# 28.E: Photochemistry (Exercises)

Exercise 28-1 Suppose absorption of light by a diatomic molecule $$\ce{A-B}$$ in the lowest vibrational level of the ground state always resulted in dissociation into $$\ce{A}$$ and $$\ce{B}$$ atoms. Would this necessarily mean that the molecule could not exist in an excited state in which the atoms were bonded together? Explain.

Exercise 28-2 The $$\pi$$-electron system of ethene has one bonding orbital and one antibonding orbital. Using the general approach of Figure 28-2, show the $$\pi$$-electron configurations for the ground state, two different excited singlet states, and a triplet state of ethene. Suppose the bonding energy of one electron in the bonding orbital is such as to be just canceled by having one electron in the antibonding orbital; would you expect the planar or a nonplanar configuration to be more stable for the excited states of ethene? Explain.

Exercise 28-3 The fluorescence of many substances can be "quenched" (diminished or even prevented) by a variety of means. Explain how concentration, temperature, viscosity, and presence of dissolved oxygen and impurities may affect the degree of fluorescence observed for solutions of a fluorescent material. Would you expect similar effects on phosphorescence? Explain.

Exercise 28-4 Explain qualitatively how temperature could have an effect on the appearance of the absorption spectrum of a diatomic molecule $$\ce{A-B}$$ with energy levels such as are shown in Figure 28-1, knowing that most molecules usually are in their lowest vibrational state at room temperature.

Exercise 28-5* Consider a molecule that has a ground state and an excited state which differ from those shown in Figure 28-1 in having potential energy curves with identical shapes, vibrational levels, and $$r_e$$ values. If we designate the vibrational energy levels of each as $$0, \: 1, \: 2, \cdots$$ and $$0^*, \: 1^*, \: 2^*, \cdots$$ (the zeroth level being the lowest), what does the Franck-Condon principle suggest about the relative probabilities of the $$0 \rightarrow 0^*$$, $$0 \rightarrow 1^*$$, and $$0 \rightarrow 2^*$$ transitions? Would the same considerations necessarily hold for the curves of Figure 28-1? Explain.

Exercise 28-6 With reference to the molecular orbital diagram of benzene shown in Figure 21-5, show the electronic configuration of three different excited singlet states of benzene corresponding to promotion of an electron from the bonding $$\pi$$ orbitals to the antibonding $$\pi$$ orbitals. Calculate the energy difference between these states in units of $$\beta$$. Assuming that $$\beta$$ is about $$20 \: \text{kcal}$$, calculate the difference in $$\lambda_\text{max}$$ between the three absorption bands corresponding to the three states. How many corresponding triplet states are there?

Exercise 28-7 The quantum yield in photochemical chlorination of hydrocarbons such as methane is quite sensitive to the experimental conditions. How would you expect $$\Phi$$ to vary with (a) the intensity of the incident light, (b) the wavelength of the incident light from $$250 \: \text{nm}$$ to $$450 \: \text{nm}$$, (c) the presence of oxygen, and (d) the presence of alkenes? Explain.

Exercise 28-8 The vapor-phase photochemical decomposition of 2-propanone proceeds in the presence of iodine vapor, but the amount of carbon monoxide formed becomes very small. Explain how this result argues against one-step process, 2-propanone $$\overset{h \nu}{\longrightarrow} 2 \ce{CH_3} \cdot + \ce{CO}$$. What do you expect the products to be in the presence of iodine?

Exercise 28-9 Write a reasonable pathway for the photochemical dissociation shown in Equation 28-6. Explain why this reaction is likely to be favored over Norrish type II reactions for this ketone.

Exercise 28-10 Write a mechanism for formation of cyclobutane from the photolysis of cyclopentanone, and ketene from the photolysis of cyclobutanone.

Exercise 28-11 What products would you expect in the photodissociation of 3-methylpentanal?

Exercise 28-12 Irradiation of benzophenone in isopropyl alcohol in the presence of oxygen gives no benzopinacol (the benzophenone is not consumed), but does give 2-propanone (with $$\Phi$$ equal to unity) and hydrogen peroxide (with $$\Phi$$ nearly unity). The reaction does not occur readily in the absence of benzophenone. Explain how benzophenone acts as a photosensitizer for the oxidation of isopropyl alcohol by oxygen.

Exercise 28-13 What would you expect to be the quantum yield of 2-propanone in the following sequence of reactions for benzopinacol formation, where $$\ce{B} =$$ diphenylmethanone, $$2$$; $$\cdot \ce{BH} =$$ diphenylhydroxymethyl radical, $$4$$; $$\ce{(BH)_2} =$$ benzopinacol, $$3$$; $$\ce{A} =$$ 2-propanone; $$\cdot \ce{AH} =$$ 2-hydroxy-2-propyl radical; and $$\ce{AH_2} =$$ 2-propanol?

\begin{align} \ce{B} + h \nu &\rightarrow \ce{B}^* \\ \ce{B}^* + \ce{AH_2} &\rightarrow \cdot \ce{BH} + \cdot \ce{AH} \\ 2 \: \cdot \ce{BH} &\rightarrow \ce{(BH)_2} \\ 2 \: \cdot \ce{AH} &\rightarrow \ce{A} + \ce{AH_2} \end{align}

How could this sequence be ruled out if formation of benzopinacol, $$3$$, in the presence of an excess of optically active 2-butanol gave no racemized alcohol?

Exercise 28-14* Suppose the rates of the processes marked $$k_c$$ and $$k_t$$ in Figure 28-4 were the same. Which isomer would be favored at photoequilibrium if the rate of the reaction represented by $$k_t^*$$ were greater than the rate represented by $$k_c^*$$? On the basis of steric hindrance, would you expect the rate of the $$k_t^*$$ process or the $$k_c^*$$ process to be greater, using benzophenone as sensitizer? Explain.

Exercise 28-15

a. Account for the formation of the trans-dihydrophenanthrene, $$6$$, in the cyclization of Equation 28-8.

b. Both cis- and trans-1,2-diphenylethene isomers can be cyclized to phenanthrene. Explain how this is possible for the trans isomer.

Exercise 28-16 Draw structures for the products expected from the following reactions. Be sure to indicate stereochemistry.

a.

b. $$\ce{C_6H_5CH=CHCO_2H}$$ (trans) $$\underset{\left[ 2 + 2 \right]}{\overset{h \nu}{\longrightarrow}}$$

c.

Exercise 28-17 1,3-Cyclopentadiene gives the following substances on irradiation in the presence of a ketone sensitizer:

Write reasonable mechanisms for the formation of these substances.

Exercise 28-18 Show the mechanistic steps by which formation of the following reaction products can be explained:

Exercise 28-19 Write structures expected for the products of the following reactions:

a.

b.

c.

Exercise 28-20* Write at least three possible reaction that $$\beta$$-carotene could undergo as a result of energy transfer from $$\ce{^1O_2}^*$$.

Exercise 28-21 What color would you expect to perceive if white light were passed through a solution containing a substance that absorbed very strongly but only within the specified wavelength ranges?

a. $$660 \pm 30 \: \text{nm}$$
b. $$530 \pm 30 \: \text{nm}$$
c.* $$560 \pm 300 \: \text{nm}$$
d.* $$480 \pm 0.1 \: \text{nm}$$

Exercise 28-22 What visible color would you expect of the substance having the spectrum shown in Figure 28-8?

Exercise 28-23 How would you expect the spectra of compound $$18$$ and $$19$$ to compare with each other and with the spectra of cis- and trans-1,2-diphenylethene (stilbene)? Explain.

Exercise 28-24 Why must the resonance forms $$20a$$, $$b$$, $$c$$, etc. correspond to a singlet state? Formulate the hybrid structure of a triplet state of butadiene in terms of appropriate contributing resonance structures.

Exercise 28-25 The $$\pi \rightarrow \pi^*$$ absorption spectra of trans,trans- trans,cis-, and cis,cis-1,4-diphenylbutadiene show maxima and $$\varepsilon$$ values (in parentheses) at about $$330 \: \text{nm}$$ $$\left( 5.5 \times 10^4 \right)$$, $$310 \: \text{nm}$$ $$\left( 3 \times 10^4 \right)$$, and $$300 \: \text{nm}$$ $$\left( 3 \times 10^4 \right)$$, respectively. What is the difference in energy between the transitions of these isomers in $$\ce{kcal mol}^{-1}$$? Why should the trans,trans isomer have a different $$\lambda_\text{max}$$ than the other isomers? (It may be helpful to make scale drawings or models.)

Exercise 28-26 Aqueous solutions of crystal violet turn from violet to blue to green to yellow on addition of successive amounts of acid. The color changes are reversed by adding alkali. What kind of chemical changes could be taking place ot give these color changes?

Exercise 28-27

a. 4-Nitro-$$\ce{N}$$,$$\ce{N}$$-dimethylbenzenamine gives a yellow solution in water which fades to colorless when made acidic. Explain.

b. 4-($$\ce{N}$$,$$\ce{N}$$-Dimethylamino)azobenzene (Section 23-10C) is bright yellow in aqueous solution $$\left( \lambda_\text{max} \: 420 \: \text{nm} \right)$$ but turns intense red $$\left( \lambda_\text{max} \: 530 \: \text{nm} \right)$$ if dilute acid is added. If the solution is then made very strongly acidic, the red color changes to a different yellow $$\left( \lambda_\text{max} \: 430 \: \text{nm} \right)$$ than the starting solution. Show how one proton could be added to 4-($$\ce{N}$$,$$\ce{N}$$-dimethylamino)azobenzene to cause the absorption to shift to longer wavelengths and how addition of a second proton could shift the absorption back to shorter wavelengths.

Exercise 28-28 The well-known indicator and laxative, phenolphthalein, undergoes the following changes as a neutral solution is made more and more basic:

Some of these forms are colorless, some intensity colored. Which would you expect to absorb at sufficiently long wavelengths to absorb visible light. Give your reasoning.

Exercise 28-29 Classify the following groups as strong or weak, chromophores or auxochromes:

$$\ce{-NO_2}$$, $$\ce{-CH_3}$$, $$\ce{-I}$$, $$\ce{-O}^\ominus$$, $$\ce{-} \overset{\oplus}{\ce{N}} \ce{(CH_3)_3}$$, $$\ce{-N=} \overset{\oplus}{\ce{N}} \ce{-} \overset{\ominus}{\ce{O}}$$, and $$\ce{-C \equiv N}$$

Exercise 28-30 Use Figure 28-10 to determine what colors you would expect in the layers of a processed color film of the type shown in Figure 28-11 if the incident light were (a) white, (b) green, (c) magenta, (d) orange? Explain.

Exercise 28-31* Write a reasonable stepwise mechanism for the formation of a cyan dye from 1-hydroxy-2-naphthalenecarboxamide in the overall reaction expressed by Equation 28-13 (review Section 26-1E).

Exercise 28-32* Quinones react with nucleophilic agents at carbon (Section 26-2D):

However, the quinonimmonium salt, $$23$$, adds preferentially at nitrogen to give $$24$$ rather than by the following path:

Explain why nucleophilic addition of $$23$$ to give $$24$$ by attack at nitrogen is more likely than the corresponding addition to a quinone by attack at oxygen. At what position would you expect nucleophilic addition to occur most readily to para-xylylene? Explain.

## Contributors

• John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format."