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For each of the following compounds determine which (if any) lone pairs are participating in aromaticity. a. b. c. d. e. f. g. h. :N-H Starting with benzene and using any other necessary reagents of your choice, design a synthesis for the following compound. -NH2 - When para-bromotoluene is treated with sodium amide, two products are obtained. Draw both products, and propose a plausible mechanism for their formation. Identify whether each transformation below involves an increase, a decrease, or no change in the number of hydrogen atoms: a. b. Draw a mechanism for the acid-catalyzed conversion of cyclohexanone into its tautomeric enol. Draw all lone pairs on each of the oxygen atoms in the compounds below. Before doing this, review in the following table, and then come back to these problems. Try to identify all lone pairs without... The vapor pressure of methanol(l) is 16.94 10 3 Pa at 298.15 K. Use this value to calculate G o f (CH 3 OH, g) G o f (CH 3 OH, l). Compare your result with those in Table 4.1. For each of the problems below, determine whether each curved arrow violates either of the two rules, and describe the violation, if any. (Dont forget to count all hydrogen atoms and all lone pairs.)... The normal melting point of H 2 O is 273.15 K, and H fusion = 6010 J mol -1 . Calculate the change in the normal freezing point at 100. and 500. bar compared to that at 1 bar assuming that the... At 298.15 K, G f (HCOOH, g) = -351.0 kJ mol -1 and G f (HCOOH, l) 361.4 kJ mol -1 . Calculate the vapor pressure of water at this temperature. Arrange the following compounds in order of increasing boiling point: -, - -, -0 For each pair of compounds, identify whether they are constitutional isomers or two representations of the same compound: (a) (b) (c) (d) In each case below, identify the highest and lowest energy conformations. In cases where two or three conformations are degenerate, draw only one as your answer. (a) (b) (c) (d) For each of the following processes predict the sign of ÎS for the reaction. In other words, will ÎS sys be positive (an increase in entropy) or negative (a decrease in entropy)? a. b. c.... In the double-slit experiment, researchers found that an equal number of electrons passes through each slit. Does this result allow you to distinguish between particle-like and wave-like behavior? Why is a diffraction pattern generated by an electron gun formed by electrons interfering with themselves rather than with one another? Calculate the highest possible energy of a photon that can be observed in the emission spectrum of H. Consider the following reaction: (a) Use Table 6.1 to estimate ÎH for this reaction. (b) ÎS of this reaction is positive. Explain. (c) Determine the sign of ÎG. (d) Is the sign of... For each of the following reactions identify the arrow-pushing pattern that is being utilized: a. b. c. d. H, Which of the following functions are eigenfunctions of the operator B if B f (x) = d 2 f (x) / dx 2 : x 2 , cos x, e 3ix ? State the eigenvalue if applicable. Find the result of operating with d 2 /dx 2 2x 2 on the function 2 e ax2 . What must the value of a be to make this function an eigenfunction of the operator? What is the eigenvalue? Find the result of operating with d 2 /dx 2 + d 2 /dy 2 + d 2 /dz 2 on the function x 2 + y 2 + z 2 . Is this function an eigenfunction of the operator? Draw curved arrows for each step of the following mechanism: : : H-OSO3H H I IN- N- NH2 OsoH : :SO3H NH2 `NH2 NH2 H-OSO3H le CsoH N- --0 N, "9 NH2 NH2 H-OSO3H CsoH HEos: .. - - NH2 H-OSO3H... In Problem 7.4, we saw that an intramolecular substitution reaction can occur when the nucleophilic center and electrophilic center are present in the same compound. Draw the transition state of the... Find the result of operating with (1/r 2 ) (d /dr) (r 2 d /dr) + 2/r on the function Ae br . What must the values of A and b be to make this function an eigenfunction of the operator? Draw a complete mechanism for the following transformation. NaOH, heat Propose an efficient synthesis for the following transformation. Take special notice of the fact that the starting material has a six-membered ring while the product has a fivemembered ring. Draw a reasonable mechanism for the following transformation. NaOH, H,0 Heat Draw the product of the Robinson annulation reaction that occurs when the following compounds are treated with aqueous sodium hydroxide. The following two drawings are resonance structures of one compound: But the following two drawings are not resonance structures: They are, in fact, two different compounds. Explain. Not resonance... Draw a plausible mechanism for the following transformation. NO2 NO2 NaOH, H,0 eat Predict the major product of the following reactions. a. b. c. d. NBS Heat or light Na,Cr,0, H,SO,, H20 One variation of the Gabriel synthesis employs hydrazine to free the amine in the final step of the synthesis. Draw the by-product obtained in this process. ? RNH, + N-R H,N-NH2 What is the relationship between the zero point energy for a H atom and a H 2 molecule in a one-dimensional box? Why must the amplitudes of the first derivatives of the energy eigenfunctions in the finite depth box and in the adjoining barrier regions have the same value at the boundary? Predict the expected product(s) when benzene is treated with each of the following alkyl halides in the presence of AlCl 3 . In each case, assume conditions have been controlled to favor... A compound with molecular formula C 8 H 8 O produces an IR spectrum with signals at 3063, 1686, and 1646 cm -1 . The 1 H NMR spectrum of this compound exhibits a singlet at 2.6 ppm (I = 3H) and a... Consider the equilibrium NO 2 (g) NO(g) + 1/2O 2 (g). One mole of NO 2 (g) is placed in a vessel and allowed to come to equilibrium at a total pressure of 1 bar. An analysis of the contents of the... The vibrational frequency for D 2 expressed in wave numbers is 3115 cm 1 . What is the force constant associated with the DD bond? How much would a classical spring with this force constant be... Predict the product(s) obtained when each of the following compounds is treated with a mixture of nitric acid and sulfuric acid: (a) (b) (c) (d) (e) Br The infrared spectrum of 7 Li 19 F has an intense line at 910.57 cm 1 . Calculate the force constant and period of vibration of this molecule. Calculate the expectation value of the radius r at which you would find the electron if the H atom wave function is 100 (r). At 47C, the vapor pressure of ethyl bromide is 10.0 Torr and that of ethyl chloride is 40.0 Torr. Assume that the solution is ideal. Assume there is only a trace of liquid present and the mole... Ions with a single electron such as He + , Li 2+ , and Be 3+ are described by the H atom wave functions with Z/a 0 substituted for 1/a 0 , where Z is the nuclear charge. The 1s wave function becomes ... The observed lines in the emission spectrum of atomic hydrogen are given by In the notation favored by spectroscopists, = 1/ = E/hc and R H =109,677 cm 1 . The Lyman, Balmer, and Paschen series... Determine in each of the following cases if the function in the first column is an eigenfunction of the operator in the second column. If so, what is the eigenvalue? a. b. c. sine cos 3x (1/x) d/dx Determine in each of the following cases if the function in the first column is an eigenfunction of the operator in the second column. If so, what is the eigenvalue? a. b. c. 1 cose sin e- sin e de... Identify the base you would use for each of the following transformations. (a) (b) 1) ? 2) , OEt OEt 1) ? 2) H,o* Identify the major product formed when each of the following compounds is treated with Et2CuLi followed by mild acid. (a) (b) (c) CN Using a Stork enamine synthesis, show how you might accomplish each of the following transformations. (a) (b) (c) H Propose an efficient synthesis for each of the following transformations: (a) (b) (c) (d) (e) (f) TH. Draw the product obtained when each of the following compounds is heated in the presence of a base to give an aldol condensation. (a) (b) (c) H. Identify the reagents you would use to convert cyclohexanone into each of the following compounds. (a) (b) (c) (d) (e) (f) (g) Show two different ways of preparing each of the following compounds via a reductive amination: (a) (b) (c) (d) (e) Z How would you use IR spectroscopy to distinguish between the following pairs of compounds? (a) (b) N. For a particle in a two-dimensional box, the total energy eigenfunctions are a. Obtain an expression for E nx , n y in terms of n x , n y , a, and b by substituting this wave function into the two... Does the average length of a quantum harmonic oscillator depend on its energy? Answer this question by referring to the harmonic potential function shown in Figure 18.7. The average length is the... Atomic chlorine has two naturally occurring isotopes, 35 Cl and 37 Cl. If the molar abundance of these isotopes is 75.4% and 24.6%, respectively, what fraction of a mole of molecular chlorine (Cl 2 )... Determine the number of permutations of size 3 that can be made from the set {1, 2, 3, 4, 5, 6}. Write down all of the permutations. In this problem, you will calculate the transmission probability through the barrier illustrated in Figure 16.10. We first go through the mathematics leading to the solution. You will then carry out... The 13 C nucleus is a spin 1/2 particle as is a proton. However, the energy splitting for a given field strength is roughly 1/4 of that for a proton. Using a 1.45-T magnet as in Example Problem 30.6,... In this problem, you will solve for the total energy eigenfunctions and eigenvalues for an electron in a finite depth box. We first go through the calculation for the box parameters used in Figure... Purification of water for drinking using UV light is a viable way to provide potable water in many areas of the world. Experimentally, the decrease in UV light of wavelength 250 nm follows the... Although the vibrational degrees of freedom are generally not in the high-T limit, is the vibrational partition function evaluated by discrete summation? Arrange v mp , v ave , and v rms in order from largest to smallest speed. Using Table 22.3, which lists the possible terms that arise from a given configuration, and Hunds rules, write the term symbols for the ground state of the atoms H through F in the form (2s+1) L J .... For N 2 at 298 K, what fraction of molecules has a speed between 200. and 300.m s 1 ? What is this fraction if the gas temperature is 500. K? You are performing an experiment using 3 H (half-life = 4.50 10 3 days) labeled phenylalanine in which the five aromatic hydrogens are labeled. To perform the experiment, the initial activity cannot... Calculate the bond order in each of the following species. Predict which of the two species in the following pairs has the higher vibrational frequency: a. Li 2 or Li + 2 b. C 2 or C + 2 c. O 2 or O... The angular functions, Î (θ)Φ(), for the one-electron HartreeFock orbitals are the same as for the hydrogen atom, and the radial functions and radial probability... VSEPR (valence state electron pair repulsion) theory was formulated to anticipate the local geometry about an atom in a molecule (see discussion in Section 25.1). All that is required is the number... When vibrational transitions are observed in an electronic absorption spectrum, these transitions can be used to determine dissociation energies. Specifically, a BirgeSponer plot is constructed where... Chemists recognize that the cyclohexyl radical is likely to be more stable than the cyclopentylmethyl radical, because they know that six-membered rings are more stable than five-membered rings and,... Determine the expression for fractional coverage as a function of pressure for the dissociative adsorption mechanism described in the text in which adsorption is accompanied by dissociation: R,(g) +... There are only two stereoisomeric ketotetroses. (a) Draw both of them. (b) Identify their stereoisomeric relationship. (c) Identify which is a d sugar and which is an l sugar. The ground electronic state of O 2 is 3 g and the next two highest energy states are 1 g (7918 cm 1 ) and 1 + g (13195 cm 1 ), where the value in parentheses is the energy of the state relative... All chemists know that benzene is unusually stable, that is, it is aromatic. They are also well aware that many other similar molecules are stabilized by aromaticity to some extent and, more often... Which of the following terms best describes the relationship between d-fructose and d-glucose? Explain your choice. (a) Enantiomers (b) Diastereomers (c) Constitutional isomers Provide a complete name for the following compound: CH- Singlet and triplet carbenes exhibit different properties and show markedly different chemistry. For example, a singlet carbene will add to a cis-disubstituted alkene to produce only... Draw the open-chain form of the following cyclic monosaccharide: CH,OH - Identify the reagents necessary to make each of the following amino acids via the amidomalonate synthesis. (a) Isoleucine (b) Alanine (c) Valine Olefins assume planar (or nearly planar) geometries wherever possible. This ensures maximum overlap between p orbitals and maximum Ï-bond strength. Any distortion away from planarity should... Identify the reagents necessary to make each of the following amino acids using a HellVolhardZelinski reaction. (a) Leucine (b) Alanine (c) Valine The energy of rotation about a single bond is a periodic function of the torsion angle, , and is, therefore, appropriately described in terms of a truncated Fourier series, the simplest acceptable... For each group of amino acids, identify the amino acid with the lowest pI (try to solve this problem by inspecting their structures, rather than performing calculations). (a) Alanine, aspartic acid,... Compound X is a d-aldohexose that can adopt a -pyranose form with only one axial substituent. Compound X undergoes a Wohl degradation to produce an aldopentose, which is converted into an optically... Explain why glucose is the most common monosaccharide observed in nature. The three vibrational frequencies in H 2 O (1595, 3657, and 3756 cm 1 ) are all much larger than the corresponding frequencies in D 2 O (1178, 2671, and 2788 cm 1 ). This follows from the fact that... Draw all of the steps and reagents necessary to prepare each of the following dipeptides from their corresponding amino acids. (a) Trp-Met (b) Ala-Ile (c) Leu-Val Identify all of the steps necessary to prepare each of the following peptides with a Merrifield synthesis. (a) Phe-Leu-Val-Phe (b) Ala-Val-Leu-Ile Molecular orbitals are most commonly delocalized throughout the molecule and exhibit distinct bonding or anti-bonding character. Loss of an electron from a specific molecular orbital from excitation... Identify the sequence of the tripeptide that would be formed from the following order of reagents. Clearly label the C terminus and N terminus of the tripeptide. Show how you would use a Strecker synthesis to make valine. Using an asymmetric catalytic hydrogenation, identify the starting alkene that you would use to make l-histidine. Chemists know that nitric and sulfuric acids are strong acids and that acetic acid is a weak acid. They would also agree that ethanol is at best a very weak acid. Acid strength is given directly by... Identify which of the following monomers would be most reactive toward cationic polymerization. OAc CN CI Explain why vinyl shower curtains develop cracks over time. Propose a mechanism for the acid-catalyzed hydrolysis of PET to regenerate the monomers terephthalic acid and ethylene glycol. Using vinyl acetate as your only source of carbon atoms, design a synthesis for the following polymer: OAc Vinyl acetate
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