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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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Beer s law colorimetry

Beer’s Law & Colorimetry


Absorbance

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 is the distance light travels through a solution.

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”


Beer s law

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
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
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

Colorimeters solution.


Transmittance
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
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
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?


Answer
Answer solution.

At 53.7% T,

A = -log(0.537)

= 0.270

From the graph,

@ 0.270 for “A”,

c = 0.338M


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