To help you with DMSO, lets first do a quick review of the vapor pressure of water.
The vapor pressure of water at 100 Celsius (212 F) is 760 mm Hg. This means, that at 760 mm Hg (or 1 atmosphere of pressure), water will boil (its vapor pressure has been reached.). All of the liquid water will become gaseous water. If the pressure remains at 760 mm Hg, but the temperature is 90 C, then there will be some liquid water converting into a gas (a small amount of 'steam' can be seen on top of the hot water, but it is not at a full boil). If you lower the pressure in a vessel (vacuum) to 92.5 mm Hg, then water will boil at 50 C.
More details of Vapor-Liquid equilibrium can be reviewed by clicking the following link: http://en.wikipedia.org/wiki/Vapor-liquid_equilibrium
Take a look at the diagram in the wiki link from above (Boiling point diagram of two components with mole fractions on the top and bottom).
In your example of 168.4 C at 550 mm Hg (less than atmospheric pressure, so a vacuum has been applied), the concentration of water decreases as the temperature is increased. The liquid concentration of the water fraction is 6.5% (or you correctly stated 0.65 moles in a 10 mole sample). The concentration of water liquid and vapor is 34.6%.
I hope this helps, and feel free to ask further questions.