14.7 Ultraviolet Spectroscopy

Ultraviolet Spectroscopy

Detection of conjugated systems

UV spectroscopy detects conjugated π electron systems by measuring how molecules absorb ultraviolet light. The technique works because conjugated π electrons undergo electronic transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) when they absorb UV photons.

The energy gap between the HOMO and LUMO determines which wavelength of light gets absorbed. Here's the key relationship to remember:

• More extensive conjugation → smaller HOMO-LUMO gap → absorption at longer wavelengths (this shift toward longer wavelengths is called a bathochromic shift, or "red shift")
• Less conjugation → larger HOMO-LUMO gap → absorption at shorter wavelengths

The functional groups responsible for UV absorption are called chromophores. Common chromophores include:

• Conjugated alkenes and alkynes
• Aromatic rings (benzene and derivatives)
• Carbonyl groups (aldehydes, ketones)
• Azo groups ($-N=N-$)

Isolated double bonds absorb in the far UV (below ~200 nm), which is hard to measure with standard instruments. That's why UV spectroscopy is most useful for conjugated systems, which absorb in the more accessible 200–400 nm range.

Wavelength vs energy absorption

The energy of a photon is inversely proportional to its wavelength:

$E = \frac{hc}{\lambda}$

• $E$ = energy of the photon
• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)
• $c$ = speed of light ($3.00 \times 10^{8}$ m/s)
• $\lambda$ = wavelength

Shorter wavelengths carry more energy; longer wavelengths carry less. This is why extending conjugation (which shrinks the HOMO-LUMO gap) shifts absorption toward longer, lower-energy wavelengths.

A UV spectrum plots absorbance ($A$) on the y-axis against wavelength ($\lambda$) on the x-axis. The peak of the absorption curve is reported as $\lambda_{max}$, the wavelength of maximum absorption. Some representative values:

• A conjugated diene like 1,3-butadiene: $\lambda_{max} \approx 217$ nm
• A conjugated triene: $\lambda_{max} \approx 270$ nm
• β-carotene (11 conjugated double bonds): $\lambda_{max} \approx 452$ nm (visible light, which is why carrots are orange)

The trend is consistent: each additional conjugated double bond pushes $\lambda_{max}$ to a longer wavelength.

Concentration from Beer-Lambert law

The Beer-Lambert law connects absorbance to concentration, making UV spectroscopy useful for quantitative analysis:

$A = \varepsilon bc$

• $A$ = absorbance (unitless)
• $\varepsilon$ = molar absorptivity (units: $L \cdot mol^{-1} \cdot cm^{-1}$), a constant that reflects how strongly a substance absorbs at a given wavelength
• $b$ = path length of the sample cell, typically 1 cm for standard cuvettes
• $c$ = molar concentration of the sample ($mol/L$)

A high $\varepsilon$ value means the compound is a strong absorber at that wavelength. Each compound has its own characteristic $\varepsilon$ at each wavelength.

Calculating concentration step-by-step:

1. Record the absorbance ($A$) of your sample at $\lambda_{max}$
2. Look up the molar absorptivity ($\varepsilon$) for the compound at that wavelength
3. Confirm the path length ($b$) of your cuvette (usually 1 cm)
4. Rearrange and solve: $c = \frac{A}{\varepsilon b}$

Example: A solution of a conjugated diene shows $A = 0.850$ at its $\lambda_{max}$. The molar absorptivity at that wavelength is $\varepsilon = 17{,}000 \; L \cdot mol^{-1} \cdot cm^{-1}$, and the cuvette path length is 1.00 cm.

$c = \frac{0.850}{17{,}000 \times 1.00} = 5.0 \times 10^{-5} \; mol/L$

One important limitation: the Beer-Lambert law is only reliable at low to moderate concentrations. At very high concentrations, the linear relationship between absorbance and concentration breaks down.

Factors Affecting UV Spectra

Electronic transitions differ in the energy they require, and this affects where peaks appear:

• $\pi \rightarrow \pi^*$ transitions involve promotion of a π bonding electron to a π antibonding orbital. These are typically high-intensity absorptions and are the main transitions you see in conjugated alkenes and aromatics.
• $n \rightarrow \pi^*$ transitions involve promotion of a nonbonding (lone pair) electron into a π antibonding orbital. These are lower-intensity absorptions, commonly seen in carbonyls. They usually appear at longer wavelengths than $\pi \rightarrow \pi^*$ transitions for the same molecule because the energy gap is smaller.

Solvent effects can shift absorption peaks. Polar solvents tend to stabilize the ground state of $n \rightarrow \pi^*$ transitions, increasing the energy gap and shifting $\lambda_{max}$ to shorter wavelengths (a hypsochromic shift, or "blue shift"). For $\pi \rightarrow \pi^*$ transitions, polar solvents often cause a slight bathochromic (red) shift. When reporting UV data, always note the solvent used.