between collisions and (∂f/∂t)collis the
rate of change of f(r,v,t) due to colli-
sions. The Boltzmann equation can
be used to calculate transport
coefÜcients, such as conductivity. The
equation was proposed by Ludwig
Boltzmann in 1872.
Boltzmann formula An equation
concerning the entropy S of a system
that derives from statistical mechan-
ics. It states that entropy is related to
the number W of distinguishable
ways in which the equation S = k
lnW, where k is the Boltzmann con-
stant, can describe the system. It ex-
presses in quantitative terms the
concept that entropy is a measure of
the disorder of a system. It was dis-
covered in the late 19th century by
Ludwig *Boltzmann while he was
studying statistical mechanics.
bomb calorimeter An apparatus
used for measuring heats of combus-
tion (e.g. caloriÜc values of fuels and
foods). It consists of a strong con-
tainer in which the sample is sealed
with excess oxygen and ignited elec-
trically. The heat of combustion at
constant volume can be calculated
from the resulting rise in tempera-
ture.
bondSee chemical bond.
bond dissociation energySee
bond energy.
bond energyAn amount of energy
associated with a bond in a chemical
compound. It is obtained from the
heat of atomization. For instance, in
methane the bond energy of the C–H
bond is one quarter of the enthalpy
of the process
CH 4 (g) →C(g) + 4H(g)Bond energies (or bond enthalpies)
can be calculated from the standard
enthalpy of formation of the com-
pound and from the enthalpies of at-
omization of the elements. Energies
calculated in this way are called aver-
age bond energies or bond–energy
terms. They depend to some extent
on the molecule chosen; the C–H
bond energy in methane will differ
slightly from that in ethane. The
bond dissociation energy is a differ-
ent measurement, being the energy
required to break a particular bond;
e.g. the energy for the process:
CH 4 (g) →CH 3 • (g) + H•(g)bond enthalpySee bond energy.bonding orbitalSee orbital.bond order A value indicating the
degree of bonding between two
atoms in a molecule relative to a sin-
gle bond. Bond orders are theoretical
values depending on the way the cal-
culation is done. For example, in
ethane the bond order of the carbon-
carbon bond is 1. In ethene, the bond
order is 2. In benzene the bond order
as calculated by molecular orbital
theory is 1.67.bone blackSee charcoal.borane(boron hydride) Any of a
group of compounds of boron and
hydrogen, many of which can be pre-
pared by the action of acid on mag-
nesium boride (MgB 2 ). Others are
made by pyrolysis of the products of
this reaction in the presence of hy-
drogen and other reagents. They are
all volatile, reactive, and oxidize
readily in air, some explosively so.
The boranes are a remarkable group
of compounds in that their structures
cannot be described using the con-
ventional two-electron covalent bond
model (see electron-deficient com-
pound). The simplest example is di-77 borane
b
HHHHBBHHBorane