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 λ_{max} and also maximum absorptivity ε_{max}:
λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo}
where,
λ_{max }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
R_{endo} is the number of rings with endocyclic double bonds in the conjugated system
R_{exo} is the number of rings with exocyclic double bonds in the conjugated system.
and
ε_{max} = (1.74 x 10^{4}) 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 (λ_{max}) and the maximum absorptivity (ε_{max})
Sample Problem 1: β-Carotene
β-carotene is a precursor of vitamin A which is a terpenoid derived from several isoprene units. The observed λ_{max} of β-carotene is 452 nm, while the observed ε_{max} is 15.2 x 10^{4}. Let us therefore use Fieser-Kuhn rules to calculate the λ_{max }and the ε_{max }for β-carotene.
Name of Compound | β-Carotene |
Base Value | 114 nm |
M (number of alkyl substituents) | 10 |
n (number of conjugated double bonds) | 11 |
R_{endo} (number of endocyclic double bonds) | 2 |
R_{exo} (number of exocyclic double bonds) | 0 |
Substituting in equation λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo} |
= 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. λ_{max} = 453.30 nm |
λ_{max} observed practically | 452nm |
Calculate ε_{max} using equation: ε_{max} = (1.74 x 10^{4}) n |
= (1.74 x 10^{4}) 11
Calc. ε_{max}= 19.14 x 10^{4} |
Practically observed ε_{max} | 15.2 x 10^{4} |
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.
Name of Compound | all-trans-lycophene |
Base Value | 114 nm |
M (number of alkyl substituents) | 8 |
n (number of conjugated double bonds) | 11 |
R_{endo} (number of endocyclic double bonds) | 0 |
R_{exo} (number of exocyclic double bonds) | 0 |
Substituting in equation λ_{max} = 114 + 5M + n (48.0 – 1.7 n) – 16.5 R_{endo} – 10 R_{exo} |
= 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. λ_{max} = 476.30 nm |
λ_{max} observed practically | 474nm |
Calculate ε_{max} using equation: ε_{max} = (1.74 x 10^{4}) n |
= (1.74 x 10^{4}) 11
Calc. ε_{max}= 19.14 x 10^{4} |
Practically observed ε_{max} | 18.6 x 10^{4} |
Also Checkout These Other Pages:
- Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Dienes and Polyenes
- Woodward-Fieser Rules to Calculate Wavelength of Maximum Absorption (Lambda-max) of Conjugated Carbonyl Compounds
- Sample Problems Using Woodward-Fieser Rules
Books on Analytical Chemistry and Spectroscopy
Check out these good books for analytical chemistry and spectroscopy
Thank you Akul for this nice presentation…