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