Additional Problems

Keep the process as simple as you can. Use what you know already, and combine orbitals in as symmetrical a fashion as you can. 

The closer in energy two orbitals are, the more strongly they interact. At this level of theory, you need only interact the pairs of orbitals closest in energy to each other. 

To order the product orbitals in energy, count the nodes. For a given molecule, the more nodes in an orbital, the higher it is in energy. 

These methods will become much easier than they seem at first, and they will provide a remarkable number of insights into structure and reactivity not easily available in other ways. 

PROBLEM 1.32 Draw Lewis dot structures for the following compounds  

Regress a third order polynomial (cp = a + bT -h cT + dT ) to results of the equation for the heat capacity at constant pressure for graphite reported in Rutland, A.T.D. and Maddison, RJ. (1973). The specific heat of graphite an evaluation of measurements. J. NucL Mater., 49, 45-56  

Calculate the enthalpy of vaporization of ethanol at 25 C and 200 C using the Watson equation. The enthalpy of vaporization at the normal boiling temperature of 351.41 K is 39.183 kj/mol. The critical temperature of ethanol can be taken from Appendix A. 

Estimate the critical data Tc, Pc, and Vc of n-hexene using the J oback-method. Determine the enthalpy of formation as well as the Gibbs energy of formation for n-hexane and benzene at 25 C and latm (ideal gas) using the )oback group contribution method. 

Retrieve the saturated liquid density data for tetrahydrofuran in the free DDBSP Explorer Version and plot the data. In Artist, estimate the liquid density at the normal boiling point and compare the results to the data. 

In the free DDBSP Explorer Version, regress the liquid vapor pressure data for trichloromethane using the Antoine equation. Remove outliers that are not in agreement with the majority of the data. Check the manual to clarify the exact formulation of the Antoine equation. Convert the parameters so that the Antoine equation employs the natural logarithm and yields the vapor pressure in the unit kPa. 

19 Identify the functional groups in the following molecules, and show the polarity of each  

20 Identify the following reactions as additions, eliminations, substitutions, or rearrangements. 

21 What is the difference between a transition state and an intermediate  

22 Draw an energy diagram for a one-slep reaction with /Cet) 1. Label the parts of the diagram corresponding to reactants, products, transition state, AG°, and ACT Is AG° positive or negative  

Calculate the pH of the following solutions assuming that the concentration and the activity of the solutions are the same  

Calculate what volumes of the salt solutions specified which would be required to prepare 1 I of the following buffers  

Indicate the percentage of ionisation of the functional groups specified in the foiiowing drugs at pH 7.0 (Fig. 2.23). 

Calculate the percentage of the following compounds that would be extracted under the conditions specified  

Extracts containing benzylpenicillin were prepared for analysis in buffer at pH 6.5 at 25°C, the rate constant for the hydrolysis of benzylpenicillin under these conditions is 1.7 x 10 s. What is the maximum length of time the solutions can be stored before analysis so that no more than 1 % decomposition occurs. 

15 Explain whether the bonds in these compounds would be ionic or covalent and show Lewis structures for them  

16 What is the formula for the simplest neutral compound formed from P and H Show a Lewis structure for this compound and predict its shape. 

18 Calculate the formal charges on all of the atoms, except hydrogens, in these compounds  

Assess your understanding of this chapter s topics with additional quizzing and conceptual-based problems at http //now.brookscole.com/ homback2 

19 Explain which of the two following structures would be more stable. Explain whether they represent isomers or are resonance structures. 

22 How many valence electrons does each of the following dietary- trace elements have  

23 Give the ground-state electron conliguration for each of the following elements  

25 Draw an electron-dot structure for acetonitrile, C2H3K, which contains a carbon nitrogen triple bond. How many electrons does the nitrogen atom have in its outer shell How many are bonding, and how many are nonbonding  

26 What is the hybridization of each carbon atom in acetonitrile (Problem 1.25)7 

27 Draw a line-bond structure for vinyi chloride, C2H3CI, the starting material from which PVC (polylvinyT chloride)] plastic is made. 

31 Show the number of valence electrons in each of the following atoms. Let the elements symbol represent its kernel, and use dots for the valence electrons. 

32 Use the relative positions of the elements in the periodic table (Table 1.3 or inside back cover) to classify the following substances as ionic or covalent  

33 When a solution of salt (sodium chloride) in water is treated with a silver nitrate solution, a white precipitate forms immediately. When tetrachloromethane is shaken with aqueous silver nitrate, no such precipitate is produced. Explain these facts in terms of the types of bonds present in the two chlorides. 

34 For each of the following elements, determine (1) how many valence electrons it has and (2) what its common valence is  

35 Write a structural formula for each of the following compounds, using a line to represent each single bond and 

All representations of the structures reached by the curved-arrow approach and connected with double-headed arrows must have all atoms in the same positions in space. Only electron motion is considered. 

All representations in a set of resonance structures must have the same number of paired and/or unpaired electrons. 

The amount that any specific resonance structure representation actually contributes to the overall hybrid will depend on the presumed energy of that contributor. Generally, the larger the number of identical representations of the lowest-energy contributor, the more stable the structure. 

Separation of unlike charges on adjacent atoms should be avoided in writing resonance structures since, even though they are acceptable, they are not likely to be major contributors to the minimum energy representation. 

Finally, it must be understood that the curved arrows are no more than an accounting technique. They must not be mistaken for reality and lent more credence than they are worth lest they be taken seriously as the movement of electrons. 

4 Calculate the percentage composition of each of the following compounds. 

5 An organometallic compound called ferrocene contains 30.02% iron. What is the minimum 

6 A gaseous compound gave the following analysis C, 40.04% H, 6.69%. At standard temperature and pressure, 1.00 g of the gas occupied a volume of746 mL. What is the molecular formula of the compound  

7 A gaseous hydrocarbon has a density of 1.251 g L at standard temperature and pressine. When subjected to complete combustion, a 1 000-L sample of the hydrocarbon gave 3.926 g of carbon dioxide and 1.608 g of water. What is the molecular formula for the hydrocarbon  

8 Nicotinamide, a vitamin that prevents the occurrence of pellagra, gave the following analysis C, 59.10% H, 4.92% N, 22.91%. The molecular weight of nicotinamide was shown in a separate determination to be 120 5. What is the molecular formula for nicotinamide  

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For femiions (especially) and bosons diere are additional problems. Let /Jbe one of the pemuitations of particle labels. Then the femiion density matrix has the symmetry... 

One therefore needs a smooth density estimation techniques that is more reliable than the histogram estimates. The automatic estimation poses additional problems in that the traditional statistical techniques for estimating densities usually require the interactive selection of some smoothing parameter (such as the bin size). Some publicly available density estimators are available, but these tended to oversmooth the densities. So we tried a number of ideas based on numerical differentiation of the empirical cdf to devise a better density estimator. 

Nearly every technical difficulty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic effects are significant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are difficult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semi-empirical and molecular mechanics methods. 

Coordination creates additional problems also. Consider the metal-Cp bond in a metallocene. One option is to have five bonds from the metal to each carbon. A second option is to have a single bond connecting to a dummy atom at the center of the Cp ring. 

The synthesis of five-, six-, and seven-membered cyclic esters or timides uses intramolecular condensations under the same reaction condifions as described for intermolecular reactions. Yields are generally excellent. An example from the colchicine synthesis of E.E. van Ta-melen (1961) is given below. The synthesis of macrocyclic lactones (macrolides) and lactams (n > 8), however, which are of considerable biochemical and pharmacological interest, poses additional problems because of competing intermolecular polymerization reactions (see p. 246ff.). Inconveniently high dilution, which would be necessary to circumvent this side-... 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

The maintenance of analytical instmmentation requkes trained personnel and is a time-consuming task (39,40). An additional problem is the necessity of frequentiy checking the caUbration of the analysis instmmentation and recahbrating if requked. Stand-alone data gathering instmmentation, once common in pilot plants, has been vktuaHy replaced in all but the simplest pilot plants by a data gathering computer, usually used for process control as well. 

Internal Plasticizers. There has been much dedicated work on the possibiUty of internally plasticized PVC. However, in achieving this by copolymerization significant problems exist (/) the affinity of the growing polymer chain for vinyl chloride rather than a comonomer implies that the incorporation of a comonomer into the chain requites significant pressure (2) since the use of recovered monomer in PVC production is standard practice, contamination of vinyl chloride with comonomer in this respect creates additional problems and (J) the increasing complexity of the reaction can lead to longer reaction times and hence increased costs. Thus, since standard external plasticizers are relatively cheap they are normally preferred. 

The SPE is defined as the ratio of the time required to produce a perceptible erythema on a site protected by a specified dose of the uv protectant product to the time required for minimal erythema development in the unprotected skin. An SPE of 8 indicates that the product allows a subject to expose the protected skin 8 times as long as the unprotected skin to produce the minimum erythema response. The measurement can be quite subjective unless skin color and the history of reactions to sun exposure of the test subjects are taken into account. The MED range for Caucasians at 300 nm averages 34 mj/cm. The range is 14—80 mj/cm. Perspiration or the use of artificial irradiation devices can create additional problems. 

As indicated above, national policies and international conventions have been invoked to curb known, and usually obvious, sources of marine pollution. National legislation is used to control coastal discharges of contaminants. A major problem remains owing to the inadequate treatment of sewage prior to emission from land-based sources. The most important deleterious effects in this case are with respect to microbial water quality. This can have a direct influence on bathing criteria and result in beach closures during contamination episodes. An additional problem from land-based sources pertains to transboundary effects, whereby pollution may inadvertently be exported from one country to another. 

After-shrinkage is an additional problem with crystalline polymers and depends on the position of the ambient temperature relative to Tg and T. This was discussed in Chapter 3. 

Many more worked examples have been included in this second edition and there are additional problems at the end of each chapter. These are seen as an important aspect of the book because in solving these the reader is... 

The purification of value-added pharmaceuticals in the past required multiple chromatographic steps for batch purification processes. The design and optimization of these processes were often cumbersome and the operations were fundamentally complex. Individual batch processes requires optimization between chromatographic efficiency and enantioselectivity, which results in major economic ramifications. An additional problem was the extremely short time for development of the purification process. Commercial constraints demand that the time interval between non-optimized laboratory bench purification and the first process-scale production for clinical trials are kept to a minimum. Therefore, rapid process design and optimization methods based on computer aided simulation of an SMB process will assist at this stage. 

The presence of low temperature conditions creates additional problems in design and selection of relieving devices, primarily because of the possibility of ice formation. 

Each chapter in this book provides many problems of different sorts. The inchapter problems are placed for immediate reinforcement of ideas just learned, while end-of-ebapter problems provide additional practice and are of several types. They begin with a short section called "Visualizing Chemistry," which helps you "see" the microscopic world of molecules and provides practice for working in three dimensions. After the visualizations are many "Additional Problems." Early problems are primarily of the drill type, providing an opportunity for you to practice your command of the fundamentals. Later problems rend to be more thought-provoking, and some are real challenges. 

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