Re: Sugar/water solution

I will try to deal with your points one at a time

--A gram of sugar also has volume.  Let's say it has 1 cc of volume.

The density of sucrose (sugar) at 17.5 deg C is 1.5805. That means that 1 
gram of sugar occupies 1/1.5805 = 0.6327 mL (or cc)
CRC Handbook of Chemistry & Physics, 56th edition, page C-497

--If you dissolve that gram/1 cc of sugar into 100 cc of water, do you
end up with 101 cc of liquid?

You cannot reliably get the volume of a solution simply by adding the 
volumes in this way. Usually there is some shrinkage; occasionally there is 
some expansion. The density of 1% sucrose solution (1 gram sucrose in 100 
gram solution, or 1 gram of sucrose mixed with 99 gram water) is 1.0039 
relative to water at 20 deg C. This corresponds to 99.61 mL volume, as 
against 99.63 by adding the two volumes. In this case the shrinkage is 
almost negligibly small. It is somewhat larger with salts.
CRC Handbook of Chemistry & Physics, 56th edition, page D-261
If we go to a 20% sucrose solution -- 20 gram sugar, 80 gram water -- the 
sum of volumes is 92.65 mL, while the solution volume is 92.34 mL. This is 
still a very small shrinkage, but the solution is becoming much more dense.

--If so, how do you explain that 100 cc of plain water has less mass
(weight)  than 100 cc of water with sugar dissolved in it?

Apart from the shrinkage factor, which is negligible in this case, the 
sugar is considerably denser than the water anyway (which you knew, because 
sugar sinks to the bottom of your teacup before you stir it up to dissolve 
it!)

--For example, a 12 ounce can of Diet Coke weighs less than a 12 ounce
can of regular Coke.

I presume you are talking about "12 ounce" as some sort of archaic American 
measure of volume, rather than a measure of mass, which it ought to be! ;-)

--I was thinking that there was a chemical reaction of sorts when
sugar dissolved with water which would not necessarily create a tit
for tat increase in volume.  As you know, there's lots of space
between those molecules to fill.

There is no chemical reaction, but there is a change in arrangement of 
molecules which might lead to changes in volume not being "tit for tat". 
That is the origin of the shrinkage I have been talking about. You are very 
much on the right track.

--I hope this makes my thoughts more clear.

You have made your thoughts clear, and they are not too far wide of the 
mark. Another time you might help the answerer by specifying city and 
country and some hint of the grade level at which you would like to be 
answered. I would answer an academic colleague in a very different way to a 
primary school student asking the same question. And city and country can 
make a difference to what analogies and references are culturally 
meaningful.