Beers law Aecb

1
Beers law Aecb
See text 18-1 to 18-4 for more details.

• Why is it important?
• How is is derived?
• How do we implement it?

2
Uses of Beers law
Beers law uses light to measure concentrations.
Different molecules absorb at different
wavelengths.
Why?
3
They have different energy levels.
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Beers law Aecb
Individual molecules absorb differently at
different wavelengths. This implies that ee(l).
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Derivation of Beers Law
Schematic of a simple spectrometer.
Pf
Pi
Irradiance, P, is the energy per second per unit
area of the beam of light.
Transmittance is TPf/Pi
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Derivation of Aecb
Consider the change in irradiance dP shown
above. What is it a function of?
Here b is a constant of proportionality and c is
concentration.
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Divide both sides by P
Now integrate both sides.
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Now integrate both sides.
To obtain
For more details see 410-411.
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Sample Calculation

• Consider a solution of benzene in hexane. If the
  absorbance of your 1cm cell is 0.266 at l200nm,
  what is the e value for benzene?
• To solve this you need to know the concentration
  of your solution.

28.8mg C6H6 1g 1000ml 1mol C6H6
c
250 ml soln 1000mg 1L 78.11 g C6H6
eA /cb A/c
cC6H61.321x10-3M
e0.266/1.321x10-3
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Implementation of Beers Law
We first need to calculate e using a standard
(see page 85). To do this we make up solutions
of know concentrations of the species for which
we wish to determine e.
or
A
A
c
c
See bottom of page 417 for more on blanks.
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A Sample Beers Law Plot
The red line is a best fit to your data. See 5.1
for least squares fitting.
A
c
Is your data consistent with Beers Law?
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The answer depends on your error bars.
A
Note that I am assuming the error is in the A.
c
What can we say about the two sets of data shown
to the left?
A
c
How well do we really know the slope? What is
De? Assume Db is negligible.
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What if you have two species in solution?
See text 433-437 for more details.
What are the knowns and unknowns in the above Eq.?
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2 Eq. and 2 Unk.
Let Eijej(li)b
or
The solution to this Eq. is
or
Determining uncertainties in cs is more
difficult.
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Mathcad solution for two unknowns.
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A model spectrum
Calculate A at 540 and 560 nm.
A(540)1.2 A(560).32
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A model spectrum
A(540)1.2 A(560).32
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Beers law Aecb

• We have derived Beers law.
• We have used it to calculate concentrations.
• We have determined the uncertainty in
  concentration.
• We have not talked about errors in Beers law.