solved, absorbed, or adsorbed gases
from a liquid or solid. Degassing is
important in vacuum systems, where
gas absorbed in the walls of the vac-
uum vessel starts to desorb as the
pressure is lowered.degeneracyThe state of being *de-
generate.
degenerateHaving quantum
states with the same energy. For ex-
ample, theÜve d-orbitals in an iso-
lated transition-metal atom have the
same energy (although they have dif-
ferent spatial arrangements) and are
thus degenerate. The application of a
magnetic or electricÜeld may cause
the quantum states to have different
energies (see crystal-field theory).
In this case, the degeneracy is said to
be ‘lifted’.
degenerate rearrangement A
rearrangement of a molecule in
which the product is chemically in-
distinguishable from the reactant.
Degenerate rearrangements can be
detected by using isotopic labelling.
degradationA type of organic
chemical reaction in which a com-
pound is converted into a simpler
compound. An example is the *Bar-
bier–Wieland degradation.degree A division on a *tempera-
ture scale.degrees absolute See absolute.
degrees of freedom 1.The num-
ber of independent parameters re-
quired to specify the conÜguration of
a system. This concept is applied in
the *kinetic theory to specify the
number of independent ways in
which an atom or molecule can take
up energy. There are however vari-
ous sets of parameters that may be
chosen, and the details of the conse-
quent theory vary with the choice.
For example, in a monatomic gas
each atom may be allotted three de-grees of freedom, corresponding to
the three coordinates in space re-
quired to specify its position. The
mean energy per atom for each
degree of freedom is the same, ac-
cording to the principle of the *equi-
partition of energy, and is equal to
kT/2 for each degree of freedom
(where k is the *Boltzmann constant
and T is the thermodynamic temper-
ature). Thus for a monatomic gas the
total molar energy is 3LkT/2, where L
is the Avogadro constant (the num-
ber of atoms per mole). As k = R/L,
where R is the molar gas constant,
the total molar energy is 3RT/2.
In a diatomic gas the two atoms re-
quire six coordinates between them,
giving six degrees of freedom. Com-
monly these are interpreted as six in-
dependent ways of storing energy: on
this basis the molecule has three de-
grees of freedom for different direc-
tions of translational motion, and in
addition there are two degrees of
freedom for rotation of the molecu-
lar axis and one vibrational degree of
freedom along the bond between the
atoms. The rotational degrees of free-
dom each contribute their share,
kT/2, to the total energy; similarly the
vibrational degree of freedom has an
equal share of kinetic energy and
must on average have as much po-
tential energy. The total energy per
molecule for a diatomic gas is there-
fore 3kT/2 (for translational energy of
the whole molecule) plus 2kT/2 (for
rotational energy) plus 2kT/2 (for vi-
brational energy), i.e. a total of 7kT/2.
2.The least number of independent
variables required to deÜne the state
of a system in the *phase rule. In this
sense a gas has two degrees of free-
dom (e.g. temperature and pressure).
dehydration1.Removal of water
from a substance. 2.A chemical re-
action in which a compound loses
hydrogen and oxygen in the ratiodegeneracy 166d