Phase diagram detennination

With these simplifications, and with various values of the as and bs, van Laar (1906-1910) calculated a wide variety of phase diagrams, detennining critical lines, some of which passed continuously from liquid-liquid critical points to liquid-gas critical points. Unfortunately, he could only solve the difficult coupled equations by hand and he restricted his calculations to the geometric mean assumption for a to equation (A2.5.10)). For a variety of reasons, partly due to the eclipse of the van der Waals equation, this extensive work was largely ignored for decades. 

The factors that determine the crystal structure of particles formed in aerosol reactors have not been studied systematically. In this section, we identify key theoretical concepts and review relevant experimental observations. Consideration is limited to single-component systems. Panicle crystal structure depends on a combination of thermodynamic (equilibrium) factors and rate processes. The equilibrium shape of a particle is detennined by the surface energies of its crystal face.s according to the Wulff construction (Chapter 8). Another factor that inay enter into the process is the excess pressure inside small particles according to the Laplace formula (Chapter 9). Thus the equilibrium form may vary with panicle size depending on the phase diagram,... 

Reaction of alkenes with BrCl proceeds via the intennediate [alkene-Br]+ rather than the intennediate [alkene-Cl]+. Explain using a two-orbital interaction diagram. (The structure of the complex between ethylene and BrCl in the gas phase has been detennined by microwave spectroscopy. It is T-shaped, with the BrCl molecule lying perpendicular to the ethylene plane and pointing bromine-end first toward the midpoint of the C=C bond Legon, A. C. Bloemink, H. L Hinds, K. Thorn, J. C., Chem. Eng. News, 1994 Nov. 7, 26-29.)... 

Detennine the amplitude A and initial phase (p of the resulting oscillations. Draw a vector diagram of the superposition in a scale chosen. 

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