Counting by Molecules vs Counting by Mass

["James Purchase" <jppurchase at rogers_com>]

Steff asked:
"Can someone straighten out for us all,
when to count by molecule and when to reckon by weight?"

You're confused. You're not alone. Sometimes basic concepts get glossed over
or forgotten in the flow.

Think of it this way - you want to make an omelet, but you're out of eggs.
You go off to the store to buy what? Eggs are (usually) sold by the "dozen",
a standard "number" of eggs (or actually, a standard number of "anything").
So, you pick up a "dozen" eggs and go home to make your omelet. You have 12
eggs in that "dozen" and depending upon your appetite, you start to break
some shells.

But enough of the cooking analogy, I'm getting hungry.....

Molecules and atoms are extremely tiny things. As a commedian once observed,
they are eenie, menny, minny (except I don't think the comic was referring
to atoms). It would be impractical to actually "count" out atoms or
molecules in everyday chemistry. Chemistry labs the world over would have to
be awfully quiet places - imagine if you got distracted and lost count after
counting out 1,456,328,673,967 atoms? You'd have start counting all over
again from 1.

A 19th century Italian scientist by the name of Amadeo Avogadro formulated a
hypothesis which held that at a given temperature, an equal volume of any
gas contains the SAME number of individual molecules as any other gas. The
"number" of individual molecules is 6.02 x 10^23 (that's a 10 followed by 23
zeros). That's a BIG number. By inference, that means that individual
molecules are REALLY small.

In the year's since Avogadro first postulated his hypothesis, it have been
recognized and accorded the status of a "law" - Avogadro's Law. It can be
applied to anything, not just gases. The "number" he came up with, 6.02 x
10^23, is referred to as "Avogadro's Number", and has proved to be very
handy as a way of "counting" anything that is really tiny. An "Avogadro's
Number" of anything contains 6.02 x 10^23 individual particles (atoms or
ions or molecules). Like the eggs you bought to make your omelet, this
"number" has a easy to remember "name". It is referred to as a "Mole"
(whoever came up with the names of these things probably didn't get out
much). A "Mole" of any substance has the SAME number of individual particles
as a "Mole" of any other substance.

If you take two identical ballons, and fill one of them with Hydrogen gas
and fill the other with Oxygen gas, they will both contain the same number
of molecules of their respective gases. But if you tie them off and let them
go, one will float up to the ceiling and the other will fall gently to the
floor. The balloon filled with Hydrogen will float in air because the
balloon doesn't weigh as much as an equivalent volume of air. Similarly, the
balloon filled with Oxygen will sink to the floor because Oxygen weighs more
that the air displaced by the balloon.

This "weight" is actually the force of the Earth's gravity acting on the
mass of gas within each balloon. Since we know that a Mole of any substance
contains exactly the same number of individual particles as a Mole of any
other substance, any difference in their "weight" MUST be attributed to the
MASS of the individual particles in each Mole. A "Mole" of Hydrogen gas
(6.02 x 10^23 atoms of H2) "weighs" 2.01588 (1.00794 x 2) grams, while a
"Mole" of Oxygen gas "weighs" 31.9988 (15.9994 x 2) grams. In both cases,
this is merely the Atomic Weight (mean relative mass) of the element
multiplied by the number of atoms in the molecule. It is much easier and
much more practical to determine the mass of a substance than it is to be
counting quantities contining many orders of magnitude.

When dealing with chemical compounds, you can easily determine the "weight"
(actually the mass) of a Mole of the compound by summing the Atomic Weights
of the individual elements in the compound. This is called the "Gram Formula
Weight" of the compound.

If you want a Mole of Potassium Nitrate (KNO3), you would measure out (on an
accurate scale) 101.10 (39.0983 + 14.00674 + 15.9994 + 15.9994 + 15.9994)
grams of the crystals. This "amount" of KNO3 contains 1 Mole of KNO3. You
can also see that it contains 1 Mole of Potassium, 1 Mole of Nitrogen, 3
Moles of Oxygen and 1 Mole of Nitrate (NO3). If you dissolve this in 1 liter
of water, guess how many parts per million K are in each cubic centimeter of
the resulting solution?

The element Nitrogen has an Atomic Weight of 14.00674. (that is a Nitrogen
atom, not a molecule of Nitrogen gas). When combined with 3 atoms of Oxygen
(each of which have an Atomic Weight of 15.9994), you get the compound
Nitrate (NO3). A Mole of Nitrate would weigh 62.00494 (14.00674 + 15.9994 +
15.9994 + 15.9994) grams. When Roger referred to the factor of 4.4 when
comparing Nitrogen-N with Nitrate, this is what he was talking about.

So to cut this off (finally!) and to answer your initial question - "when to
count by molecule and when to count by weight?" - the answer is that
counting by weight is the same thing as counting by molecule, IF you stick
to counting Moles of substances. And that is basically what we are doing
here.

James Purchase
Toronto