1. Beer’s Law and Concentration: Determination of Allura Red in Mouthwash
Experiment 9

2. #9 Beer’s Law and Concentration: Determination of Allura Red in Mouthwash
Goal:
To employ spectroscopic quantitative analysis of Allura Red concentrations using Beer’s Law
Method:
Perform serial dilutions to vary concentration
Measure %transmittance measurements
Determine absorbance
Relate absorbance to concentration

3. Absorption and Emission

4. Molecular Absorption and Emission
Atoms:
Electronic states only
Molecules:
Vibrational states within electronic states

5. Molecular Spectra Bands vs. Lines (atoms) Absorption Emission 400 500
600
700
l (nm)
Absorption
Emission
Intensity
Bands vs. Lines (atoms)

6. Absorbed vs. Observed Color absorbed → Complementary color observed RBG B YG BV V Y RV O G
Color absorbed → Complementary color observed

7. Allura Red
2Na+
Formula: C18H14N2Na2O8S2
Molar mass: g/mol

8. During Absorption…
Starting e- arrangement:
After photon absorption:

9. Absorption is random Photons collide with molecules
Certain probability of absorption

10. Transmittance, T I0 I1 T: ratio of light “in” vs. “out”
= fraction of light passing through
Depends on:
# of molecules b & c
molecules’ identity e
Pathlength, b I0 I1
Concentration,c

11. Transmittance and Pathlength
For cell with same pathlength: constant T I0 I1 I2

12. Transmittance and Pathlength
For cells with same pathlength: constant T
Double pathlength: square T #1 #2 I0 I2

13. … T and Pathlength I0 Ib For b cells (b pathlengths = 1cm)  Tb #1 #b
b in power

14. Concentration
# photons absorbed depends on # molecules in path I0 I1

15. Transmittance and Concentration
1.0 M reference solution gives I0 I1 I2 …
2.0 M: Double concentration,c→“Double pathlength, b”…
bc in power
pathlength and concentration

16. Molar Extinction Coefficient, 
T: concentration c & pathlength b
What about: molecular identity?
 Probability of absorption
Specific to molecule
Function of l
lmax Most efficient absorption
Peak of absorption curve
“Best l” for experiment

17. b, c, and  Therefore: bc in power in power
pathlength and concentration
in power
molar extinction coeff.
Therefore:

18. A: Directly proportional to concentration
Absorbance
Beer’s Law: Defines absorbance, A
A: Directly proportional to concentration
high A ≡ low T

19. Part 1 Spectral Profile of Allura Red, lmax
Use stock solution (record conc.) cstock
Record %T, 400 – 700 nm %T
10 nm intervals near lmax
20 nm intervals elsewhere
Record cell width, b = pathlength b
Calculate A A
Plot A vs. l
Determine lmax lmax

20. Part 1: lmax Find l where %T is lowest Absorption A is highest
400
500
600
700
l (nm)
Absorption
Transmittance
Intensity
Find l where
%T is lowest
A is highest
This is not necessarily Allura Red
(but would appear red)

21. Spectral Profile l (nm) Absorbance 400 0.078 420 0.130 440 0.268 460
0.555
480
0.966
490
1.189
500
1.383
510
1.485
520
1.515
530
1.459
540
1.217
560
0.395
580
0.063
600
0.019
620
0.015
640
0.010
660
0.009
680
0.006
700
0.000

22. Part 2 Absorbance for Various Concentrations
Stock solution, 4 dilutions, and blank
n1 = n2
M1 . V1 = M2 . V2
Determine %T at lmax for each %T
Calculate A A
Plot A vs. conc (Beer’s Law plot)
Slope = eb eb

23. Part 2 Concentrations 1 blank: pure DI water M0 = 0.00 M allura red
1 stock: % allura red M5 = 4×10-5 M
4 dilutions, each by ½:
(4×10-5 M)(25.00 mL) = (M1)(50.00 mL) M1 = 2×10-5 M
(2×10-5 M)(25.00 mL) = (M2)(50.00 mL) M2 = 1×10-5 M
(1×10-5 M)(25.00 mL) = (M3)(50.00 mL) M3 = 5×10-6 M
(5×10-6 M)(25.00 mL) = (M4)(50.00 mL) M4 = 2×10-6 M

24. Beer’s Law
e,b constant
c varied

25. Beer’s Law Plot
y = 1.9 x

26. Beer’s Law Plot example
Dilution Factor
M (mol/L) T
A = -logT
1.00
0.000
1/16
2.E-06
0.87
0.060
1/8
5.E-06
0.73
0.137
1/4
1.E-05
0.58
0.240
1/2
2.E-05
0.32
0.495 1
4.E-05
0.10
1.000
Stock M
4E-05
mol/L
A =
e×b×c
Slope =
DA/Dc
Here:
e×b =
24943
A 1-cm cell:
e =
24943
cm-1M-1

27. Part 3 Allura Red Concentration in Mouthwash
Use 1:25 dilution
Determine %T at lmax %T
Calculate A A
Measure b b
Find concentration, c c

28. Part 3 Example Mouthwash trials (1:25 dilution): T A MdiluteT A
Mdilute
Mconcentrated
0.68
0.167
7E-06
1.7E-04
0.70
0.155
6E-06
1.6E-04
0.65
0.187
8E-06
1.9E-04
0.69
0.161
Mdilute= A/(b×e) if cell length b is constant
Average Mconcentrated = 1.7×10-4 M = 2×10-4 M

29. Report Abstract Data/Results Sample calculations including:
Absorbance from transmittance
Dilution
Slope and extinction coefficient
[Allura red]cuvette and [Allura red]mouthwash
# allura red molecules in 1 mL mouthwash
Discussion/review questions