P athlength b e ffects since we now understand that

P
ATHLENGTH
( b ) E
FFECTS
Since we now understand that more light will be absorbed as the amount of solute increases
oncentratio akes sense that, in passing though a thicker sample, more light will be
hat light travels through the sample is called
e bottom in the deep end. The light reflected off the
hort path length”
( I
out
[2] ) is greatly reduced.
ed.
(c n effect), it m
absorbed. The distance t

max

max
I
in
I
out
[1
the pathlength.
You may have noticed this looking for something lost in a swimming
pool. Looking into the shallow end you can easily see the bottom. It’s
harder to see th
I
in
I
out
[2]
]
bottom encounters more solute particles passing though more liquid.
See the figure to the right. Again the measurements are made at 
max
,
and the incident intensities are the same. Much more light passes thro
sample ( I
out
[1] ). In the longer pathlength case, the transmitted light
ugh a “s
You can imagine that, at some pathlength, effectively no light is transmitt
Because absorbance is directly proportional to path length ( b A  ), in designing an experiment,
you need to ensure that all measurements are made using the same pathlength. Fortunately, the
cuvets we use the standard pathlength of 1 cm.
M
OLAR
A
BSORPTIVITY
( a ) E
FFECTS
Different substances absorb light of different wavelengths to different extents. Where chlorophyll
s reen light least, the dye in strawberry Kool-Aid® absorbs green wavelengths the most.
ependent on the particular substance, wavelength, and, to a
absorb g
Molar absorptivity, a, (
a A 
) is d
lesser degree, the instrument and concentration. Molar absorptivity is also known as the molar
extinction coefficient ( ε ).
B
EER
’
S
L
AW
E
QUATION
Currently we know that molar absorptivity (a), path length (b), and concentration (c) are all directly
ortional t absorbance (A). We can write a mathematical expression relating all of these
w (names sometimes include Bouguer and/or Lambert):
prop o
variables called Beer’s La
c b a A    ( 7 )
This should be an easy equation to remember, it’s as easy as your “abc’s”.
Unitless
ol L
c b a A  





   
L mol cm
   

m
(cm) 

 
The above dimensional-analysis equation shows that absorbance is unitless.
Given that our cuvets have a 1 cm pathlength, if absorbances set of standards of known
r absorptivity of the
ined by plotting a
for a
concentrations are measured by the spectrophotometer, then only the mola
solute at that wavelength is an unknown. Molar absorptivity can be determ
calibration curve. If we think of Beer’s Law as the general equation for a line as follows,

b mx y
c b a A
 
  
(“b” above is pathlength, “b” below is y-intercept!)
where y is absorbance (meas is the solute
concentration of the solution to which the absorbance corresponds. The slope of the calibration
ht:
ured by the spectrophotometer or colorimeter), x
curve equals the molar absorptivity times the pathlength. Pathlength (b) is 1 cm, leaving the
numerical value of the slope equal to the molar absorptivity.