solved, absorbed, or adsorbed gases
from a liquid or solid. Degassing is
important in vacuum systems, where
gas absorbed in the walls of the vacuum vessel starts to desorb as the
pressure is lowered.
degeneracy The state of being *degenerate.
degenerate Having quantum
states with the same energy. For example, the Üve d-orbitals in an isolated transition-metal atom have the
same energy (although they have different spatial arrangements) and are
thus degenerate. The application of a
magnetic or electric Üeld 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 indistinguishable from the reactant.
Degenerate rearrangements can be
detected by using isotopic labelling.
degradation A type of organic
chemical reaction in which a compound is converted into a simpler
compound. An example is the *Barbier–Wieland degradation.
degree A division on a *temperature scale.
degrees absolute See absolute.
degrees of freedom 1. The number of independent parameters required 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 various sets of parameters that may be
chosen, and the details of the consequent theory vary with the choice.
For example, in a monatomic gas
each atom may be allotted three degrees of freedom, corresponding to
the three coordinates in space required to specify its position. The
mean energy per atom for each
degree of freedom is the same, according to the principle of the *equipartition of energy, and is equal to
kT/2 for each degree of freedom
(where k is the *Boltzmann constant
and T is the thermodynamic temperature). Thus for a monatomic gas the
total molar energy is 3LkT/2, where L
is the Avogadro constant (the number 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 require six coordinates between them,
giving six degrees of freedom. Commonly these are interpreted as six independent ways of storing energy: on
this basis the molecule has three degrees of freedom for different directions of translational motion, and in
addition there are two degrees of
freedom for rotation of the molecular axis and one vibrational degree of
freedom along the bond between the
atoms. The rotational degrees of freedom 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 potential energy. The total energy per
molecule for a diatomic gas is therefore 3kT/2 (for translational energy of
the whole molecule) plus 2kT/2 (for
rotational energy) plus 2kT/2 (for vibrational 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 freedom (e.g. temperature and pressure).
dehydration 1. Removal of water
from a substance. 2. A chemical reaction in which a compound loses
hydrogen and oxygen in the ratio
degeneracy
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from a liquid or solid. Degassing is
important in vacuum systems, where
gas absorbed in the walls of the vacuum vessel starts to desorb as the
pressure is lowered.
degeneracy The state of being *degenerate.
degenerate Having quantum
states with the same energy. For example, the Üve d-orbitals in an isolated transition-metal atom have the
same energy (although they have different spatial arrangements) and are
thus degenerate. The application of a
magnetic or electric Üeld 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 indistinguishable from the reactant.
Degenerate rearrangements can be
detected by using isotopic labelling.
degradation A type of organic
chemical reaction in which a compound is converted into a simpler
compound. An example is the *Barbier–Wieland degradation.
degree A division on a *temperature scale.
degrees absolute See absolute.
degrees of freedom 1. The number of independent parameters required 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 various sets of parameters that may be
chosen, and the details of the consequent theory vary with the choice.
For example, in a monatomic gas
each atom may be allotted three degrees of freedom, corresponding to
the three coordinates in space required to specify its position. The
mean energy per atom for each
degree of freedom is the same, according to the principle of the *equipartition of energy, and is equal to
kT/2 for each degree of freedom
(where k is the *Boltzmann constant
and T is the thermodynamic temperature). Thus for a monatomic gas the
total molar energy is 3LkT/2, where L
is the Avogadro constant (the number 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 require six coordinates between them,
giving six degrees of freedom. Commonly these are interpreted as six independent ways of storing energy: on
this basis the molecule has three degrees of freedom for different directions of translational motion, and in
addition there are two degrees of
freedom for rotation of the molecular axis and one vibrational degree of
freedom along the bond between the
atoms. The rotational degrees of freedom 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 potential energy. The total energy per
molecule for a diatomic gas is therefore 3kT/2 (for translational energy of
the whole molecule) plus 2kT/2 (for
rotational energy) plus 2kT/2 (for vibrational 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 freedom (e.g. temperature and pressure).
dehydration 1. Removal of water
from a substance. 2. A chemical reaction in which a compound loses
hydrogen and oxygen in the ratio
degeneracy
166
d
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