methanal (formaldehyde) in water
with methanol as a stabilizer; r.d.
1.075–1.085. When kept at temperatures below 25°C a white polymer of
methanal separates out. It is used as
a disinfectant and preservative for
biological specimens.
formate See methanoate.
formic acid See methanoic acid.
formula A way of representing a
chemical compound using symbols
for the atoms present. Subscripts are
used for the numbers of atoms. The
molecular formula simply gives the
types and numbers of atoms present.
For example, the molecular formula
of ethanoic acid is C 2 H 4 O 2 . The empirical formula gives the atoms in
their simplest ratio; for ethanoic acid
it is CH 2 O. The structural formula
gives an indication of the way the
atoms are arranged. Commonly, this
is done by dividing the formula into
groups; ethanoic acid can be written
CH 3 .CO.OH (or more usually simply
CH 3 COOH). Structural formulae can
also show the arrangement of atoms
or groups in space.
formula weight The relative molecular mass of a compound as calculated from its molecular formula.
formylation A chemical reaction
that introduces a formyl group
(methanoyl, –CHO) into an organic
molecule.
formyl group The group HCO–.
fossil fuel Coal, oil, and natural
gas, the fuels used by man as a
source of energy. They are formed
from the remains of living organisms
and all have a high carbon or hydrogen content. Their value as fuels relies on the exothermic oxidation of
carbon to form carbon dioxide (C +
O 2 → CO 2 ) and the oxidation of hydrogen to form water (H 2 + ½O 2 →
H 2 O).
four-circle diffractometer An instrument used in X-ray crystallography to automatically determine the
shape and symmetry of the unit cell
of a crystal. The crystal is placed in
the goniometer head with an arbitrary orientation. If the dimensions
of the unit cell have been determined, they can be used to calculate
the settings of the four angles of the
diffractometer needed to observe a
speciÜc (h k l) reÛection, where (h k l)
are Miller indices. A computer controls the settings so that each (h k l)
is examined in turn and the diffraction intensity measured. This information enables the electron density
to be calculated, as the intensity of
the reÛection for a set of (h k l)
planes is proportional to the square
of the modulus of a function called
the structure factor F hkl of the set,
which is related to the electron density.
Fourier analysis The representation of a function f(x), which is periodic in x, as an inÜnite series of sine
and cosine functions:
f(x) = a 0 /2 + ∑
n=1
∞
(a n cosnx + b n sinnx)
A series of this type is called a
*Fourier series. If the function is periodic with a period 2π, the coefÜcients a 0 , a n , b n are:
a 0 = ∫
+π
–π f(x)dx,
a n = ∫
+π
–π f(x) cosnxdx, (n = 1,2,3,…),
b n = ∫
+π
–π 1/π f(x)sinnxdx, (n = 1,2,3,…).
Fourier analysis and Fourier series
are named after the French mathematician and engineer Joseph Fourier
(1768–1830). Fourier series have
many important applications in
mathematics, science, and engineering, having been invented by Fourier
in the Ürst quarter of the 19th century in his analysis of the problem of
heat conduction.
Fourier series An expansion of a
formate
232
f
www.AzShimi.ir www.AzShimi.com
with methanol as a stabilizer; r.d.
1.075–1.085. When kept at temperatures below 25°C a white polymer of
methanal separates out. It is used as
a disinfectant and preservative for
biological specimens.
formate See methanoate.
formic acid See methanoic acid.
formula A way of representing a
chemical compound using symbols
for the atoms present. Subscripts are
used for the numbers of atoms. The
molecular formula simply gives the
types and numbers of atoms present.
For example, the molecular formula
of ethanoic acid is C 2 H 4 O 2 . The empirical formula gives the atoms in
their simplest ratio; for ethanoic acid
it is CH 2 O. The structural formula
gives an indication of the way the
atoms are arranged. Commonly, this
is done by dividing the formula into
groups; ethanoic acid can be written
CH 3 .CO.OH (or more usually simply
CH 3 COOH). Structural formulae can
also show the arrangement of atoms
or groups in space.
formula weight The relative molecular mass of a compound as calculated from its molecular formula.
formylation A chemical reaction
that introduces a formyl group
(methanoyl, –CHO) into an organic
molecule.
formyl group The group HCO–.
fossil fuel Coal, oil, and natural
gas, the fuels used by man as a
source of energy. They are formed
from the remains of living organisms
and all have a high carbon or hydrogen content. Their value as fuels relies on the exothermic oxidation of
carbon to form carbon dioxide (C +
O 2 → CO 2 ) and the oxidation of hydrogen to form water (H 2 + ½O 2 →
H 2 O).
four-circle diffractometer An instrument used in X-ray crystallography to automatically determine the
shape and symmetry of the unit cell
of a crystal. The crystal is placed in
the goniometer head with an arbitrary orientation. If the dimensions
of the unit cell have been determined, they can be used to calculate
the settings of the four angles of the
diffractometer needed to observe a
speciÜc (h k l) reÛection, where (h k l)
are Miller indices. A computer controls the settings so that each (h k l)
is examined in turn and the diffraction intensity measured. This information enables the electron density
to be calculated, as the intensity of
the reÛection for a set of (h k l)
planes is proportional to the square
of the modulus of a function called
the structure factor F hkl of the set,
which is related to the electron density.
Fourier analysis The representation of a function f(x), which is periodic in x, as an inÜnite series of sine
and cosine functions:
f(x) = a 0 /2 + ∑
n=1
∞
(a n cosnx + b n sinnx)
A series of this type is called a
*Fourier series. If the function is periodic with a period 2π, the coefÜcients a 0 , a n , b n are:
a 0 = ∫
+π
–π f(x)dx,
a n = ∫
+π
–π f(x) cosnxdx, (n = 1,2,3,…),
b n = ∫
+π
–π 1/π f(x)sinnxdx, (n = 1,2,3,…).
Fourier analysis and Fourier series
are named after the French mathematician and engineer Joseph Fourier
(1768–1830). Fourier series have
many important applications in
mathematics, science, and engineering, having been invented by Fourier
in the Ürst quarter of the 19th century in his analysis of the problem of
heat conduction.
Fourier series An expansion of a
formate
232
f
www.AzShimi.ir www.AzShimi.com