Beer’s Law and Concentration: Determination of Allura Red in Mouthwash Experiment 9.
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Beer’s Law and Concentration:Determination of Allura Red in
Mouthwash
Experiment 9
#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
Absorption and Emission
Molecular Absorption and Emission
Atoms:
Electronic states only
Molecules:
Vibrational states within electronic states
Molecular Spectra
400
500
600
700 (nm)
Absorption
Emission
Inte
nsi
ty
Bands vs. Lines (atoms)
Absorbed vs. Observed
Color absorbed → Complementary color observed
R
BGB
YG BV
VY
RVO
G
Allura Red
Formula:C18H14N2Na2O8S2
Molar mass: 496.42 g/mol
2Na+
During Absorption…
Starting e- arrangement:
After photon absorption:
Absorption is random
Photons collide with molecules
Certain probability of absorption
Transmittance, T
I0 I1 TI
I
0
1
T: ratio of light “in” vs. “out”= fraction of light passing through
Depends on:# of molecules b & cmolecules’ identity
Pathlength, b
Concentration,c
Transmittance and Pathlength
1
2
0
1
I
I
I
I
For cell with same pathlength: constant T
1
2
I
I
I0 I1
0
1
I
I
I2
Transmittance and Pathlength
1
2
I
I
0
1
I
I
2
0
1
1
2
0
1
0
2
I
I
I
I
I
I
I
I
I0
For cells with same pathlength: constant TDouble pathlength: square T
I2
#1
#2
2121total TTTT
T and Pathlength
1-b
b
I
I
0
1
I
I
1-b
b
0
1
b
0
1
0
b
I
I
I
I
I
I
I
I
I0
For b cells (b pathlengths = 1cm) Tb
Ib
#1
#b
b1b
1total TTTT
…
b in power
Concentration
# photons absorbed depends on # molecules in path
I0 I1
Transmittance and Concentration
1
2
I
I
b
0
cm 1
I
IT
0
1
I
I
I0 I1 I2
1.0 M reference solution gives
2.0 M: Double concentration,c→“Double pathlength, b”…
bc
0
1M cm, 1bc1 I
ITT
…
bc in powerpathlength and concentration
Molar Extinction Coefficient,
Probability of absorption
–Specific to molecule–Function of
max Most efficient
absorption –Peak of absorption curve –“Best ” for experiment
T: concentration c & pathlength bWhat about: molecular identity?
b, c, and
εcb-bcε-
bc
0
1M cm, 1 1010I
IT
I
Ilogε
0
1M cm, 1
in powermolar extinction coeff.
ε
0
1M cm, 1 10I
I
Therefore:
bc
0
1M cm, 1bc1 I
ITT
bc in powerpathlength and concentration
Absorbance
Beer’s Law: Defines absorbance, A
εbcA
A
TAεbc
10log
log
A: Directly proportional to concentration
high A ≡ low T
Part 1 Spectral Profile of Allura Red, max
Use stock solution (record conc.) cstock
Record %T, 400 – 700 nm %T 10 nm intervals near max
20 nm intervals elsewhere
Record cell width, b = pathlength b
Calculate A A
Plot A vs.
Determine max max
Part 1: max
400
500
600
700 (nm)
Absorption Transmitta
nceIn
ten
sit
y
Find where
%T is lowest
A is highest
This is not necessarily Allura Red
(but would appear red)
Spectral Profile (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
Spectral profile - Allura Red
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
400 450 500 550 600 650 700
wavelength (nm)
Abs
orba
nce
Part 2 Absorbance for Various Concentrations
Stock solution, 4 dilutions, and blank
n1 = n2
M1 . V1 = M2 . V2
Determine %T at max for each %T
Calculate A A
Plot A vs. conc (Beer’s Law plot)
Slope = b b
Part 2 Concentrations1 blank: pure DI water M0 = 0.00 M allura red
1 stock: 0.002% 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
MsolutionLsolutiong
redalluragredalluramol
solutiongredallurag 5
001.01
42.4961
100002.0 104%002.0
diluteedconcentratdilutediluteedconcentratedconcentrat n nVMVM
Beer’s Law
,b constant
xm
y
cεb A
TlogA
A 1010%100
%TT εbc
c varied
Beer’s Law Plot
cεbA xy m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Molarity
Abs
orba
nce
y = 1.9 x
y
εb
x
yslope
x
Beer’s Law Plot example
Dilution Factor
M (mol/L) T
A = -logT
0 0 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 = ×b×c
Slope = A/c
Here: ×b = 24943
A 1-cm cell: 24943 cm-1M-1
Absorbance vs. Concentration - Allura Red
y = 24943x
R2 = 0.9995
0.000
0.200
0.400
0.600
0.800
1.000
1.200
0.E+00 1.E-05 2.E-05 3.E-05 4.E-05
Molarity (mol/ L)
Abs
orba
nce
Part 3 Allura Red Concentration in Mouthwash
Use 1:25 dilution
Determine %T at max %T
Calculate A A
Measure b b
Find concentration, c c
soεbcA b
Ac
Part 3 Example
Mouthwash trials (1:25 dilution):
T A Mdilute
Mconcentrate
d
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 6E-06 1.6E-04Mdilute= A/(b×) if cell length b is constant
Average Mconcentrated = 1.7×10-4 M = 2×10-4 M
ReportAbstract
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
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