thermodynamics; it can be shown
that the standard equilibrium con-
stant KŠis given by exp(–∆GŠ/RT),
where ∆GŠis 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 lawSee equilibrium
constant.equipartition of energyThe
theory, proposed by Ludwig *Boltz-
mann and given some theoretical
support by James Clerk *Maxwell,
that the energy of gas molecules in a
large sample under thermal *equilib-
rium 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 impor-
tant, but is frequently a good approx-
imation.equivalence pointThe point in a
titration at which reaction is com-
plete. See indicator.
equivalent proportions See
chemical combination.
equivalent weightThe mass of
an element or compound that could
combine with or displace one gram
of hydrogen (or eight grams of oxy-
gen or 35.5 grams of chlorine) in a
chemical reaction. The equivalent
weight represents the ‘combining
power’ of the substance. For an el-
ement it is the relative atomic mass
divided by the valency. For a com-
pound it depends on the reaction
considered.
erbiumSymbol 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, gadolin-
ite, and xenotine from certain
sources. There are six natural iso-
topes, which are stable, and twelve
artiÜcial isotopes are known. It has
been used in alloys for nuclear tech-
nology as it is a neutron absorber; it
is being investigated for other poten-
tial uses. It was discovered by Carl
Mosander (1797–1858) in 1843.
A- Information from the WebElements site
ergocalciferol See vitamin d.
ergodic hypothesisA hypothesis
in *statistical mechanics concerning
phase space. If a system of N atoms
or molecules is enclosed in aÜxed
volume, the state of this system is
given by a point in 6N-dimensional
phase space with qirepresenting co-
ordinates and pirepresenting mo-
menta. Taking the energy E to be
constant, a representative point in
phase space describes an orbit on the
surface E(qi,pi) = c, where c is a con-
stant. 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 sur-
face. In general, it is very difÜcult to
prove the ergodic or quasi-ergodic
hypotheses for a given system. See
also ergodicity.ergodicityA property of a system
that obeys the *ergodic hypothesis.
The ergodicity of systems has been
discussed extensively in the founda-
tions of *statistical mechanics, al-
though it is now thought by many
physicists to be irrelevant to the
problem. Considerations of ergodic-
ity occur in dynamics, since the be-equilibrium law 210e