The Mole: Calculations involving mass
, volume and moles
The mole is the unit of amount in chemistry. It provides a bridge between the atom and the macroscopic amounts of material that we work with in the laboratory. It allows the chemist to weigh out amounts of two substances, say iron and sulfur, such that equal numbers of atoms of iron and sulfur are obtained. A mole of a substance is defined as:
The mass of substance containing the same number of fundamental units as there are atoms in exactly 12.000 g of 12C.
Fundamental units may be atoms, molecules, or formula units, depending on the substance concerned. At present, our best estimate of the number of atoms in 12.000 g of 12C is 6.022 x 1023, a huge number of atoms. This is obviously a very important quantity. For historical reasons, it is called Avogadro's Number, and is given the symbol NA.
Unfortunately, the clumsy definition of the mole obscures its utility. It is nearly analogous to defining a dozen as the mass of a substance that contains the same number of fundamental units as are contained in 733 g of Grade A large eggs. This definition completely obscures the utility of the dozen: that it is 12 things! Similarly, a mole is NA things.
The mole is the same kind of unit as the dozen -- a certain number of things. But it differs from the dozen in a couple of ways. First, the number of things in a mole is so huge that we cannot identify with it in the way that we can identify with 12 things. Second, 12 is an important number in the English system of weights and measures, so the definition of a dozen as 12 things makes sense.
However, the choice of the unusual
number, 6.022 x 1023, as the number of things in a mole seems odd.
Why is this number chosen? Would it not make more sense to define a
mole as 1.0 x 1023 things, a nice (albeit large) integer that
everyone can easily remember? To understand why the particular
number, 6.022 x 1023 is used, it is necessary to resurrect an older,
in some ways more sensible and useful, definition of the mole, which
is grounded in the atomic weight scale addressed above.
The atomic weight scale defines the masses of atoms relative to the mass of an atom of 12C, which is assigned a mass of exactly 12.000 atomic mass units (amu). The number 12 is chosen so that the least massive atom, hydrogen, has a mass of about 1 (actually 1.008) on the scale. The atomic mass unit is a very tiny unit of mass appropriate to the scale of single atoms.
Originally, of course, chemists had no
idea of its value in laboratory-sized units like the gram. The early
versions of the atomic weight scale were established by scientists
who had no knowledge of the electron, proton, or neutron. When these
were discovered in the late 19th and early 20th centuries, it turned
out that the mass of an atom on the atomic weight scale was very
nearly the same as the number of protons in its nucleus. This is a
very useful correspondence, but it was discovered only after the
weight scale had been in use for a long time.
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