Calculating results exercise

This exercise is based on an important practical technique of gas collection using a gas syringe. Following through the exercise should help develop your skills in presenting experimental data and calculating results from it. You will also be asked how the experiment could be modified to provide further data. 

In the limit r one can obtain many analytical results about the Lorenz equations. For instance, Robbins (1979) used perturbation methods to characterize the limit cycle at large r. For the first steps in her calculation, see Exercise 9.5.5. For more details, see Chapter 7 in Sparrow (1982). 

The THM response of the buffer and rock mass were monitored by a network of instruments. For example, sensors to measure water content, temperature, pore pressure, stress and strain in the bentonite were installed at three radial sections. In the calibration exercise, tbe evolution of the temperature, water content, pore pressure, stress and strain along one radial axis intersecting the centre of the heater will be calculated and the calculated results will be compared and adjusted to the measured results. 

Figure 6.8b The Fock worksheet for the HFS-SCF calculations on dihydrogen. These results are for the equilibrium experimental bond length of 1.4 a.u. found for H2, but show the situation before iteration, with the density matrix set to zero. Again, note, the calculation follows Exercise 6.1.

In order to facilitate the discussion, it is interesting first to know the concentrations of the hydroxo complexes resulting from the hydrolysis phenomenon, no other ligand being present at that time. With the mercuric ion Hg +, we calculate (see Exercise 1 ahead) that in an aqueous solution containing 10 mol/L of mercuric nitrate and whose acidity is such that pH = 3.00, the concentrations are [Hg +] = 5.9 X 10 mol/L, [Hg(OH)+] = 1.2 x 10 mol/L, and [Hg(OH)2] = 2.9 x 10 mol/L. This is an interesting result. It shows that in these conditions, only half of the mercuric ions remain as such, although Hg(N03)2 is totally ionized. 

It has been shown " that shift-term effects in strongly bonded molecular systems are usually not significant and can be kept under control both by proper choice of shift coordinates and by the CPS technique. On the other hand, treatment of systems having weak intermolecular interactions or large-amplitude vibrational motions is more difficult considerable care should be exercised when interpreting calculated results. 

While the result should not have very exact physical meaning, as an exercise, calculating the f potential of lithium ion, knowing that its equivalent conductivity is 39 cm /(eq)(ohm) in water at 25°C. 

Note that agreement with Pariser and Parr s empirical value is better for Y13 than for Yn ) Use Salem s values to calculate election densities on the three carbon atoms of the allyl anion for one iteration beyond the initial Huckel values, as was done in Exercise 8.9.1. Comment on the results you get, as to the qualitative picture of the anion, the influence of election repulsion on the charge densities, and agreement or lack of agreement with the results already obtained with the Pariser and Parr parameters. 

In this problem you will collect and analyze data in a simulation of the sampling process. Obtain a pack of M M s or other similar candy. Obtain a sample of five candies, and count the number that are red. Report the result of your analysis as % red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and standard deviation for your data. Remove all candies, and determine the true % red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and expected standard deviation, and compare to your experimental results. 

Problems can also arise when allocating overheads on the basis of direct labor cost. Let us consider a company that evaluates overheads at 125 percent of direct labor cost. A process plant employs seven operators, each with a direct cost of 10,000 per budget period. As a result of a works-study exercise, it is found that the plant can operate satisfactorily with six operators. The ac tual cost saving is hkely to oe far nearer to the direct labor savings of 10,000 per period than to the calculated saving of 10,000 -t- 10,000(125/100) = 22,500 per period. The 22,500 calculated saving is the direct labor cost plus overheads taken as 125 percent of the direct labor cost. 

A frequency job must use the same theoretical model and basis set as produced the optimized geometry. Frequencies computed with a different basis set or procedure have no validity. We U be using the 6-31G(d) basis set for all of the examples and exercises in this chapter. This is the smallest basis set that gives satisfactory results for frequency calculations. 

The frequency job on this structure will confirm that it is a minimum. We ll consider more of the results of this frequency calculation in the next exercise. ... 

In Exercise 3.5, we predicted the NMR properties of benzene and calculated the relative shift for the carbon atom with respect to TMS. In this exercise, we will compare those results with ones computed using other basis sets. 

Determine the effect of basis set on the predicted chemical shifts for benzene. Compute the NMR properties for both compounds at the B3LYP/6-31G(d) geometries we computed previously. Use the HF method for your NMR calculations, with whatever form(s) of the 6-31G basis set you deem appropriate. Compare your results to those of the HF/6-311+G(2d,p) job we ran in the earlier exercise. How does the basis set effect the accuracy of the computed chemical shift for benzene ... 

Calculate the rotational barrier between the anti and anticlinal forms of N-butane using the AMI (or PM3 if you prefer) and HF/6-31G(d) model chemistries. Use the results for the anti form that you obtained in Exercise 6.1. Note that the anticlinal form is a transition structure you will find the Opt TS,CalcFC] keyword helpful in optimizing this structure. 

Use the same model chemistries as in Exercise 8.5. Here are results from earlier calculations that may be helpful ... 

Each chapter focuses on a single topic, and includes explanations of the chemical properties or phenomena under consideration and the relevant computational procedures, one or two detailed examples of setting up such calculations and interpreting their results, and several exercises designed to both provide practice in the area and to introduce its more advanced aspects. Full solutions are provided for all... 

Chapter 10, the last chapter in this volume, presents the principles and applications of statistical thermodynamics. This chapter, which relates the macroscopic thermodynamic variables to molecular properties, serves as a capstone to the discussion of thermodynamics presented in this volume. It is a most satisfying exercise to calculate the thermodynamic properties of relatively simple gaseous systems where the calculation is often more accurate than the experimental measurement. Useful results can also be obtained for simple atomic solids from the Debye theory. While computer calculations are rapidly approaching the level of sophistication necessary to perform computations of... 

The literature on RM certification indicates that there are two broad types of approaches for the characterization of RMs (i) statistical, and (2) measurement. The statistical approach relies on the in-depth application of statistical calculations to a body of analytical results obtained from diverse exercises, often widely scattered and discordant. The approach based on measurement emphasizes laboratory measurement aspects and deals more in detail with various diverse analytical measure-... 

Once the "distances" between the animals have been calculated using equation (3.1), we lay the animals out on a piece of paper, so that those that share similar characteristics, as measured by the distance between them, are close together on the map, while those whose characteristics are very different are far apart. A typical result is shown in Figure 3.3. What we have done in this exercise is to squash down the many-dimensional vectors that represent the different features of the animals into two dimensions. 

If quantum theory is to be used as a chemical tool, on the same kind of basis as, say, n.m.r. or mass spectrometry, one must be able to carry out calculations of high accuracy for quite complex molecules without excessive cost in computation time. Until recently such a goal would have seemed quite unattainable and numerous calculations of dubious value have been published on the basis that nothing better was possible. Our work has shown that this view is too pessimistic semiempirical SCF MO treatments, if properly applied, can already give results of sufficient accuracy to be of chemical value and the possibilities of further improvement seem unlimited. There can therefore be little doubt that we are on the threshold of an era where quantum chemistry will serve as a standard tool in studying the reactions and other properties of molecules, thus bringing nearer the fruition of Dirac s classic statement, that with the development of quantum theory chemistry has become an exercise in applied mathematics. 

The results of interlaboratory study II are presented in Fig. 4.5.1. Five sets of results were obtained for the LAS exercise, and four sets for the NPEO exercise. For LAS, the within-laboratory variability ranged between 2 and 8% (RSD) for sample III (distilled water spiked with lmgL-1 LAS), 1 and 13% for sample 112 (wastewater influent), and 3 and 8% for sample 113 (sample 112 spiked with lmgL-1 LAS). Between-laboratory variations (calculated from the mean of laboratory means, MOLM) amounted to RSDs of 15, 30 and 30% for samples III, 112 and 113, respectively. The LAS values reported were in the range of 700—1100 p,g L-1 in sample III, 1100-1800 p,g L-1 in sample 112 and 1900-3000 p,g L-1 in sample 113, indicating that even in the matrix wastewater influent, the spiked concentration of lmgL-1 LAS could be almost quantitatively determined by all laboratories. 

Logarithmic scales and power laws make extrapolation look too easy. The wide confidence limits are often overlooked and particular care should be exercised because small deviations can result in large changes in predicted lifetime. Precise calculations can lose their value when the extent of the confidence limits is noticed ( predicted life 10 years, upper limit 600 years, lower limit two months ). 

In summary, we selected one database (Pedley s) to quote the standard enthalpies of formation of the pure organic compounds and another database (NBS) to derive the solution enthalpies. Although these databases are not mutually consistent, that did not affect our final result because the experimental enthalpies of solution were calculated with NBS data only. The exercise illustrates the sort of caution one should keep in mind whenever two or more nonconsistent databases are used. 

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