what he had discovered was an im-
pure form of chromium. The el-
ement was rediscovered and named
by Nils Sefström (1787–1854) in 1880.
A
- Information from the WebElements site
vanadium(V) oxide (vanadium
pentoxide)A crystalline compound,
V 2 O 5 , used extensively as a catalyst in
industrial gas-phase oxidation
processes.
vanadium pentoxide See vana-
dium(v) oxide.
van der Waals’ equation See
equation of state.
van der Waals’ force An attrac-
tive force between atoms or mol-
ecules, named after Johannes van der
Waals (1837–1923). The force ac-
counts for the term a/V^2 in van der
Waals’ equation (see equation of
state). These forces are much weaker
than those arising from valence
bonds and are inversely proportional
to the seventh power of the distance
between the atoms or molecules.
They are the forces responsible for
nonideal behaviour of gases and for
the lattice energy of molecular crys-
tals. There are three factors causing
such forces: (1) dipole–dipole interac-
tion, i.e. electrostatic attractions
between two molecules with per-
manent dipole moments; (2) dipole-
induced dipole interactions, in which
the dipole of one molecule polarizes
a neighbouring molecule; (3) disper-
sion forces arising because of small
instantaneous dipoles in atoms.
van’t Hoff, Jacobus See hoff.
van’t Hoff factor Symbol i. A fac-
tor appearing in equations for *col-
ligative properties, equal to the ratio
of the number of actual particles pre-
sent to the number of undissociated
particles.
van’t Hoff’s isochore An equation
formulated by van’t Hoff for the vari-
ation of equilibrium constant with
temperature:
(d logeK)/dT = ∆H/RT^2 ,
where K is the equilibrium constant,
R is the gas constant, T is the thermo-
dynamic temperature, and ∆H the en-
thalpy of the reaction.Van Urk’s reagent See p-dimethyl-
aminobenzaldehyde.vapour densityThe density of a
gas or vapour relative to hydrogen,
oxygen, or air. Taking hydrogen as
the reference substance, the vapour
density is the ratio of the mass of a
particular volume of a gas to the
mass of an equal volume of hydrogen
under identical conditions of pres-
sure and temperature. Taking the
density of hydrogen as 1, this ratio is
equal to half the relative molecular
mass of the gas.
vapour pressure The pressure ex-
erted by a vapour. All solids and liq-
uids give off vapours, consisting of
atoms or molecules of the substances
that have evaporated from the con-
densed forms. These atoms or mol-
ecules exert a vapour pressure. If the
substance is in an enclosed space, the
vapour pressure will reach an equi-
librium value that depends only on
the nature of the substance and the
temperature. This equilibrium value
occurs when there is a dynamic equi-
librium between the atoms or mol-
ecules escaping from the liquid or
solid and those that strike the sur-
face of the liquid or solid and return
to it. The vapour is then said to be a
saturated vapour and the pressure it
exerts is the saturated vapour pres-
sure.variational principleIn calcula-
tions in quantum mechanics the
principle that if a trial *wave func-
tion is used to calculate the energy of545 variational principle
v