If you wish to make 1 liter of solution that is 6 M into 3 M solution, how much
water must be added?
Solving this expression:x L = 2 L. This is the total volume of the solution after dilution and
means that 1 liter of water had to be added to the original volume of 1
liter to get a total of 2 liters for the dilute solution volume.An important use of the molarity concept is in the solution of titration
problems, which are covered in Chapter 11, along with pH expressions of
concentration for acids.
COLLIGATIVE PROPERTIES OF SOLUTIONS
Colligative properties are properties that depend primarily on the concentration
of particles and not the type of particle. There is usually a direct relationship
between the concentration of particles and the effect recorded.
The vapor pressure of an aqueous solution is always lowered by the addition
of more solute. From the molecular standpoint, it is easy to see that there are
fewer molecules of water per unit volume in the liquid, and therefore fewer
molecules of water in the vapor phase are required to maintain equilibrium. The
concentration in the vapor drops and so does the pressure that molecules exert.
This is shown graphically below.
Notice that the effects of this change in vapor pressure are registered in the
freezing point and the boiling point. The freezing point is lowered, and the boiling
point is raised, in direct proportion to the number of particles of solute present.
For water solutions, the concentration expression that expresses this relationship
is molality (m), that is, the number of moles of solute per kilogram of solvent. For
molecules that do not dissociate, it has been found that a 1 m solution freezes at
−1.86°C (271.14 K) and boils at 100.51°C (373.51 K). A 2 m solution would
then freeze at twice this lowering, or −3.72°C (269.28 K), and boil at twice the 1
molal increase of 0.51°C, or 101.02°C (374.02 K).
Vapor Pressure Versus Temperature for Water and a Solution