Chemistry Reference
In-Depth Information
Log (
I
0
/
I
) is a dimensionless quantity (strictly speaking, a logarithm of a
ratio of light intensities) and is defined as
absorbance
. Absorbance is the
quantity measured and plotted in spectrophotometry. Thus Beer's law states
that absorbance is proportional to concentration.
The second relationship is Lambert's law, (named after the German
physicist Johann Heinrich Lambert) which states that the 'intensity of a
beam of parallel, monochromatic light decreases exponentially as the
light travels through a thickness of
homogeneous medium', expressed
mathematically as
I
0
e
k
l
(7.2)
where
I
and
I
0
are as before,
l
is the thickness of the medium (or path length)
through which the light passes and
k
I
is (another) constant.
Taking logarithms,
I
0
log
—
k
l
I
i.e. absorbance is proportional to path length.
These two fundamental equations are so similar that they can be
combined into one relationship, the Beer-Lambert law or equation, which
can be expressed as
I
0
Absorbance log
—
kcl
I
(7.3)
Here
k
is yet another constant, the value of which depends on the units used
for the concentration term,
c
, and on the path length, although this is
usually 1 cm.
If the units of concentration are molarity (i.e. number of moles per
litre), then the constant is
e
(the Greek letter 'epsilon') and is known as the
molar absorptivity
, with units of L mol
-1
cm
-1
, although the units are
seldom expressed.
e
is equal to the absorbance of a 1
M
solution in a cell of
path length 1 cm and is usually a large number, approximately
10 000-20 000. In this case the Beer-Lambert equation is written as
A
ecl
(7.4)
When the concentration of the sample is expressed in percentage weight in
volume (% w/v) or g/100 mL, the constant used is
A
1%, 1 cm, usually written
as
A
1
, and is called the
specific absorbance
, with units of dL g
-1
cm
-1
although, again, the value is usually quoted without units. The
A
1
value is
very useful in pharmacy and pharmaceutical analyses where the molecular
weight of the sample may be unknown (e.g. when analysing a macro-
