First, they don’t weigh things in grams, and second they
don’t use gamus (pronounced gam'-oos) because they don’t know what a logical
and handy unit it is. Allow me to explain.
Physicists quit weighing things in grams or kilograms
years ago. They mass things. Kilograms and grams are units of mass, not units
of weight. Weight is a force, and forces are measured in dynes (old physicists)
or newtons (young physicists). The balances scientists use do not weigh things.
They balance the mass of the object in question with some known masses and infer
the mass of the sample from that experiment. Weight is involved in this
process, but cancels out; therefore, the balance instruments are, to a degree,
independent of altitude and give the same result in Bogalusa, Louisiana and in
Ouray, Colorado. Because the whole process of using a balance involves
balancing two weights, chemists in orbit who want to mass things traditionally
radio in and say “Houston. We have a problem.”
For some reason difficult to understand, chemists still
say, “weigh out a sample” rather than “mass out a sample.” Chemists are using
the balance principle that cancels the weights, so they are massing their
samples. When they are through with the operation, they do not know the weight
of the object in question. Yet, they still say, “weigh,” as if they were using
spring scales (which do measure the force). Don’t try to get chemists to
change; they probably won’t [1–3]. Chemists may forever say, “weigh out a
sample,” though they know full well that they do not want the student to come
back and say, “This sample weighs 12.3 millinewtons in this geographic
location.”
Students catch on quickly. They say, “This sample weighs
1.256 grams.” They don’t say “This sample masses 1.256 grams” because their
teachers don’t. The use of weigh (determine the force) instead of determine the
mass is confusing only to the students who just had beginning physics. Some day
chemists will have to face the fact that, on balance, this is not the weigh to
go [4].
Now for the second question. Why do chemists not mass things
in gamus? I really don’t know a good answer to this one. A very likely answer
is that I haven’t told enough of them about gamus yet. Otherwise, why would
chemists not use such a logical and simple unit of mass, which totally
un-confuses the students about the distinctions between the macroscopic and the
microscopic worlds of chemistry? The answer requires that the reader be
familiar with a small mass unit called the amu (atomic mass unit), the gram (an
arbitrary mass unit), and the gamu (grand atomic mass unit). Also the reader
needs to appreciate that Avogadro’s number is simply the conversion factor
between amus and grams. There are 6.02 ´ 1023
amus per gram.
I digress here briefly to tell you a story. This happened
to me when I was a chemistry graduate student at a large university. I was
sharing an office with one of the department’s famous inorganic chemists (who
will remain anonymous) when a student of Dr. X’s came in to ask a very good
question. “Dr. X. You told us that recently they changed the standard of atomic
masses from O (natural isotopic mixture) equals exactly 16 amu to carbon 12
equals exactly 12 amu. What I want to know is, did that change Avogadro’s
number?” After brief thought Dr. X said, “No, it did not.”
Tactlessly, I (a mere graduate student) butted in and said
“Excuse me Dr. X, but since Avogadro’s number is the number of amus per gram,
and they just changed the size of the amu, but not the size of the gram, then
this redefinition of the amu did change Avogadro’s number, though very
slightly.” It says a lot for Dr. X that he was not angry at this correction,
but thought about it calmly and finally agreed that I was right and he was
wrong.
So, back to the concept of there is Avogadro’s number of
amus per gram. The gamu, short for the grand amu, I hereby define as a
trillion trillion amus. 1 ´ 1024 amus equal 1 gamu; therefore, if in
your lab, you mass out 24.31 gamus of magnesium you obviously have massed out a
trillion trillion atoms of magnesium. If you then oxidize this magnesium (close
your eyes during this process) and find that the resulting compound masses out
at 16 gamus bigger than the starting material, it isn’t such a big mental
hurdle to see that if 24.31 gamus of Mg combined with 16 gamus of O, then a
trillion trillion Mgs combined with a trillion trillion Os to give a trillion
trillion MgOs, or that there is one O for each Mg.
The same experiment done in grams would, of course, give
the same ratio of masses, but the number of atoms that reacted and the number
of MgO pairs formed would not be the large but comprehensible number
trillion trillion, but the less comprehensible number 6.02 ´ 1023
. In other words, by defining a new mass unit (the gamu) we change the
equivalent of Avogadro’s number from 6.02 ´ 1023 to 1024,
a trillion trillion.
And so, just as Avogadro’s number is 6.02 ´ 1023
things, our new number of things is 1024. Because a mole is
Avogadro’s number of things, then 1024 things cannot also be called
a mole. We shall call it a mule. If chemists mass out their reagent in mules,
it is much simpler to see that this is a macroscopic mass exactly 1024
times larger than what goes on at the atomic and molecular level.
If you are confused as to how this makes things simpler
for the students, do this: show your students a beaker containing 180 grams of
water and ask them to tell you how many atoms are in this sample. If you allow
calculators, some of the students will arrive at the correct solution. Now,
hold up a beaker containing 180 gamus of water and ask how many atoms are
there. No calculators are necessary. Obviously, this is ten mules, or 1025
molecules times 3 atoms per molecule equals 3 ´ 1025 atoms.
Now ask the class to calculate the mass of a single carbon
dioxide molecule in grams and in gamus. Again, they will need calculators for
the first job. The answer to the second question is 44 ´ 10-24 gamus,
of course.
So, how much larger is a gamu than a gram? It is 1 ´ 1024
divided by 6.02 ´
1023, which is approximately 1.66 times larger. Can we persuade
balance manufacturers to provide a gamu scale on the balances? With modern
electronic balances this would be no problem. Of course both gram and gamu
readout would be available. If a sample of chromium masses at 52 milligamus we
know immediately this is 1 ´ 1021 atoms of chromium. How convenient. Is
this a millimole of chromium? No. It is too large to be a millimole. It is a
millimule of chromium. Mules are larger than moles, as everyone knows.
I know what you are thinking. If we change the standard
from grams to gamus will it not change important constants like R and k?
Well let us see. R, the gas law constant, has units of joules per (mole
Kelvin). If we wish to change it to joules per (mule kelvin) we need only
multiply by 1.66 which gives a gas law constant of 13.8. Now the gas law
constant per molecule (Boltzman’s constant) will be 13.8 ´ 10–24,
because 1024 is the number of molecules in a mule. No need to
remember two numbers any more. The values of R and k differ only
in their power of ten. To take an example of using the new R value:
What is the pressure exerted by the gas in a container of
volume one cubic meter if the gas is 32 gamus of oxygen at 25 degrees C?
ANSWER: P = nRT/V= {1 mule ´ 13.8
joules/mule/Kelvin ´
(25 + 273) Kelvin}/1 m3 = 4110 N/m2..
OLD ANSWER: P = nRT/V = {[32
´
1.66] g}/32g mol-1} ´ 8.314 J mol-1 K-1 ´ (25
+ 273) Kelvin}/1m3 = 4110 N/m2.
In a similar fashion R = 0.082 L atm mol-1
K1) becomes 0.082 ´ 1.66 = 0.136 L atm mule-1 K-1).
The famous 22.4 L mol-1 at STP becomes 37.2 L mule-1 at
the same conditions, because this volume contains 1024 molecules,
not 6.02 ´
10 23 molecules.
This probably seems confusing. Is this really going to
help anybody understand chemistry? Yes, it will help students. It will not help
teachers who grew up on moles. If a student learns mules instead of moles they
need not learn Avogadro’s big magical number. A mule of things will become as
simple a concept as 100 things, except the number is larger. What really is
happening here is that, becuase I cannot change the mass of atoms, and because
the number relating these small masses to visible large masses depends upon the
arbitrary unit of mass that was adopted before Avogadro (the gram), then I
propose changing the arbitrary unit of mass. Grams are not sacred, though admittedly
quite ingrained in the culture. Gamus, symbolized gm, could catch on, and
chemistry students the world over would be grateful. When that happens, the
world we see can be said to be a trillion trillion times as large as the world
we symbolize on our blackboards.
Which reminds me: If blackboards can
disappear, replaced by something more convenient, then so can grams. Goodbye
grams. Hello gamus.
References and Notes
1.
Plumsky, R. J. Chem.
Educ. 1996, 73, 451–454.
2.
Smith, M. W.; Russell, C. E. J. Chem. Educ. 1997, 74, 900.
3.
What do the Books Say? Actually, authors of general chemistry
texts are trying to change. They now use the term molecular mass instead of
molecular weight. They say, “The mass of a sample of…is….” They almost always
have a brief paragraph stating that weight and mass is not the same thing. Most
chemists, however, still tell students to “Weigh the beaker, then the beaker
with sample, and subtract the weights.” There are even cases of “Determine the
mass of the sample and container and then subtract the weight of the
container.” This definitely cannot be done.
Quotations From Some Texts.
Caution: The SI
units for mass and weight are often misused in everyday life. Incorrect expressions such as “This box
weighs 6 kg” are nearly universal. What is meant is that the mass of the box,
probably determined indirectly by weighing, is 6 kg. This usage is so common
that there is probably no hope of straightening things out, but be sure you
recognize that the term weight is often used when mass is meant. Be careful to
avoid this kind of mistake in your own work! In SI units weight (a force) is
measured in newtons, while mass is measured in kilograms [Young, H. D.;
Freedman, R. A. Sears and Zemansky’s University Physics, 10 ed.;
Addison-Wesley: Reading, MA, 2000; p106].
Chemists are
interested primarily in mass, which can be determined readily with a balance;
the process of measuring mass, oddly, is called weighing. [Chang, R. Chemistry, 7 ed.; McGraw-Hill: New
York, 2002, p. 15].
Strictly
speaking, the pound is a unit of weight rather than mass. The weight of an
object depends on the local force of gravity. For measurements made at the
earth’s surface the distinction between mass and weight is not generally
useful. [Moore, J. W.; Stanitski, C. L.; Jurs, P. C. Chemistry: The Molecular
Science; Harcourt College Publishers: Orlando, FL, 2002, p 46].
Because weighing
something on a chemical balance (see Fig. 1.5) involves comparing the mass of
that object to a standard mass, the terms weight and mass are sometimes used
interchangeably, although this is incorrect. [Zumdahl, S, S.; Zumdahl, S. A.
Chemistry, 5th ed., Houghton-Mifflin: Boston, MA, 2000, p 9].
The object on a
balance pushes the pan down with a force equal to m × g, where m is the mass of
the object and g is the acceleration of gravity. The electronic balance uses an
electromagnetic restoring force to return the pan to its original
position. The electric current required
to generate the force is proportional to the mass, which is displayed on a
digital readout. [Harris, D. C. Quantitative Chemical Analysis, 5th ed.; W. H.
Freeman: New York. 1999, p. 32.
4.
Let’s Make Mass a Verb. One could say, “why should we care
whether the process is called weighing or massing?” There are several reasons:
1. The student is
taught something that is demonstrably incorrect. Namely, that one can think of
weight and mass as the same thing. One surely cannot, for they don’t even have
the same units. All the examples about “mass is the same on Mars as on Earth,
but the weight is different” seem to suggest to the student that on Earth the
mass and the weight are well behaved, that
is, equal to each other.
2. The statement
that the observed weight = g × m is not really true. A more
correct statement is observed weight ± buoyancy correction = (g ± location
correction) × m. The location correction is taken care of by calibration with
standard masses, commonly called standard weights. The buoyancy correction is
technically required in all cases where the density of the calibration masses
is not the same as the density of the sample; however, this buoyancy correction
is often ignored except when massing gases. Buoyancy corrections are not easy
to explain to a student who has adopted the idea that weight and mass are
interchangeable.
3. How can one be
said to weigh a sample
when, after the operation is concluded, one does not know the weight?
4. I cannot think
of any other measurement we commonly make that we do not say, “measure the
(current, volume, pH, conductivity, etc.),” rather than use one operation name
like “weigh.” If we refuse to say measure the mass, we should make mass a verb,
and say mass your sample.
The
Chemical Educator, Vol. 7, No. 4,
Published on Web 06/07/2002, 10.1007/s00897020575a, © 2002 Springer-Verlag
New York, Inc.