Section II

Directions CLEARLY SHOW THE METHOD USED AND STEPS INVOLVED IN ARRIVING AT YOUR ANSWERS. It is to your advantage to do this because you may earn partial credit if you do, and you will receive little or no credit if you do not. Attention should be paid to significant figures. 

Answer question 1 below. The Section II weighting for this question is 20 percent. Write all of your answers in the space provided following each question. 

Directions Answer questions 2 and 3. The Section II weight for these questions is 40 percent. 

0015 mol each of I2 and Br2 were placed into an evacuated 5.0 L vessel at 150°C. The contents are allowed to come to equilibrium at this temperature, and the equilibrium constant Kc is measured at 1.2 X 102. 

Directions Answer EITHER Question 2 OR Question 3. Only one of these questions will be graded. If you start both questions, make sure you cross out the one you do not want scored. The Section II weight for the question you choose is 20 percent. 

Carbohydrates and glycosides Aldehydes, ketones and related con unds Quinones Carboxylic acids Phenols and enols Esters, lactones and acid anhydrides of carboxylic acids Alcohols Ethers Hydrocarbons 

All of these compoimds in their simple unsubstituted forms contain carbon, hydrogen and oxygen only, with the exception of hydrocarbons (hydrogen and carbon only). 

The compounds are considered in the order given above, and where appropriate, for a given class of compound, brief reference is made to the chemistry of important related polyfunctional compounds. These polyfunctional substances may contain elements (other than sulphur) in addition to carbon, hydrogen and possibly oxygen, but in those cases chosen for mention here the more characteristic reactions remain due to the oxygen function. 

All the common members of these classes are solids. Mono- and disaccharides are soluble in water and sparingly soluble in ether. Many polysaccharides dissolve in water to give colloidal solutions. 

Dissolve or suspend a small quantity (ca 50 mg) of the substance in 2 ml of water, add two drops of an alcoholic solution of a-naphthol (10%) and shake the mixture well. Carefully pour 1 ml of concentrated sulphuric acid down the side of the test-tube and allow to stand. Within a minute or two a violet or red colour should have formed at the junction of the sulphuric add and the aqueous layer, and on shaking the whole should assume a violet hue, with formation of a blue precipitate. A positive result indicates that the substance is a carbohydrate or a glycoside. This is a very sensitive test traces of filter-paper will give a positive result. Other com-poxmds, e.g. benzilic acid, yield reddish colours. 

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In actual practice, a weight W is obtained, which is less than the ideal value W. The reason for this becomes evident when the process of drop formation is observed closely. What actually happens is illustrated in Fig. 11-10. The small drops arise from the mechanical instability of the thin cylindrical neck that develops (see Section II-3) in any event, it is clear that only a portion of the drop that has reached the point of instability actually falls—as much as 40% of the liquid may remain attached to the tip. 

A jet emerging from a nonciicular orifice is mechanically unstable, not only with respect to the eventual breakup into droplets discussed in Section II-3, but, more immediately, also with respect to the initial cross section not being circular. Oscillations develop in the Jet since the momentum of the liquid carries it past the desired circular cross section. This is illustrated in Fig. 11-20. 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

The capillary rise on a Wilhelmy plate (Section II-6C) is a nice means to obtain contact angles by measurement of the height, h, of the meniscus on a partially immersed plate (see Fig. 11-14) [111, 112]. Neumann has automated this technique to replace manual measurement of h with digital image analysis to obtain an accuracy of 0.06° (and a repeatability to 95%, in practice, of 0.01°) [108]. The contact angle is obtained directly from the height through... 

The total effective Hamiltonian H, in the presence of a vector potential for an A + B2 system is defined in Section II.B and the coupled first-order Hamilton equations of motion for all the coordinates are derived from the new effective Hamiltonian by the usual prescription [74], that is. 

The vanishing of the YM field intensity tensor can be shown to follow from the gauge transformation properties of the potential and the field. It is well known (e.g., Section II in [67]) that under a unitary transfoiination described by the matrix... 

As discussed in Section II.A, the adiabatic electronic wave functions and depend on the nuclear coordinates Rx only through the subset... 

In what is called BO MD, the nuclear wavepacket is simulated by a swarm of trajectories. We emphasize here that this does not necessarily mean that the nuclei are being treated classically. The difference is in the chosen initial conditions. A fully classical treatment takes the initial positions and momenta from a classical ensemble. The use of quantum mechanical distributions instead leads to a seraiclassical simulation. The important topic of choosing initial conditions is the subject of Section II.C. 

In Section II, molecular dynamics within the BO approximation was introduced. As shown in Appendix A, the full nuclear Schrodinger equation is, however. 

As shown above in Section UFA, the use of wavepacket dynamics to study non-adiabatic systems is a trivial extension of the methods described for adiabatic systems in Section H E. The equations of motion have the same form, but now there is a wavepacket for each electronic state. The motions of these packets are then coupled by the non-adiabatic terms in the Hamiltonian operator matrix elements. In contrast, the methods in Section II that use trajectories in phase space to represent the time evolution of the nuclear wave function cannot be... 

In this chapter, recent advances in the theory of conical intersections for molecules with an odd number of electrons are reviewed. Section II presents the mathematical basis for these developments, which exploits a degenerate perturbation theory previously used to describe conical intersections in nonrelativistic systems [11,12] and Mead s analysis of the noncrossing rule in molecules with an odd number of electrons [2], Section III presents numerical illustrations of the ideas developed in Section n. Section IV summarizes and discusses directions for future work. 

By following Section II.B, we shall be more specific about what is meant by strong and weak interactions. It turns out that such a criterion can be assumed, based on whether two consecutive states do, or do not, form a conical intersection or a parabolical intersection (it is important to mention that only consecutive states can form these intersections). The two types of intersections are characterized by the fact that the nonadiabatic coupling terms, at the points of the intersection, become infinite (these points can be considered as the black holes in molecular systems and it is mainly through these black holes that electronic states interact with each other.). Based on what was said so far we suggest breaking up complete Hilbert space of size A into L sub-Hilbert spaces of varying sizes Np,P = 1,..., L where... 

Metallic sodium. This metal is employed for the drying of ethers and of saturated and aromatic hydrocarbons. The bulk of the water should first be removed from the liquid or solution by a preliminary drying with anhydrous calcium chloride or magnesium sulphate. Sodium is most effective in the form of fine wire, which is forced directly into the liquid by means of a sodium press (see under Ether, Section II,47,i) a large surface is thus presented to the liquid. It cannot be used for any compound with which it reacts or which is affected by alkalis or is easily subject to reduction (due to the hydrogen evolved during the dehydration), viz., alcohols, acids, esters, organic halides, ketones, aldehydes, and some amines. 

Sodium. The preparation of sodium wire is described in Section II,47,i. Granulated sodium (also termed molecular sodium and powdered sodium) may be prepared by either of the following methods ... 

Allyl Chloride. Comparatively poor yields are obtained by the zinc chloride - hydrochloric acid method, but the following procedure, which employs cuprous chloride as a catalyst, gives a yield of over 90 per cent. Place 100 ml. of allyl alcohol (Section 111,140), 150 ml. of concentrated hydrochloric acid and 2 g. of freshly prepared cuprous chloride (Section II,50,i one tenth scale) in a 750 ml. round-bottomed flask equipped with a reflux condenser. Cool the flask in ice and add 50 ml. of concen trated sulphuric acid dropwise through the condenser with frequent shaking of the flask. A little hydrogen chloride may be evolved towards the end of the reaction. Allow the turbid liquid to stand for 30 minutes in order to complete the separation of the allyl chloride. Remove the upper layer, wash it with twice its volume of water, and dry over anhydrous calcium chloride. Distil the allyl chloride passes over at 46-47°. 

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