1.5. Other key ideas from physics and chemistry[[Student version, December 8, 2002]] 21
since the density of water is 1gcm−^3 and1 m^3 ×(
100 cm
1 m) 3
×^1 g
1 cm^3×^1 kg
1000 g
= 1000 kg.Wewantto know how many molecules of water make up a mole. Since each water
molecule consists of one oxygen and two hydrogen atoms, its total mass is about
16+1+1=18 times as great as that of a single hydrogen atom. So we must ask, if
6. 4 · 1025 molecules have mass 1000kg,then how many molecules does it take to
make 18g,or0.018kg?Nmole=0. 018 kg×6. 4 · 1025
1000 kg
=0. 011 · 1023. (estimate)The estimate for Avogadro’s number just found is not very accurate (the modern value is
Nmole=6. 0 · 1023 ). But it’s amazingly good, considering that the data on which it is based were
taken nearly a quarter of a millennium ago. Improving on this estimate, and hence nailing down
the precise dimensions of atoms, proved surprisingly difficult. Chapter 4 will then show how the
dogged pursuit of this quarry led Albert Einstein to a key advance in our understanding of the
nature of heat.
Your Turn 1a
Using the modern value of Avogadro’s number, turn the above calculation around and find the
volume occupied by a single water molecule.
1.5.2 Molecules are particular spatial arrangements of atoms
There are only about a hundred kinds of atoms. Every atom of a given kind is exactly like every
other: Atoms have no individual personalities. For example, every atom of (ordinary) hydrogen
has the same mass as every other one. One way to express an atom’s mass is simply to give it in
grams, but usually it’s more convenient to quote the mass ofNmoleatoms (themolar mass).
Similarly, every molecule of a given chemical type has a fixed, definite composition, a rule we
attribute to J. Dalton and J. Gay-Lussac. For example, carbon dioxide always consists of exactly
twooxygen atoms and one of carbon, in a fixed spatial relationship. Every CO 2 molecule is like
every other, for example equally ready or unwilling to undergo a given chemical change.
There may be more than one allowed arrangement for a given set of atoms, yielding two chem-
ically distinct molecules calledisomers.Some molecules flip back and forth rapidly between their
isomeric states: They are “labile.” Others do so very rarely: They are rigid. For example, Louis
Pasteur discovered in 1857 that two sugars containing the same atoms, but in mirror-image ar-
rangements, are chemically different and essentially never spontaneously interconvert (Figure 1.5).
Amolecule whose mirror image is an inequivalent stereoisomer is called “chiral”; such molecules
will play a key role in Chapter 9.
T 2 Section 1.5.2′on page 26 discusses the division of elements into isotopes.