthalene shows,
hydrogen-bonded solvents are poor solvents for a
substance that cannot form hydrogen bonds

24. E LEVATI ON OF T H E BOILING POI
NT

27. Osmotic Pressure
The level of the sugar solution in the tube is observed to rise until it reaches a definite
height, which depends on the concentration of the solution. The hydrostatic pressure
resulting from the difference in levels of the sugar solution in the tube and the surface of
the pure water is the osmotic pressure of the solution

28. Observation shows that:
1- no sugar has escaped through the membrane into the pure water in the beaker.
2-The increase in volume of the solution that caused it to rise in the tube is a result of the
passage of water through the membrane into the bag.
3-The collodion functions as a semipermeable membrane, which allows water to pass freely
through it but does not allow sugar to pass.
4-When the system reaches equilibrium, the sugar solution at any depth below the level of
the pure water is under an excess hydrostatic pressure due to the extra height of the sugar
solution in the tubing.

29. The van't Hoff Equation

30. van't Hoff equation for osmotic pressure.

31. In the experiment shown in Fig. 13.7, the membrane is attached to a movable piston.
As the solvent diffuses through the membrane, the piston is pushed to the right; this
continues until the piston is flush against the right-hand wall.
The observed effect is the same as if the solution exerted a pressure against the membrane to
push it to the right. The situation is comparable to the free expansion of a gas into vacuum.

32. If the volume of the solution doubles in this experiment, the dilution will reduce the
final osmotic pressure by half, just as the pressure of a gas is halved by doubling its
volume
it is deceptive to consider the osmotic pressure as a sort of pressure that is somehow
exerted by the solute
Osmosis, the passage of solvent through the membrane, is due to the inequality of the
chemical potential on the two sides of the membrane.
The kind of membrane and solute does not matter, but it must be permeable only to
the solvent.
. A membrane could conceivably be like a sieve that allows small molecules such as
water to pass through the pores while it blocks larger molecules. Another membrane
might dissolve the solvent and so be permeated by it, while the solute is not soluble in
the membrane. The mechanism by which a solvent passes through a membrane must
be examined for every membrane-solvent pair using the methods of chemical kinetics.
Thermodynamics cannot provide an answer, because the equilibrium result is the
same for all membranes.

33. Measurement of Osmotic Pressure
useful for determining the molar masses of materials that are only slightly soluble in the
solvent
or which have very high molar masses (for example, proteins, polymers of various types,
colloids)
This pressure corresponds to a height of a column of water of the order of 800 ft: Simply to
keep the experiment in the laboratory, the solutions must be less than 0.01 molar, and are
preferably of the order of 0.001 molar