6.2 Diatomic Molecules
295
Fig. 6.11 Temperature dependence of the percentage pH 2 in an equilibrium mixture of oH 2 and
pH 2
constituent H atoms, their interconversion requires either interaction between an H 2
molecule and a species possessing a magnetic moment to enable the decoupling of
the atomic nuclear spin angular momenta of one spin modification followed by a
subsequent recoupling to give the other spin modification, or dissociation (typically
on a surface) of an H 2 molecule having one value of the net nuclear spin I followed
by recombination of the two H atoms to form an H 2 molecule having the other value
of I .
Because their characteristic rotational temperatures are so large and their boiling
temperatures are so low, the hydrogen isotopologues are the only molecules for
which the high-temperature limit does not apply over the entire temperature
range for which they are gases. We shall examine in detail only the case of H 2 .
The rotational contribution to the thermodynamic internal energy, U rot (T ), for
equilibrium H 2 is obtained from z rot−nuc (T ), given in Eq. (6.2.101) as
U rot−nuc (T ) =
Nk B rot
z rot−nuc (T )
⎡
⎣ 3
j =odd
j (j + 1)(2j + 1)e
−j (j+1)) rot /T
+
j =even
j (j + 1)(2j + 1)e
j (j+1)) rot /T
⎤
⎦ ,
(6.2.103)
295
Fig. 6.11 Temperature dependence of the percentage pH 2 in an equilibrium mixture of oH 2 and
pH 2
constituent H atoms, their interconversion requires either interaction between an H 2
molecule and a species possessing a magnetic moment to enable the decoupling of
the atomic nuclear spin angular momenta of one spin modification followed by a
subsequent recoupling to give the other spin modification, or dissociation (typically
on a surface) of an H 2 molecule having one value of the net nuclear spin I followed
by recombination of the two H atoms to form an H 2 molecule having the other value
of I .
Because their characteristic rotational temperatures are so large and their boiling
temperatures are so low, the hydrogen isotopologues are the only molecules for
which the high-temperature limit does not apply over the entire temperature
range for which they are gases. We shall examine in detail only the case of H 2 .
The rotational contribution to the thermodynamic internal energy, U rot (T ), for
equilibrium H 2 is obtained from z rot−nuc (T ), given in Eq. (6.2.101) as
U rot−nuc (T ) =
Nk B rot
z rot−nuc (T )
⎡
⎣ 3
j =odd
j (j + 1)(2j + 1)e
−j (j+1)) rot /T
+
j =even
j (j + 1)(2j + 1)e
j (j+1)) rot /T
⎤
⎦ ,
(6.2.103)