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Beer’s Law & Colorimetry. 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.

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### Absorbance

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

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

less dark “neck”

darker “belly”

A = solution.abc

### Beer’s Law

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 solution.

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.

absorbance 

concentration 

Using Graphs solution.

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

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

absorbance 

concentration 

### Colorimeters solution.

Transmittance solution.

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

A Comparison solution.

%Transmittance

absorbance 

concentration 

concentration 

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 solution. %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 solution. 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 solution.

• Calculate “A” for the transmittances in this data table.

• Graph “c” vs. “A” and get a best fit straight line.

• If an unknown K2CrO4 (aq) solution was measured at 53.7%T, what would be it’s concentration?