Page 28 - Physical Chemistry

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1.4 THE MOLE Section 1.4
The Mole
We now review the concept of the mole, which is used in chemical thermodynamics.
The ratio of the average mass of an atom of an element to the mass of some cho-
sen standard is called the atomic weight or relative atomic mass A of that element
r
1
(the r stands for “relative”). The standard used since 1961 is 12 times the mass of the
12
12
isotope C. The atomic weight of C is thus exactly 12, by definition. The ratio of the
1 12
average mass of a molecule of a substance to times the mass of a C atom is called
12
the molecular weight or relative molecular mass M of that substance. The statement
r
that the molecular weight of H O is 18.015 means that a water molecule has on the
2
12
average a mass that is 18.015/12 times the mass of a C atom. We say “on the aver-
age” to acknowledge the existence of naturally occurring isotopes of H and O. Since
atomic and molecular weights are relative masses, these “weights” are dimensionless
numbers. For an ionic compound, the mass of one formula unit replaces the mass of
one molecule in the definition of the molecular weight. Thus, we say that the molec-
ular weight of NaCl is 58.443, even though there are no individual NaCl molecules in
an NaCl crystal.
12
12
The number of C atoms in exactly 12 g of C is called Avogadro’s number.
Experiment (Sec. 18.2) gives 6.02 10 23 as the value of Avogadro’s number.
12
Avogadro’s number of C atoms has a mass of 12 g, exactly. What is the mass of
Avogadro’s number of hydrogen atoms? The atomic weight of hydrogen is 1.0079, so
12
each H atom has a mass 1.0079/12 times the mass of a C atom. Since we have equal
12
numbers of H and C atoms, the total mass of hydrogen is 1.0079/12 times the total
12
mass of the C atoms, which is (1.0079/12) (12 g) 1.0079 g; this mass in grams is
numerically equal to the atomic weight of hydrogen. The same reasoning shows that
Avogadro’s number of atoms of any element has a mass of A grams, where A is the
r
r
atomic weight of the element. Similarly, Avogadro’s number of molecules of a sub-
stance whose molecular weight is M will have a mass of M grams.
r
r
The average mass of an atom or molecule is called the atomic mass or the mole-
cular mass. Molecular masses are commonly expressed in units of atomic mass units
12
(amu), where 1 amu is one-twelfth the mass of a C atom. With this definition, the
atomic mass of C is 12.011 amu and the molecular mass of H O is 18.015 amu. Since
2
23
23
12
12
12 g of C contains 6.02 10 atoms, the mass of a C atom is (12 g)/(6.02 10 )
23
and 1 amu (1 g)/(6.02 10 ) 1.66 10 24 g. The quantity 1 amu is called 1 dal-
ton by biochemists, who express molecular masses in units of daltons.
A mole of some substance is defined as an amount of that substance which con-
tains Avogadro’s number of elementary entities. For example, a mole of hydrogen
23
atoms contains 6.02 10 H atoms; a mole of water molecules contains 6.02 10 23
H O molecules. We showed earlier in this section that, if M is the molecular weight
r,i
2
of species i, then the mass of 1 mole of species i equals M grams. The mass per
r,i
mole of a pure substance is called its molar mass M. For example, for H O, M
2
18.015 g/mole. The molar mass of substance i is
m
M i (1.4)*
i
n i
where m is the mass of substance i in a sample and n is the number of moles of i in
i i
the sample. The molar mass M and the molecular weight M of i are related by M
i r,i i
M 1 g/mole, where M is a dimensionless number.
r,i r,i
After Eq. (1.4), n was called “the number of moles” of species i. Strictly speak-
i
ing, this is incorrect. In the officially recommended SI units (Sec. 2.1), the amount of
substance (also called the chemical amount) is taken as one of the fundamental
physical quantities (along with mass, length, time, etc.), and the unit of this physical