Page 29 - Physical Chemistry

lev38627_ch01.qxd 2/20/08 11:38 AM Page 10

10
Chapter 1 quantity is the mole, abbreviated mol. Just as the SI unit of mass is the kilogram, the
Thermodynamics SI unit of amount of substance is the mole. Just as the symbol m stands for the mass
i
of substance i, the symbol n stands for the amount of substance i. The quantity m i
i
is not a pure number but is a number times a unit of mass; for example, m might be
i
4.18 kg (4.18 kilograms). Likewise, n is not a pure number but is a number times a
i
unit of amount of substance; for example, n might be 1.26 mol (1.26 moles). Thus the
i
correct statement is that n is the amount of substance i. The number of moles of i is a
i
pure number and equals n /mol, since n has a factor of 1 mol included in itself.
i
i
Since Avogadro’s number is the number of molecules in one mole, the number of
molecules N of species i in a system is
i
,
#
N 1n >mol2 1Avogadro s number2
i
i
where n /mol is the number of moles of species i in the system. The quantity
i
(Avogadro’s number)/mol is called the Avogadro constant N . We have
A
23
N n N where N 6.02 10 mol 1 (1.5)*
i
A
i A
Avogadro’s number is a pure number, whereas the Avogadro constant N has units of
A
1
mole .
Equation (1.5) applies to any collection of elementary entities, whether they are
atoms, molecules, ions, radicals, electrons, photons, etc. Written in the form n N /N ,
i
i
A
Eq. (1.5) gives the definition of the amount of substance n of species i. In this equa-
i
tion, N is the number of elementary entities of species i.
i
If a system contains n moles of chemical species i and if n is the total number
i
tot
of moles of all species present, then the mole fraction x of species i is
i
x n >n tot (1.6)*
i
i
The sum of the mole fractions of all species equals 1; x x n /n n /n
2
tot
1
tot
1
2
(n n )/n n /n 1.
2
tot
1
tot
tot
1.5 IDEAL GASES
The laws of thermodynamics are general and do not refer to the specific nature of
the system under study. Before studying these laws, we shall describe the proper-
ties of a particular kind of system, namely, an ideal gas. We shall then be able to il-
lustrate the application of thermodynamic laws to an ideal-gas system. Ideal gases
also provide the basis for a more fundamental temperature scale than the liquid-
mercury scale of Sec. 1.3.
Boyle’s Law
Boyle investigated the relation between the pressure and volume of gases in 1662 and
found that, for a fixed amount of gas kept at a fixed temperature, P and V are inversely
proportional:
PV k constant u, m (1.7)
where k is a constant and m is the gas mass. Careful investigation shows that Boyle’s
law holds only approximately for real gases, with deviations from the law approach-
ing zero in the limit of zero pressure. Figure 1.6a shows some observed P-versus-V
curves for 28 g of N at two temperatures. Figure 1.6b shows plots of PV versus P for
2
28 g of N . Note the near constancy of PV at low pressures (below 10 atm) and the sig-
2
nificant deviations from Boyle’s law at high pressures.
Note how the axes in Fig. 1.6 are labeled. The quantity P equals a pure number
times a unit; for example, P might be 4.0 atm 4.0 1 atm. Therefore, P/atm (where