Page 46 - Essentials of physical chemistry

8 Essentials of Physical Chemistry

Avogadro’s hypothesis: Equal volumes of different gases at the same temperature and pressure have
the same number of molecules.

Amedeo Avogadro (1776–1856) was an Italian physicist who published a basic argument in
1811 that related atomic and molecular weights to definite proportions in compounds but that era
was a period of intellectual groping by chemists regarding the meaning of the concepts of atoms and
molecules. In 1856 Stanislao Cannizzaro (1826–1910) published a unifying set of course notes that
clarified Avogadro’s hypothesis and led to the general acceptance of the idea that became the mole
concept chemists use today. It is interesting that Avogadro did not know the number that is named
for him but by expressing his hypothesis in terms of the number of atoms=molecules he avoided the
problem that different gases have different molecular weights. Thus, if we convert the mass of a gas
to its mole quantity by dividing by the gram molecular weight M to obtain n ¼ w=M for what is
called the mole quantity today and based on the standard of 12.000 g of 12 C we now know
Avogadro’s number ¼ 6.02214179 10 23 as given by a least-squares refinement of modern values
of physical constants tabulated in the 90th edn. of the Chemical Rubber handbook. For our purposes
23
we will often use the shorter form as 6.022 10 . This number is a pure number and can refer to
one ‘‘mole’’ of anything, ping-pong balls, H atoms, N 2 molecules, etc.
Now we are ready to determine R with the added fact that 1 g molecular weight of many gases
has (nearly) the same volume. Actually there are some very slight differences in the molar volume of
different gases but the average value at 1 atm and 08C is 22.414 liters (L). Then
PV (1 atm)(22:414 L)
¼ 0:082057 (L atm= K mol)

R ¼ ¼
nT (1 mol)(273:15 K)

Based on the values in the formula the least number of significant figures is five so we need to round
off R to five significant figures as 0.082057 (L atm=8K mol). We note that 22.414 L is about the size
of a 5 gal solvent can and we need to tabulate some key unit facts in this first chapter. At this point it
is easy to introduce the SI equivalent of the gas constant since the only difference is that the pressure
is measured in bars where 1 atm ¼ 1.01325 bar. (Note that a ‘‘barometer’’ measures bars.) However,
at the lower pressure the molar volume will be larger at about 22.711 L:

PV (1 bar)(22:711 L)
¼ 0:08314 (L bar= K mol)

nT (1 mol)(273:15 K)
R ¼ ¼

We will attempt to use the SI units throughout this text and a new generation of students may
have only seen SI units in previous texts and hopefully they can ‘‘think’’ in SI units. However, the
conversion of the older pressure units in atmospheres or mm of mercury will persist in older literature
and some equipment so each student needs to work in their own personal way of dealing with
these conversions. In bygone days when slide rules were used instead of calculators, three significant
figures were the norm and often answers were only good to two. Under those circumstances we would
say R ¼ 0:082 (L atm= K mol) or R ¼ 0:083 (L bar= K mol), easily remembered numbers.

USEFUL UNITS

3
The density of water is defined to be 1.000000 g=cm at 48C.
1 pound (avoirdupois) ¼ 453.6 g ¼ 0.4536 kg (on earth)
1 in. ¼ 2.54 cm (exact)
3
1 mile ¼ 5280 ft ¼ 1.609344 10 m ¼ 1.609344 km
1 quart (U.S.) ¼ 946 cc ¼ 0.946 L (check a quart oil can)
1 gallon (U.S.) ¼ 4 quarts (U.S.) ¼ 3.784 L
2 2
1 erg ¼ 1g cm =s