cal compound contains an excess of
an element, e.g. a peroxide.
perchlorate See chlorates.
perchloric acid See chloric(vii)
acid.
perdisulphuric acid See peroxo-
sulphuric(vi) acid.
perfect gas See ideal gas; gas.
perfect solutionSee raoult’s law.
pericyclic reaction A type of con-
certed chemical reaction that pro-
ceeds through a cyclic conjugated
transition state. Pericyclic reactions
include cheletropic reactions, some
cycloadditions, sigmatropic reac-
tions, and electrocyclic reactions.
They can be understood using fron-
tier orbital theory or the Woodward–
Hoffmann rules.
peridotSee olivine.
period1.The time taken for one
complete cycle of an oscillating sys-
tem or wave. 2.See periodic table.
period doubling A mechanism for
describing the transition to chaos in
certain dynamical systems. If the
force on a body produces a regular
orbit with a speciÜc period a sudden
increase in the force can suddenly
double the period of the orbit and
the motion becomes more complex.
The original simple motion is called
a one-cycle, while the more compli-
cated motion after the period dou-
bling is called a two-cycle. The
process of period doubling can con-
tinue until a motion called an n-cycle
is produced. As n increases to inÜnity
the motion becomes non-periodic.
The period-doubling route to chaos
occurs in many systems involving
nonlinearity, including lasers and
certain chaotic chemical reactions.
The period-doubling route to chaos
was postulated and investigated by
the US physicist Mitchell Feigen-
baum in the early 1980s. Routes to
chaos other than period doubling
also exist.periodic acidSee iodic(vii) acid.
periodic lawThe principle that
the physical and chemical properties
of elements are a periodic function of
their proton number. The concept
wasÜrst proposed in 1869 by Dimitri
*Mendeleev, using relative atomic
mass rather than proton number, as
a culmination of efforts to rationalize
chemical properties by Johann
Döbereiner (1817), John Newlands
(1863), and Lothar Meyer (1864). One
of the major successes of the periodic
law was its ability to predict chemi-
cal and physical properties of undis-
covered elements and unknown
compounds that were later conÜrmed
experimentally. See periodic table.periodic tableA table of elements
arranged in order of increasing pro-
ton number to show the similarities
of chemical elements with related
electronic conÜgurations. (The origi-
nal form was proposed by Dimitri
Mendeleev in 1869 using relative
atomic masses.) In the modern short
form, the *lanthanoids and *acti-
noids are not shown. The elements
fall into vertical columns, known as
groups. Going down a group, the
atoms of the elements all have the
same outer shell structure, but an in-
creasing number of inner shells. Tra-
ditionally, the alkali metals were
shown on the left of the table and
the groups were numbered IA to
VIIA, IB to VIIB, and 0 (for the noble
gases). All the elements in the middle
of the table are classiÜed as *transi-
tion elements and the nontransition
elements are regarded as main-group
elements. Because of confusion in
the past regarding the numbering of
groups and the designations of sub-
groups, modern practice is to num-
ber the groups across the table from403 periodic table
p