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Chapter 2: Problem 27

The ultraviolet spectrum of \(3,6,6\) -trimethylcyclohex-2- en-1one, is shown below. The concentration is \(1.486 \times 10^{-5} \mathrm{~g}\) \(\mathrm{ml}^{-1}\) in ethanol and the path length is \(1.0 \mathrm{~cm} .\) Calculate \(\varepsilon\) and compare \(\lambda_{\max }\) with the value predicted by Woodward's rules.

Short Answer

Expert verified
Calculate the molar absorptivity (ε) using the Beer-Lambert Law: \(ε = \frac{A}{cl}\), where A is the maximum absorbance, c is the concentration in moles per liter, and l is the path length. Convert the given concentration to moles per liter and use the given path length of 1.0 cm. After calculating ε, compare the λ_max obtained from the ultraviolet spectrum with the value predicted by Woodward's rules.

Step by step solution

01

Find the maximum absorbance

Identify the maximum absorbance (A) from the ultraviolet spectrum of 3,6,6-trimethylcyclohex-2-en-1one. This value can be found at the highest peak in the spectrum.
02

Convert concentration to moles per liter

We have the concentration given as \(1.486 \times 10^{-5}\) g/mL. To convert this concentration to moles per liter (M), we need to multiply the concentration by the molecular weight of 3,6,6-trimethylcyclohex-2-en-1one and convert the volume to liters. The molecular weight of 3,6,6-trimethylcyclohex-2-en-1one is approximately 166.23 g/mol. \(c_{M} = \frac{1.486 \times 10^{-5} \mathrm{~g/mL}}{166.23\mathrm{~g/mol}}\) \(c_{M} = 8.936 \times 10^{-8}\mathrm{~mol/mL}\) Now, convert the volume to liters: \(c_{M} = 8.936 \times 10^{-8} \cdot \frac{1000 \mathrm{~mL}}{1 \mathrm{~L}}\) \(c_{M} = 8.936 \times 10^{-5} \mathrm{~M}\)
03

Calculate ε using the Beer-Lambert Law

Now, we will use the Beer-Lambert Law (A = εcl) to calculate ε. \(ε = \frac{A}{cl}\) We found the A in step 1, c in step 2, and the path length (l = 1.0 cm) is given in the problem statement.
04

Compare the λ_max with Woodward's rules

Finally, we will compare the λ_max obtained from the ultraviolet spectrum of 3,6,6-trimethylcyclohex-2-en-1one to the value predicted by Woodward's rules. These rules help estimate wavelengths at maximum absorbance depending on the type of chromophore and substituents present in the molecule. After working on each of the steps mentioned above, we will have the molar absorptivity (ε) of 3,6,6-trimethylcyclohex-2-en-1one, and we will be able to compare its λ_max with the predicted wavelengths according to Woodward's rules.

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Most popular questions from this chapter

Although all electrons spin, only molecules containing unpaired electrons - only free radicals - give esr spectra. Why is this? (Hint: Consider the possibility (a) that one electron of a pair has its spin reversed, or (b) that both electrons of a pair have their spins reversed.)

Classify the following molecules according to the general characteristics expected for their infrared and Raman spectra: (a) \(\mathrm{Cl}_{2} ;\) (b) \(\mathrm{HCl} ;\) (c) CO; (d) CF \(2=\mathrm{CH}_{2}\) (double bond stretch only).

Explain how a mass spectrometer, capable of distinguishing between ions with \(\mathrm{m} / \mathrm{e}\) values differing by 1 part in 50,000 , could be used to tell whether an ion of mass 29 is \(\mathrm{C}_{2} \mathrm{H}_{5} \oplus\) or \(\mathrm{CHO}^{\oplus}\)

Compounds A, B and C have the formula \(\mathrm{C}_{5} \mathrm{H}_{8}\) and on hydrogenation all yield n-pentane. Their ultraviolet spectra show the following values of \(\lambda_{\max }: A, 176 \mathrm{~nm} ; \mathrm{B}, 211 \mathrm{~nm}\) C, \(215 \mathrm{~nm}\). (1-Pentene has \(\lambda_{\max } 178 \mathrm{~nm}\).) (a) What is a likely structure for \(\mathrm{A} ?\) For \(\mathrm{B}\) and \(\mathrm{C}\) ? (b) What kind of information might enable you to assign specific structures to \(\mathrm{B}\) and \(\mathrm{C}\) ?

(a) On catalytic hydrogenation, compound \(\mathrm{A}, \mathrm{C}_{5} \mathrm{H}_{8}\), gave cis-1, 2-dimethy lcyclopropane. On this basis, three isomeric structures were considered possible for \(\mathrm{A}\). What were they? (b) Absence of infrared absorption at \(890 \mathrm{~cm}^{-1}\) made one of the structures unlikely. Which one was it? (c) The nmr spectrum of A showed signals at \(\delta 2.22\) and \(\delta\) \(1.04\) with intensity ratio \(3: 1\). Which of the three structures in (a) is consistent with this? (d) The base peak in the mass spectrum was found at \(\mathrm{m} / \mathrm{e} 67\). What ion was this peak probably due to, and how do you account for its abundance? (e) Compound A was synthesized in one step from openchain compounds. How do you think this was done?
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