Beer’s Law & Colorimetry

AbsorbanceABSORBANCE 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 LengthPATH LENGTH is the distance light travels through a solution.

Note how the solution in the “belly” of this volumetric flask is darker than the solution in the neck.

PATH LENGTH (b) is directly proportional to absorbance (A) : A = kb.

less dark “neck”

darker “belly”

Beer’s Law

A = abc

absorbance

path length

concentration

constant (nature of solute)

Beer’s Law puts all the factors that affect absorbance together in one equation.

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.

Beer’s Law Graphs

concentration

ab

sorb

an

ce

Then, we can find the concentration of any “unknown” by measuring it’s absorbance and interpolating the concentration.

Using Graphs

concentration

ab

sorb

an

ce

If we can measure the absorbance of several known concentrations of a solution, we can make a straight line graph.

Colorimeters

Transmittance

• “100%” = a perfectly transparent material that lets all light through.

• “0%” = a completely opaque material that does not let any light through

Colorimeters actually measure TRANSMITTANCE: the amount of light that goes through a solution.

A Comparison

concentration

ab

sorb

an

ce

concentration

%Tr

ansm

itta

nce

At c =0, A = 0.

At c = ∞, A = ∞.A and c are directly proportional.

At c =0, %T =100.

At c = ∞, A = 0.A and c are exponentially related.

A %TAbsorbance 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 1000.125 79.40.250 63.10.375 50.1

Answer

At 53.7% T,A = -log(0.537) = 0.270

From the graph, @ 0.270 for “A”, c = 0.338M