thermodynamics; it can be shown
that the standard equilibrium constant KŠ is given by exp(–∆GŠ/RT),
where ∆GŠ is the standard Gibbs
free energy change for the complete
reaction. Strictly, the expressions
above for equilibrium constants are
true only for ideal gases (pressure) or
inÜnite dilution (concentration). For
accurate work *activities are used.
equilibrium law See equilibrium
constant.
equipartition of energy The
theory, proposed by Ludwig *Boltzmann and given some theoretical
support by James Clerk *Maxwell,
that the energy of gas molecules in a
large sample under thermal *equilibrium is equally divided among their
available *degrees of freedom, the
average energy for each degree of
freedom being kT/2, where k is the
*Boltzmann constant and T is the
thermodynamic temperature. The
proposition is not generally true if
quantum considerations are important, but is frequently a good approximation.
equivalence point The point in a
titration at which reaction is complete. See indicator.
equivalent proportions See
chemical combination.
equivalent weight The mass of
an element or compound that could
combine with or displace one gram
of hydrogen (or eight grams of oxygen or 35.5 grams of chlorine) in a
chemical reaction. The equivalent
weight represents the ‘combining
power’ of the substance. For an element it is the relative atomic mass
divided by the valency. For a compound it depends on the reaction
considered.
erbium Symbol Er. A soft silvery
metallic element belonging to the
*lanthanoids; a.n. 68; r.a.m. 167.26;
r.d. 9.006 (20°C); m.p. 1529°C; b.p.
2863°C. It occurs in apatite, gadolinite, and xenotine from certain
sources. There are six natural isotopes, which are stable, and twelve
artiÜcial isotopes are known. It has
been used in alloys for nuclear technology as it is a neutron absorber; it
is being investigated for other potential uses. It was discovered by Carl
Mosander (1797–1858) in 1843.
A
• Information from the WebElements site
ergocalciferol See vitamin d.
ergodic hypothesis A hypothesis
in *statistical mechanics concerning
phase space. If a system of N atoms
or molecules is enclosed in a Üxed
volume, the state of this system is
given by a point in 6N-dimensional
phase space with q i representing coordinates and p i representing momenta. Taking the energy E to be
constant, a representative point in
phase space describes an orbit on the
surface E(q i ,p i ) = c, where c is a constant. The ergodic hypothesis states
that the orbit of the representative
point in phase space eventually goes
through all points on the surface.
The quasi-ergodic hypothesis states
that the orbit of the representative
point in phase space eventually
comes close to all points on the surface. In general, it is very difÜcult to
prove the ergodic or quasi-ergodic
hypotheses for a given system. See
also ergodicity.
ergodicity A property of a system
that obeys the *ergodic hypothesis.
The ergodicity of systems has been
discussed extensively in the foundations of *statistical mechanics, although it is now thought by many
physicists to be irrelevant to the
problem. Considerations of ergodicity occur in dynamics, since the beequilibrium law
210
e
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that the standard equilibrium constant KŠ is given by exp(–∆GŠ/RT),
where ∆GŠ is the standard Gibbs
free energy change for the complete
reaction. Strictly, the expressions
above for equilibrium constants are
true only for ideal gases (pressure) or
inÜnite dilution (concentration). For
accurate work *activities are used.
equilibrium law See equilibrium
constant.
equipartition of energy The
theory, proposed by Ludwig *Boltzmann and given some theoretical
support by James Clerk *Maxwell,
that the energy of gas molecules in a
large sample under thermal *equilibrium is equally divided among their
available *degrees of freedom, the
average energy for each degree of
freedom being kT/2, where k is the
*Boltzmann constant and T is the
thermodynamic temperature. The
proposition is not generally true if
quantum considerations are important, but is frequently a good approximation.
equivalence point The point in a
titration at which reaction is complete. See indicator.
equivalent proportions See
chemical combination.
equivalent weight The mass of
an element or compound that could
combine with or displace one gram
of hydrogen (or eight grams of oxygen or 35.5 grams of chlorine) in a
chemical reaction. The equivalent
weight represents the ‘combining
power’ of the substance. For an element it is the relative atomic mass
divided by the valency. For a compound it depends on the reaction
considered.
erbium Symbol Er. A soft silvery
metallic element belonging to the
*lanthanoids; a.n. 68; r.a.m. 167.26;
r.d. 9.006 (20°C); m.p. 1529°C; b.p.
2863°C. It occurs in apatite, gadolinite, and xenotine from certain
sources. There are six natural isotopes, which are stable, and twelve
artiÜcial isotopes are known. It has
been used in alloys for nuclear technology as it is a neutron absorber; it
is being investigated for other potential uses. It was discovered by Carl
Mosander (1797–1858) in 1843.
A
• Information from the WebElements site
ergocalciferol See vitamin d.
ergodic hypothesis A hypothesis
in *statistical mechanics concerning
phase space. If a system of N atoms
or molecules is enclosed in a Üxed
volume, the state of this system is
given by a point in 6N-dimensional
phase space with q i representing coordinates and p i representing momenta. Taking the energy E to be
constant, a representative point in
phase space describes an orbit on the
surface E(q i ,p i ) = c, where c is a constant. The ergodic hypothesis states
that the orbit of the representative
point in phase space eventually goes
through all points on the surface.
The quasi-ergodic hypothesis states
that the orbit of the representative
point in phase space eventually
comes close to all points on the surface. In general, it is very difÜcult to
prove the ergodic or quasi-ergodic
hypotheses for a given system. See
also ergodicity.
ergodicity A property of a system
that obeys the *ergodic hypothesis.
The ergodicity of systems has been
discussed extensively in the foundations of *statistical mechanics, although it is now thought by many
physicists to be irrelevant to the
problem. Considerations of ergodicity occur in dynamics, since the beequilibrium law
210
e
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