Beer’s Law &
Colorimetry
Absorbance
ABSORBANCE is the amount of light that gets
“stopped” by a material
• “Zero” = a perfectly transparent material that lets
all light through.
• “Infinity” = a completely opaque material that does
not let any light through.
Absorbance (A) is directly proportional to
concentration (c) : A = kc.
This is a mathematical model for something you
already know: a darker solution is a more
concentrated one.
Path Length
PATH LENGTH is the distance light travels through a
solution.
PATH LENGTH (b) is directly proportional to
absorbance (A) : A = kb.
less dark
“neck”
darker “belly”
Note how the solution in the
“belly” of this volumetric flask is
darker than the solution in the
neck.
Beer’s Law
A = abc
absorbance
constant
(nature of solute)
path length
concentration
Beer’s Law puts all the factors
that affect absorbance together
in one equation.
Beer’s Law Graphs
absorbance 
If we are using only one solute, then “a” is a constant. If we
are are careful to always use the same path length, then
“b” is a constant, too.
This simplifies Beer’s Law to: A = kc.
concentration 
If we can measure the
absorbance of several
known concentrations of a
solution, we can make a
straight line graph.
absorbance 
Using Graphs
concentration 
Then, we can find the concentration of any
“unknown” by measuring it’s absorbance and
interpolating the concentration.
Colorimeters
Transmittance
Colorimeters actually measure TRANSMITTANCE: the
amount of light that goes through a solution.
• “100%” = a perfectly transparent
material that lets all light through.
• “0%” = a completely opaque material
that does not let any light through
absorbance 
%Transmittance
A Comparison
concentration 
concentration 
At c =0, A = 0.
At c =0, %T =100.
At c = ∞, A = ∞.
A and c are directly
proportional.
At c = ∞, A = 0.
A and c are exponentially
related.
A %T
Absorbance and transmittance are related exponentially.
10-A = %T/100
so if A = 1: 10-1 = 0.1 = T, or %T = 10%
if A = 2, 10-2 = 0.01 = T or %T = 1%
We will usually deal with A < 1.
if A = 0.5, 10-0.5 = 0.316 = T or %T = 31.6%
if A = 0.1, 10-0.1 = 0.794 = T or %T = 79.4%
Make sure you can duplicate these calculations on
YOUR calculator!
%T A
Most of the time, we need to convert %T (from the colorimeter)
to A (so we can plot the direct relationship between A and c.
A = -log(%T/100)
so if %T = 90%, A = -log (90/100) = -log(.90) = 0.045
if %T = 45%, A = -log (45/100) = 0.347
Make sure you can duplicate these calculations on YOUR
calculator!
Sample Problem
1. Calculate “A” for the
transmittances in this data
table.
2. Graph “c” vs. “A” and get a
best fit straight line.
3. If an unknown K2CrO4 (aq)
solution was measured at
53.7%T, what would be it’s
concentration?
K2CrO4 (aq)
Concentration (M)
%Transmittance
0.000
0.125
100
79.4
0.250
0.375
63.1
50.1
Answer
At 53.7% T,
A = -log(0.537)
= 0.270
From the graph,
@ 0.270 for “A”,
c = 0.338M