The amount of molecular ____________in a substance determines its
phase.  This is measured as_______________.

I believe the answer is:

The amount of molecular motion in a substance determines its phase.
This is measured as temperature.

Since I can't be positive, I'm posting this as a comment. If you
believe this to be the answer, let me know and I will post it as the
answer.

Best regards,
Rainbow

Actually it should be:
The amount of molecular energy in a substance determines its phase.
This is measured as temperature.

The amount of molecular attraction in a substance determines its phase.
This is measured as viscosity.

Best Regards,
Rexy.

Dear Mom,

I believe all of the previous answers are closely related.

Molecular attraction determines if a substance is solid, liquid or
gaseous. In solids, molecules are closely attracted to one another,
which produces a dense packing of substance and thus, a solid.

To overcome that attraction you need to apply energy, which increases
molecular movement (manifested as a higher temperature). Increasing
the temperature of a solid melts it into a liquid, then makes it boil
and finally evaporate as a gas. In "chem-speak," the substance will
have changed from a solid phase to a liquid phase, and then to a
gaseous phase. The measure of how "solid" is a liquid is called
viscosity, a concept that cannot really be applied to a solid.

Thus, you have the following factors, all entailing one another:

solid, high molecular attraction, low energy, low molecule motion, low
temperature, high viscosity

Therefore, the answer you seek really has multiple answers!

If you download this short PDF file, it will explain very clearly all
of the above concepts:
http://web.chem.ucla.edu/~harding/cfqpp/noncoval.pdf

And after you read it, perhaps you'll agree with me:

1) attraction
2) boiling point

However, if this is part of a chemistry test, there's nothing like the
book you were supposed to study!

Regards,

Daniel