Ultraviolet-Visible (UV-Vis) Spectroscopy – Fieser-Kuhn Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Polyenes (with Sample Problems)

Introduction

Woodward-Fieser rules work well for conjugated dienes and polyenes with upto 4-double bonds or less. Certain plant pigments such as carotenoids have even more than 4 conjugated double bonds. For conjugated polyenes having more than 4 double bonds, the Fieser-Kuhn rules must be applied in order to obtain the wavelength of maximum absorption.

Fieser-Kuhn Rule for Conjugated Polyenes

According to the Fieser-Kuhn rule the following equation can be used to solve for the wavelength of maximum absorption λmax and also maximum absorptivity εmax:

λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo

where,
λmax is the wavelength of maximum absorption
M is the number of alkyl substituents / ring residues in the conjugated system
n is the number of conjugated double bonds
Rendo is the number of rings with endocyclic double bonds in the conjugated system
Rexo is the number of rings with exocyclic double bonds in the conjugated system.

and

εmax = (1.74 x 104) n

where,
εmax
is the maximum absorptivity
n is the number of conjugated double bonds.

Thus using the above equations, one can get the wavelength of maximum absorbance (λmax) and the maximum absorptivity (εmax)

Sample Problem 1: β-Carotene

β-carotene is a precursor of vitamin A which is a terpenoid derived from several isoprene units. The observed λmax of β-carotene is 452 nm, while the observed εmax is 15.2 x 104. Let us therefore use Fieser-Kuhn rules to calculate the λmax and the εmax for β-carotene.

beta-carotene solved using fieser-kuhn rules

Name of Compound β-Carotene
Base Value 114 nm
M (number of alkyl substituents) 10
n (number of conjugated double bonds) 11
Rendo (number of endocyclic double bonds) 2
Rexo (number of exocyclic double bonds) 0
Substituting in equation
λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo
= 114 + 5(10) + 11 (48.0-1.7(11)) – 16.5 (2) – 10 (0)

= 114 + 50 + 11 (29.3) – 33 – 0

= 114 + 50 + 322.3 – 33

Calc. λmax = 453.30 nm

λmax observed practically 452nm
Calculate εmax using equation:
εmax = (1.74 x 104) n
= (1.74 x 104) 11

Calc. εmax= 19.14 x 104

Practically observed εmax 15.2 x 104

Sample Problem 2: all-trans-Lycophene

Lycophene (all-trans-lycophene) is a bright red carotenoid pigment found in tomatoes and other red fruits and vegetables. However, lycophene has no vitamin A like activity.

Wavelength of maximum absorption for all-trans-lycophene

Name of Compound all-trans-lycophene
Base Value 114 nm
M (number of alkyl substituents) 8
n (number of conjugated double bonds) 11
Rendo (number of endocyclic double bonds) 0
Rexo (number of exocyclic double bonds) 0
Substituting in equation
λmax = 114 + 5M + n (48.0 – 1.7 n) – 16.5 Rendo – 10 Rexo
= 114 + 5(8) + 11 (48.0-1.7(11)) – 16.5 (0) – 10 (0)

= 114 + 40 + 11 (29.3) – 0 – 0

= 114 + 40 + 322.3 – 0

Calc. λmax = 476.30 nm

λmax observed practically 474nm
Calculate εmax using equation:
εmax = (1.74 x 104) n
= (1.74 x 104) 11

Calc. εmax= 19.14 x 104

Practically observed εmax 18.6 x 104

Also Checkout These Other Pages:

  1. Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Dienes and Polyenes
  2. Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Carbonyl Compounds
  3. Sample Problems Using Woodward-Fieser Rules

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