1. 13.4 Expressing Concentrations of Solutions
1. Mass Percentage
mass of A in soln
total mass of solution
Mass % of X =
 100

2. 2. Parts per Million andParts per Billion
Parts per Million (ppm)
mass of A in solution
total mass of solution
ppm =
 106
Parts per Billion (ppb)
mass of A in solution
total mass of solution
ppb =
 109

3. total moles in solution
3. Mole Fraction (X)
moles of A
total moles in solution
XA =
In some applications, one needs the mole fraction of solvent, not solute—make sure you find the quantity you need!

4. 4. Molarity (M)
mol of solute
L of solution
M =
You will recall this concentration measure from Chapter 4.
Because volume is temperature dependent, molarity can change with temperature.

5. 5. Molality (m)
mol of solute
kg of solvent
m =
Because both moles and mass do not change with temperature, molality (unlike molarity) is not temperature dependent.

6. Conversion of Concentration Units
If we know the density of the solution, we can calculate the molality from the molarity, and vice versa.
See sample exercises and 13.7

7. 13.5 Colligative Properties
Colligative properties of solutions are properties that depend upon the concentration of solute molecules or ions, but not upon the identity of the solute.
Colligative properties include:
Vapor pressure lowering
Boiling point elevation
Freezing point depression
Osmotic pressure

8. 1. Vapor Pressure Lowering
Because of solute-solvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase.
Therefore, the vapor pressure of a solution containing a nonvolatile solute is always lower than that of the pure solvent.
The extent to which a nonvolatile solute lowers the vapor pressure is proportional to its concentration.

9. Raoult’s Law expresses the relationship between vapor pressure and solute concentration:
Where:
PA is the partial pressure by solvent vapor above a solution
XA is the mole fraction of compound A
P A is the normal vapor pressure of A at that temperature
Vapor pressure over a solution is reduced as the mole fraction of a nonvolatile solute increases.
Ideal solutions obey Raoult’s Law, but real solutions approximate ideal behavior when solute concentration is low and when solute and solvent particles have similar sizes and intermolecular attractions.

10. 2. Boiling Point Elevation
The addition of a nonvolatile solute to a pure solvent lowers the vapor pressure of the solution, thereby increasing the temperature at which its vapor pressure will equal atmospheric pressure.
Thus, the boiling point of a solution is greater than that of the pure liquid.

11. The change in boiling point is proportional to the molality of the solution:
Tb = Kb  m
where Kb is the molal boiling point elevation constant, a property of the solvent.
Tb is added to the normal boiling point of the solvent.

12. 3. Freezing Point Depression
The change in freezing point can be found similarly:
Tf = Kf  m
Here Kf is the molal freezing point depression constant of the solvent.
Tf is subtracted from the normal freezing point of the solvent.

13. Note that in both equations, for boiling point elevation and freezing point depression, T does not depend on what the solute is, but only on how many particles are dissolved.
Tb = Kb  m
Tf = Kf  m

14. 4. Osmosis
Some substances form semipermeable membranes, allowing some smaller particles to pass through, but blocking other larger particles.
In biological systems, most semipermeable membranes allow water to pass through, but solutes are not free to do so.

15. In osmosis, there is net movement of solvent from the area of higher solvent concentration (lower solute concentration) to the are of lower solvent concentration (higher solute concentration).

16. The pressure required to stop osmosis, known as osmotic pressure, , isV
 = ( )RT = MRT
where M is the molarity of the solution.
If the osmotic pressure is the same on both sides of a membrane (i.e., the concentrations are the same), the solutions are isotonic.

17. Osmosis in Blood Cells
If the solute concentration outside the cell is greater than that inside the cell, the solution is hypertonic.
Water will flow out of the cell, and crenation results.

18. If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic.
Water will flow into the cell, and hemolysis results.

19. Molar Mass from Colligative Properties
Any of the four colligative properties can be used to determine the molar mass of the solute.
See sample exercises and

20. Colligative Properties of Electrolytes
Since colligative properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes.
The difference is due to the electrostatic attractions between ions in a solution with electrolytes.

21. For example, a 1 M solution of NaCl does not show twice the change in freezing point that a 1 M solution of methanol does. Why?
One mole of NaCl in water does not really give rise to two moles of ions.
Some Na+ and Cl− ions reassociate for a short time, so the true concentration of particles is somewhat less than two times the concentration of NaCl.

22. The van’t Hoff factor
The extent to which electrolytes dissociate is called the van’t Hoff factor, i
i = ΔTf (measured) / ΔTf(calculated for nonelectrolyte)
The previous equations are modified by multiplying by the van’t Hoff factor.
Tf = Kf  m  i
Reassociation is more likely at higher concentrations.
Therefore, the number of particles present is concentration dependent.

23. 13.6 Colloids
Colloids are composed of suspensions of particles larger than individual ions or molecules, but too small to be settled out by gravity.
They represent the dividing line between homogeneous and heterogeneous mixtures.

24. Tyndall Effect Colloidal suspensions can scatter rays of light.
This phenomenon is known as the Tyndall effect.

25. Colloids in Biological Systems
Some molecules have a polar, hydrophilic (water-loving) end and a nonpolar, hydrophobic (water-hating) end.

26. Sodium stearate is one example of such a molecule.
These molecules can aid in the emulsification of fats and oils in aqueous solutions.
Emulsification of fats and oils allows them to be mixed with water to permit digestion and absorption of fat-soluble vitamins through the intestinal wall.

27. Removal of colloidal particles
Colloidal particles cannot be removed from their dispersing medium by filtering, as, being so small, they will pass through the filter.
They must be enlarged through coagulation and then can be filtered out or simply allowed to settle out of the dispersing medium.
Heating a colloid causes more motion of particles which increases collisions and the formation of larger particles.
The addition of electrolytes neutralizes surface charges allowing the particles to come together.

28. Semipermeable membranes can also be used to separate suspended colloidal particles.
In blood dialysis suspended waste particles are removed by a washing solution (dialysate) which is isotonic in ions (e.g., Ca2+, K+) that must be retained by the blood.