Paragraphs

It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

The differences between the measured cetane numbers and the cetane indices calculated by the above formula are relatively small for cetane indices between 40 and 55. Nevertheless, for diesel fuels containing a pro-cetane additive, the CCl will be much less than the actual value (refer to paragraph d). 

Nevertheless, this type of analysis, usually done by chromatography, is not always justified when taking into account the operator s time. Other quicker analyses are used such as FIA (Fluorescent Indicator Analysis) (see paragraph 3.3.5), which give approximate but usually acceptable proportions of saturated, olefinic, and aromatic hydrocarbons. Another way to characterize the aromatic content is to use the solvent s aniline point the lowest temperature at which equal volumes of the solvent and pure aniline are miscible. 

The tendency for a solvent to form deposits by polymerization of impurities such as olefins is measured by the test for potential gums . Olefin content can also be represented by the bromine index , which is a measure of the degree of unsaturation (see paragraph 3.4.1). 

Naphthas constitute a special category of petroleum solvents whose boiling points correspond to the class of white-spirits (see paragraph 6.1). 

Different treatments provide lubricant bases having accentuated isoparaffinic structures these are the bases from hydrorefining, hydrocracking and hydroisomerization (see paragraph 10.3.2.2.c.2). 

Although lubricant base stocks have been subjected to dewaxing processes, they still contain large amounts of paraffins that result in a high pour point for the oil. In the paragraph on the cold behavior of diesel fuels, additives were mentioned that modify the paraffin crystalline system and oppose the precipitation of solids. 

All the features presented in the last paragraphs are determined on profiles along the y axis of the filtered images. They are evaluated for each scan of the images and afterwards all features are added up for all y-scans and divided by the number of columns. 

The deconvolution is the numerical solution of this convolution integral. The theory of the inverse problem that we exposed in the previous paragraph shows an idealistic character because it doesn t integrate the frequency restrictions introduced by the electro-acoustic set-up and the mechanical system. To attenuate the effect of filtering, we must deconvolve the emitted signal and received signal. 

Before describing these methods, in the next paragraph we describe the measuring system. Magnetometer System... 

Benjamin Franklin s experiment is mentioned in the opening paragraphs of this chapter. Estimate, from his results, an approximate value for Avogadro s number make your calculation clear. The answer is a little off explain whether more accurate measurements on Franklin s part would have helped. 

Verily the calculation of v in the paragraph preceding Eq. V-37. (Watch the units )... 

Calculate f for the example in the second paragraph following Eq. V-46. Note... 

This is Amontons law as stated in the opening paragraphs of this chapter. 

One feature of this inequality warrants special attention. In the previous paragraph it was shown that the precise measurement of A made possible when v is an eigenfiinction of A necessarily results in some uncertainty in a simultaneous measurement of B when the operators /land fido not conmuite. However, the mathematical statement of the uncertainty principle tells us that measurement of B is in fact completely uncertain one can say nothing at all about B apart from the fact that any and all values of B are equally probable A specific example is provided by associating A and B with the position and momentum of a particle moving along the v-axis. It is rather easy to demonstrate that [p, x]=- ih, so that If... 

The existence of intennolecular interactions is apparent from elementary experimental observations. There must be attractive forces because otherwise condensed phases would not fomi, gases would not liquefy, and liquids would not solidify. There must be short-range repulsive interactions because otherwise solids and liquids could be compressed to much smaller volumes with ease. The kernel of these notions was fomuilated in the late eighteenth century, and Clausius made a clear statement along the lines of this paragraph as early as 1857 [1]. 

Although the previous paragraphs hint at the serious failure of the van der Waals equation to fit the shape of the coexistence curve or the heat capacity, failures to be discussed explicitly in later sections, it is important to recognize that many of tlie other predictions of analytic theories are reasonably accurate. For example, analytic equations of state, even ones as approximate as that of van der Waals, yield reasonable values (or at least ball park estmiates ) of the critical constants p, T, and V. Moreover, in two-component systems... 

Interactions between macromolecules (protems, lipids, DNA,.. . ) or biological structures (e.g. membranes) are considerably more complex than the interactions described m the two preceding paragraphs. The sum of all biological mteractions at the molecular level is the basis of the complex mechanisms of life. In addition to computer simulations, direct force measurements [98], especially the surface forces apparatus, represent an invaluable tool to help understand the molecular interactions in biological systems. 

The paragraphs below are arranged in alphabetical order and are intended only as a short reference. For readers interested in a particular topic a few references are given which serve as a link for further reading. Generally, it should be noted that the separation of the categories below is to a large extent based on historic evolution rather than physicochemical mechanisms. 

We will now explain the meaning of the word identical used above. Physically, it is meant for particles that possess the same intrinsic attributes, namely, static mass, charge, and spin. If such particles possess the same intrinsic attributes (as many as we know so far), then we refer to them as physically identical. There is also another kind of identity, which is commonly refeiTed to as chemical identity [56]. As discussed in the next paragraph, this is an important concept that must be steessed when discussing the permutational properties of nuclei in molecules. 

As pointed out in the previous paragraph, the total wave function of a molecule consists of an electronic and a nuclear parts. The electrons have a different intrinsic nature from nuclei, and hence can be treated separately when one considers the issue of permutational symmetry. First, let us consider the case of electrons. These are fermions with spin and hence the subsystem of electrons obeys the Fermi-Dirac statistics the total electronic wave function... 

Locate the element titanium (Ti) in the Periodic Table. Read the following paragraph about its chemistry and answer the questions which follow. 

Coni pile th e ch ern. nil file Lo a n ew Lypenile.bin file as described in the previon s paragraph. 

The precautions mentioned in the previous paragraph if observed will prevent this occurrence. 

Plot the calculated first IPs as a function of the atomic number Z for the elements from H to Ne in the atomic table. The plot has a characteristic shape that should be familiar from earlier courses. These plots are frequently given in the experimental units of electron volts (eV hartrees x 27.21 = eV) or kilojoules per mole (kJ mol hartrees x 2625 = kJmol ). Write a paragraph or two in your project report explaining why the graph of IP vs. Z appears as it does. 

Many pairs of partially miscible liquids possess neither a lower nor an upper C.S.T. for reasons outlined in the previous paragraph. Thus consider the two liquid phases from the two components water and diethyl ether. Upon cooling the system at constant pressure, a point will be reached when a third phase, ice, will form, thus rendering the production of a lower C.S.T. impossible, likewise, if the temperature of the two layers is raised, the critical point for the ether rich layer will be reached while the two liquid phases have different compositions. Above the critical point the ether-rich layer will be converted into vapour, and hence the system will be convert into a water rich liquid and an ether rich vapour the upper C.S.T. cannot therefore be attained. 

Solvents with boiling points above 90-95°. The apparatus of Fig. 77,13, 3 (with closed filter flask and rubber lead-off tube) or of Fig. 77,13, 4 (see discussion in previous paragraph but one) should be vtilised vrith an air bath or oil bath as the source of heat. Heating on a Wire gauze is not recommended. 

It is recommended that the tsopropanol be tested for peroxides and, if present, removed by refluxing with solid stannous chloride (for details, see concluding paragraph of Section VI,12)... 

The aolventa, enumerated under 10 and 11, may contain traces of peroxides. These can be removed either by refiuxing over anhydrous stannous ofiloride (see concluding paragraph of Section VI, 12) or by filtration under slight pressure through a column of activated alumina. 

In addition to the orthodox method, just described, for the determination of the boiling points of liquids, the student should determine the boiling points of small volumes (ca. 0 5 ml.) by Siwolobofifs method. Full details are given iri Section 11,12. Determine the boiling points of the pure liquids listed in the previous paragraph. Observe the atmospheric pressure and if this differs by more than 5 mm. from 760 mm., correct the boiling point with the aid of Table II,9,B. Compare the observed boiling points with the accepted values, and draw a calibration curve for the thermometer. 

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