What is Beer-Lambert Law?

Contributed by:

Jonathan James Fri, Jan 14, 2022 10:58 PM UTC

The highlights are:
1. Introduction
2. Quantitative analysis
3. Statistical analysis
4. Confidence limits
5. Control data
6. Significance

1. Lab 6: Saliva Practical
Beer-Lambert Law
University of
Lincoln
presentation
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2. This session….
• Overview of the practical…
• Statistical analysis….
• Take a look at an example control
chart…
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3. The Practical
• Determine the thiocyanate (SCN-) in a
sample of your saliva using a colourimetric
method of analysis
• Calibration curve to determine the [SCN-] of
the unknowns
• This was ALL completed in the practical
class
• Some of your absorbance values may have
been higher than the absorbance values of
your top standards… is this a problem????
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4. Types of data
Non numerical i.e what is present?
Numerical: i.e. How much is present?
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5. Beer-Lambert Law
Beers Law states that absorbance is
proportional to concentration over a
certain concentration range
A = cl
A = absorbance
 = molar extinction coefficient (M-1 cm-1 or mol-1 L cm-1)
c = concentration (M or mol L-1)
l = path length (cm) (width of cuvette)
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6. Beer-Lambert
Law
• Beer’s law is valid at low concentrations,
but breaks down at higher
concentrations
• For linearity, A < 1
1
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7. Beer-Lambert Law
• If your unknown has a
higher concentration
than your highest
standard, you have to
ASSUME that linearity 1
still holds (NOT GOOD
for quantitative
analysis)
• Unknowns should
ideally fall within the
standard range
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8. Quantitative Analysis
– If A > 1:
• Dilute the sample
• Use a narrower cuvette
– (cuvettes are usually 1 mm, 1 cm or 10 cm)
• Plot the data (A v C) to produce a
calibration ‘curve’
• Obtain equation of straight line (y=mx)
from line of ‘best fit’
• Use equation to calculate the
concentration of the unknown(s)
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9. Quantitative Analysis
Calibration curve showing absorbance as
a function of metal concentration
1.2
Absorbance ( no units)
1 y =0.9982x
2
0.8 R =0.9996
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
-1
Concentration (mg L )
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10. Statistical Analysis
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11. Mean
The mean provides us with a typical value
which is representative of a distribution
thesum(å) of all theobservatio
ns
Mean
thenumber(N) of observations
thesum(å) of all theobservatio
ns
thenumber(N) of observations
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12. Normal Distribution
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13. Mean and Standard
Deviation
MEAN
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14. Standard Deviation
• Measures the variation of the
samples:
– Population std ()
– Sample std (s)
  = √((xi–µ)2/n)
• s =√((xi–µ)2/(n-1))
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15.  or s?
In forensic analysis, the rule of thumb
is:
If n > 15 use 
If n < 15 use s
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16. Absolute Error and Error %
• Absolute Error
Experimental value – True Value
• Error % Experiment
al value– TrueValue
100%
True value
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17. Confidence limits
1 = 68%
2 = 95%
2.5  = 98%
3 = 99.7%
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18. Control Data
• Work out the mean and standard
deviation of the control data
– Use only 1 value per group
• Which std is it?  or s?
• This will tell us how precise your
work is in the lab
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19. Control Data
• Calculate the Absolute Error and the
Error %
– True value of [SCN–] in the control = 2.0 x 10–3 M
• This will tell us how accurately you
work, and hence how good your
calibration is!!!
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20. Control Data
Plot a Control Chart for the control
data Quality Control Chart
4.00E-03
3.50E-03
Control thiocyanate concentration (mol/L)
3.00E-03
Control value
inner limit
inner limit
2.50E-03
outer limit
outer limit
group values
2.00E-03
1.50E-03
2
2.5 
1.00E-03
1 6 11 16 21 26 31
Measurement number
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21. Significance
• Divide the data into six groups:
– Smokers
– Non-smokers
– Male
– Female
– Meat-eaters
– Rabbits
• Work out the mean and std for each
group ( or s?)
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22. Significance
• Plot the values on a bar chart
• Add error bars (y-axis)
– at the 95% confidence limit – 2.0 
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23. Significance
Variation in [SCN-] in Saliva for VariousGroupsof
Forensic Science Students(not REAL data)
9
8
Mean [SCN-] (M)
7
6
5
4
3
2
1
0
Smokers Non- Male Female Lions Rabbits
Smokers
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24. Identifying Significance
• In the most simplistic terms:
– If there is no overlap of error bars
between two groups, you can be fairly
sure the difference in means is
significant
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25. Acknowledgements
• JISC
• HEA
• Centre for Educational Research and
Development
• School of natural and applied sciences
• School of Journalism
• SirenFM
• http://tango.freedesktop.org
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