beer’s law & colorimetry
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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 LawA = 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
abso
rban
ce
Then, we can find the concentration of any “unknown” by measuring it’s absorbance and interpolating the concentration.
Using Graphs
concentration
abso
rban
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
abso
rban
ce
concentration
%Tr
ansm
ittan
ce
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 AMost 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 Problem1. 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