who spent his entire academic career
at Yale University. During the 1870s
he developed the theory of chemical
thermodynamics, devising functions
such as Gibbs *free energy; he also
derived the *phase rule. In mathe-
matics he introduced vector notation.
Gibbs–Duhem equationAn equa-
tion describing the relation between
the chemical potentials of species in
a mixture. If niis the amount of
species i and μiis the chemical poten-
tial of species i, the Gibbs–Duhem
equation states that
∑
inidμi= 0
This equation implies that the chemi-
cal potentials for the species in a
mixture do not change indepen-
dently. Thus, in the case of a binary
mixture, if the chemical potential of
one species increases, the chemical
potential of the other species must
decrease. The equation was derived
independently by J. W. *Gibbs and
the French physicist P. Duhem
(1861–1916).Gibbs free energy (Gibbs function)
See free energy.Gibbs–Helmholtz equationAn
equation used in thermodynamics to
show the temperature dependence of
the *Gibbs free energy. It has the
form:
(∂G/∂T)p= (G – H)/T,
where G is the Gibbs free energy, H is
the enthalpy, T is the thermody-
namic temperature, and p is the pres-
sure (which is held constant). The
Gibbs–Helmholtz equation can be de-
rived from (∂G/∂T)p= – S and S = (H –
G)T using the rules of differentiation.
The equation was derived by J. W.
*Gibbs and H. L. F. von *Helmholtz.gibbsiteA mineral form of hy-
drated *aluminium hydroxide
(Al(OH) 3 ). It is named after the US
mineralogist George Gibbs (d. 1833).giga-Symbol G. A preÜx used in the
metric system to denote one thou-
sand million times. For example, 10^9
joules = 1 gigajoule (GJ).
gilbertSymbol Gb. The c.g.s. unit
of magnetomotive force equal to
10/4π(= 0.795 77) ampere-turn. It is
named after the English physician
and physicist William Gilbert
(1544–1603), who studied magnet-
ism.glacial ethanoic acidSee
ethanoic acid.glassAny noncrystalline solid; i.e. a
solid in which the atoms are random
and have no long-range ordered pat-
tern. Glasses are often regarded as su-
percooled liquids. Characteristically
they have no deÜnite melting point,
but soften over a range of tempera-
tures.
The common glass used in win-
dows, bottles, etc., is soda glass,
which is made by heating a mixture
of lime (calcium oxide), soda (sodium
carbonate), and sand (silicon(IV)
oxide). It is a form of calcium silicate.
Borosilicate glasses (e.g. Pyrex) are
made by incorporating some boron
oxide, so that silicon atoms are re-
placed by boron atoms. They are
tougher than soda glass and more re-
sistant to temperature changes,
hence their use in cooking utensils
and laboratory apparatus. Glasses for
special purposes (e.g. optical glass)
have other elements added (e.g. bar-
ium, lead). See also spin glass.glass electrode A type of *half
cell having a glass bulb containing an
acidic solution ofÜxed pH, into
which dips a platinum wire. The
glass bulb is thin enough for hydro-
gen ions to diffuse through. If the
bulb is placed in a solution contain-
ing hydrogen ions, the electrode po-
tential depends on the hydrogen-ionGibbs–Duhem equation 246g