[HughMyron]

My book is being disappointingly useless on this question. Let's assume that we have a methanol/water mixture and a fractional distillation curve that looks sigmoidal, as it should.

At what point does the methanol stop distilling? Is it the point where the concavity of the curvature changes? The point where the line tapers off? Or something else?

[Arkcon]

Well, that's a question more of engineering than of chemistry.  Technically, as the concavity of the sigmoid plot changes, the first one is done.  But a few drops may still be carrying over in the rig.  One could say, at the midpoint of the sigma plot, all has come through, but you might not see the concavity or enough of plot to notice.  If you were watching the receiving vessel, you might see a refractive index mixing, as the first drop of water hits the collected methanol, then again, you might not.  Kinda hard to be very precise, with distillation, sometimes.

[HughMyron]

Well, that's a question more of engineering than of chemistry.  Technically, as the concavity of the sigmoid plot changes, the first one is done.  But a few drops may still be carrying over in the rig.  One could say, at the midpoint of the sigma plot, all has come through, but you might not see the concavity or enough of plot to notice.  If you were watching the receiving vessel, you might see a refractive index mixing, as the first drop of water hits the collected methanol, then again, you might not.  Kinda hard to be very precise, with distillation, sometimes.

Ok thanks. So basically, if we had a graph that looked like this:

http://www.pharmainfo.net/files/images/stories/article_images/Fractional%20distillation%201.gif

Then the point where the first substance stopped distilling (on the fractional graph) would be around 95 degrees?

[HughMyron]

Also, one more question: if we have a fractional distillation curve, can we use it to determine how much methanol was originally present in the solution? Is it just the inflection point?

[Arkcon]

I don't know.  If I wanted to know the volumes, I might simply measure the two after distillation.  I really don't understand the use of the plot  in this way for a distillation. 

[fledarmus]

If you had an ideal fractional distillation, with infinite plates for separation, you would not see that exact graph. What you would see was the temperature at the still head rising to the boiling point of the first component as the first drops begin to condense on the bulb, then dropping again as the last drops distill over. The temperature would then rise straight up to the boiling point of the second component as the first drops of that component began condensing on the bulb, and drop again when the last drop of that component had gone over.

The curves at the top and bottom of your graph indicate the impure fractions - the pure components are the straight lines on the left and right.

If by "the point where the first substance stopped distilling" you mean "the point where the material being collected is pure second component", that doesn't really start until your head temperature is very close to 120°C.