In response to questions about words like quantity and units,
I would say that there are three distinct words/ideas needed.
For measuring sugar, I would say we have the following...
The property being measured might be mass.
The units would likely be grams, kilograms, or slugs.
The quantity requires a number and a unit, such as 500 grams.
We could also measure sugar using the property of volume.
The units would likely be teaspoons, tablespoons, cups, pints.
The quantity could be something like 2 cups.
We could also measure sugar using the property of weight.
The everyday units would most likely be pounds.
The quantity might be a 5 pounds or 10 pounds.
I do all of these.
At the grocery I buy sugar by weight.... 5-pound bag.
When I make cookies I measure volume with measuring cups.
When I make bread in a bread machine I have an electronic
balance and I measure sugar mass in grams.
Note: I use mass for bread-machine ingredients because I have
found it gives the most reproducible results. Sugar is not the problem.
Flour is the problem, the flour to liquid ratio seems to determine how
much the loaf will rise. I did not get good consistency measuring
flour by volume, so I switched to mass. Once I got an electronic
balance I just started measuring everything (for bread) by mass.
Denker makes the point that some people in some countries
might use measuring cups and say they are measuring mass.
The recipes in Amsterdam might be adjusted so the recipe
works out correctly even when measuring substances with
different densities.
But... (1) that is a different country where they speak a different
language. And... (2) If they really mean the same thing by mass as
we mean when we say mass, then I would argue with this usage
of the word from a physics viewpoint. Measuring cups are
measuring the property of volume. Measuring volume
does not amount to measuring mass unless the density is figured in.
Our chemistry students indeed sometimes measure this way.
If we want them to measure 50 grams of methanol, they might
convert this to this 63.3 ml and measure the methanol with a
graduated cylinder. Having done so, they will have a volume of
63.3 ml, and they will have a mass of 50 grams.
But, if they want equal masses of water and methanol, they
cannot measure 50 ml of water and 50 ml of methanol.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu