dation of propan-1,2-diol using dilute
nitric acid. Lactic acid is manufac-
tured by the fermentation of lactose
(from milk) and used in the dyeing
and tanning industries. It is an alpha
hydroxy *carboxylic acid. See also op-
tical activity.
Lactic acid is produced from pyru-
vic acid in active muscle tissue when
oxygen is limited and subsequently
removed for conversion to glucose by
the liver. During strenuous exercise
it may build up in the muscles, caus-
ing cramplike pains. It is also pro-
duced by fermentation in certain
bacteria and is characteristic of sour
milk.
lactimsSee lactams.
A- Information about IUPAC nomenclature
lactonesOrganic compounds con-
taining a ring of atoms in which the
group –CO.O– forms part of the ring.
Lactones can be formed (or regarded
as formed) by reaction of an –OH
group in one part of a molecule with
a –COOH group in the other to
give a cyclic ester (see illustration).
This type of reaction occurs with
γ-hydroxy carboxylic acids such as the
compound CH 2 (OH)CH 2 CH 2 COOH (in
which the hydroxyl group is on the
third carbon from the carboxyl
group). The resulting γ-lactone has
aÜve-membered ring. Similarly,
δ-lactones have six-membered rings.
β-lactones, with a four-membered
ring, are not produced directly fromβ-hydroxy acids, but can be synthe-
sized by other means.
A- Information about IUPAC nomenclature
lactose(milk sugar)A sugar com-
prising one glucose molecule linked
to a galactose molecule. Lactose is
manufactured by the mammary
gland and occurs only in milk. For
example, cows’ milk contains about
4.7% lactose. It is less sweet than su-
crose (cane sugar).Ladenburg benzeneAn (erro-
neous) structure for *benzene pro-
posed by Albert Ladenburg (1842–
1911), in which the six carbon atoms
were arranged at the corners of a tri-
angular prism and linked by single
bonds to each other and to the six
hydrogen atoms.laevo formSee optical activity.
laevorotatory Designating a
chemical compound that rotates the
plane of plane-polarized light to the
left (anticlockwise for someone fac-
ing the oncoming radiation). See opti-
cal activity.
laevuloseSee fructose.Lagrange multipliers (undeter-
mined multipliers)Parameters, usu-
ally denoted λ, introduced to assist in
Ünding the maximum or minimum
value of a function f of several vari-
ables x 1 ,x 2 ,...xn, subject to some con-
straint that connects the variables.
An important application of the
method of Lagrange multipliers is its
use in the derivation of the Boltz-
mann distribution in statistical me-
chanics, in which one of the
Lagrange multipliers is –1/kT, where k
is the *Boltzmann constant and T is
the thermodynamic temperature. La-
grange multipliers were introduced
by the Italian-born French mathe-
matician Joseph-Louis Lagrange
(1736–1813).lactims 312l
Lactones