26 Chapter 1. What the ancients knew[[Student version, December 8, 2002]]
T 2 Track 2
1.5.2′ There is an important elaboration of the rule that atoms of a given species are all identical.
Atoms that behave identicallychemicallymay nevertheless subdivide into a few distinct classes
of slightly different mass, the “isotopes” of that chemical element. Thus we specifiedordinary
hydrogen above, to acknowledge the existence of two other, heavier forms (deuterium and tritium).
Despite this complication, however, there are only a handful of different stable isotopes of each
element, so the number of distinct species is still small, a few hundred. The main thing is that the
distinction between them is discrete, not continuous.
1.5.4′Physics textbooks generally use molecular quantities, while chemistry textbooks generally
use the corresponding molar versions. Like most artificial barriers to friendship, this one is easily
overcome. The SI gives “amount of substance” its own dimension, with a corresponding fundamental
unit calledmol.This book will not use any quantities containing this unit.Thus we will not measure
amounts using the quantityn,with unitsmol,nor will we use the quantitiesRTr= 2470 Jmol−^1
orF=96 000 coul mol−^1 ;instead we use respectively the number of moleculesN,the molecular
thermal energy,kBTr,and the charge on one proton,e. Similarly, we do not use the quantity
N 0 =6. 0 · 1023 mol−^1 ;ourNmoleis the dimensionless number 6. 0 · 1023 .And we don’t use the unit
dalton, defined as 1gmol−^1 ;instead we measure masses in kilograms.
Amore serious notational problem is that different books use the same symbolμ(the “chemical
potential” defined in Chapter 8) to mean two slightly different things: either the derivative of the
free energy with respect ton(with unitsJmol−^1 ), or the derivative with respect toN(with unitsJ).
This book always uses the second convention(see Chapter 8). We choose this convention because
wewill frequently want to studysingle molecules,not mole-sized batches.^6
Toavoid this confusion, recall that in this book the word “mole” in formulas is just an abbrevia-
tion for the numberNmole.When convenient, we can express our molecular energies as multiples of
mole−^1 ;then the numerical part of our quantities just equals the numerical part of the corresponding
molar quantities. For example, we can write
kBTr=4. 1 · 10 −^21 J×6. 0 · 1023
mole
= 2500 J/mole,whose numerical part agrees with that ofRTr.
(^6) Similar remarks apply to the standard free energy change ∆G.