Chapter 15, Problem 15.7YT

Interpretation Introduction

Interpretation:

For each compound from Table 15-1 that contains only carbon and hydrogen, the number of conjugated $\text{π}$ bonds that make up the largest $\text{π}$ system is to be determined and this number is to be compared to the compound’s longest-wavelength ${\text{λ}}_{\text{max}}$.

Concept introduction:

A compound containing at least one $\text{π}$ bond absorbs photons in the UV region. The UV spectrum of such compounds contains one or more bands or peaks. The wavelength at which the absorbance is maximum is ${\text{λ}}_{\text{max}}$ for that band or peak. The longest wavelength peak (${\text{λ}}_{\text{max}}$) corresponds to the HOMO-LUMO transition as it requires the lowest energy. The value of ${\text{λ}}_{\text{max}}$ for this peak depends on the number of $\text{π}$ bonds that are conjugated. As the number of conjugated $\text{π}$ bonds increases, the value of the longest-wavelength ${\text{λ}}_{\text{max}}$ increases.

Answer to Problem 15.7YT

The value of longest-wavelength ${\text{λ}}_{\text{max}}$ increases with the number of conjugated double bonds in the compound.

Explanation of Solution

The compounds from Table 15-1 that contain only C and H, the number of conjugated double bonds in them and their longest-wavelength ${\text{λ}}_{\text{max}}$ values are

Compound	Conjugated $\text{π}$ bonds	${\text{λ}}_{\text{max}}$ (nm)	Compound	Conjugated $\text{π}$ bonds	${\text{λ}}_{\text{max}}$ (nm)
Alkanes, cycloalkanes	0	< 150		2	223
	0	161		2	223.5
	0	177		2	224
	0	178		2	239
	0	182		2	256
	0	185		3	274
	2	217		4	290
				11	455

For compounds that contain only one double/triple bond – ethene, $\text{hex-1-ene}$, cyclohexene, and $\text{hex-1-yne}$– the longest-wavelength ${\text{λ}}_{\text{max}}$ is about 180 nm or less. It is about the same for the non-conjugated compound $\text{penta-1, 4-diene}$. For compounds with two conjugated $\text{π}$ bonds – $\text{buta-1, 3-diene}$, cis and trans $\text{penta-1, 3-diene}$, $\text{methylbuta-1, 3-diene}$, cyclopentadiene, and $\text{cyclohexa-1, 3-diene}$ – it is about 225 nm. For $\text{hexa-1, 3, 5-triene}$ with three conjugated double bonds, it is 274 nm. For $\text{octa-1, 3, 5, 7-tetraene}$ with four conjugated double bonds, it is 290 nm. Finally, for $\text{β-carotene}$ which has eleven conjugated double bonds, it is 450 nm.

As the number of conjugated $\text{π}$ bonds increases, the energy gap between HOMO and LUMO decreases. Consequently, the value of the longest-wavelength ${\text{λ}}_{\text{max}}$ increases.

Conclusion

The value of the longest-wavelength ${\text{λ}}_{\text{max}}$ depends on the number of $\text{π}$ bonds in the conjugated $\text{π}$ system.