Intermolecular forces phase diagrams

Chapter 6. The outer contour in this map is for a density of 0.001 au, which has been found to represent fairly well the outer surface of a free molecule in the gas phase, giving a value of 190 pm for the radius in the direction opposite the bond and 215 pm in the perpendicular direction. In the solid state molecules are squashed together by intermolecular forces giving smaller van der Waals radii. Figure 5.2b shows a diagram of the packing of the Cl2 molecules in one layer of the solid state structure of chlorine. From the intermolecular distances in the direction opposite the bond direction and perpendicular to this direction we can derive values of 157 pm and 171 pm for the two radii of a chlorine atom in the CI2 molecule in the solid state. These values are much smaller than the values for the free molecule in the gas phase. Clearly the Cl2 molecule is substantially compressed in the solid state. This example show clearly that the van der Waals of an atom radius is not a well defined concept because, as we have stated, atoms in molecules are not spherical and are also compressible. 

Types of intermolecular forces Properties of liquids Surface tension Viscosity Capillary action Structures of solids Phase changes and diagrams... 

Whether a substance exists as a gas, liquid, or solid depends on the nature of its intermolecular attractive forces and on its temperature and pressure. A phase diagram is a graphical way to summarize the environmental conditions under which the different states of a substance are stable. The diagram is divided into three areas representing the three possible states of the substance (gas, liquid, or solid). Temperature and pressure determine the phase of a substance and are shown on the x-axis and y-axis of the phase diagram, respectively. 

In this chapter we describe the methods used to calculate solubility isotherms as well as the entire phase diagram for binary and ternary solute-SCF mixtures. The objective of the first part of the chapter is to discuss the relevant physical properties of the solute and solvent pair that are needed to describe the intermolecular forces in operation between molecules in a mixture that ultimately fix solubility levels. A brief description is provided on the application of solubility parameters to supercritical fluids. 

A discussion of the properties of various molecular models and what they teach us about the connections between intermolecular forces and phase diagrams ... 

Whether a substance exists as a gas, liquid, or solid depends on the nature of its intermolecular attractive forces and on its temperature and pressure. This information is often visualized as a phase diagram for the substance. 

The Txx diagram shown in Figure 8.20 is typical of most binary liquid-liquid systems the two-phase curve passes through a maximum in temperature. The maximum is called a consolute point (also known as a critical mixing point or a critical solution point), and since T is a maximum, the mixture is said to have an upper critical solution temperature (UCST). A particular example is phenol and water, shown in Figure 9.13. At T > T, molecular motions are sufficient to counteract the intermolecular forces that cause separation. 

Make reasonable assumptions. By considering the state of the system and the nature of its components, we can introduce sensible approximations that may vastly simplify the analysis but do little harm to the accuracy of the calculation. A consideration of the state would include identification of the phases present (solid, liquid, gas), estimates for temperature and pressure, and rough estimates for the composition. (For example, is a mixture dominated by one component or are any components present in very small amounts ). In general, it is helpful to locate known state points on phase diagrams, or at least to find where a mixture temperature lies relative to the pure-component melting and critical temperatures. By nature of the components we mean the kinds of intermolecular forces, such as simple van der Waals interactions, hydro-... 

Figure 1. Potential energy diagrams, a. external translation (gas phase) h. external translation (condensed phase) c. internal vibration (gas phase) d. internal vibration (condensed phase). In a, r denotes the average intermolecular distance in the gas phase, in b, r denotes the value of the intermolecular distance evaluated at the minimum, and in c and d, r denotes the value of the coordinate descril ng the molecular distortion evaluated at the minimum. Notice for the external motions the zero point energy change on condensation, (E — Ee) — E — EJ > 0, because E E 0, but for the internal motions it may be positive, negative, or zero depending on the effect of the intermolecular forces on the specific motion under consideration.

Use the phase diagram of neon to answer the following questions. (a) What is the approximate value of the normal boiling point (b) What can you say about the strength of the intermolecular forces in neon and argon based on the critical points ofNe and Ar (see Table 11.6.) ... 

In a closed system, a phase change is reversibie, and the system reaches a state of dynamic equiiibrium. As a liquid vaporizes in a closed container at a given temperature, the rates of vaporization and condensation become equal, so the pressure of the gas (vapor pressure) becomes constant. The vapor pressure increases with temperature and decreases with stronger intermolecular forces. The Ciausius-Ciapeyron equation relates vapor pressure to temperature. A phase diagram shows the range of pressure and temperature at which each phase is stable and at which phase changes occur. (Section 12.2)... 

The most successful form of the theory is briefly outlined in the Theory Section. In the Section on Results the theory is used to classify mixture phase diagrams in terms of the intermolecular forces involved, and also to predict vapor-liquid equilibria for several binary and ternary mixtures. 

In this section we give as examples two uses of the theory outlined above (a) the classification of binary phase diagrams, critical behavior, etc. in terms of the intermolecular forces involved, and (b) comparison with experiment for some binary and ternary systems. 

A method based on thermodynamic perturbation theory is described which allows strong directional Intermolecular forces to be taken into account when calculating thermodynamic properties. This is applied to the prediction of phase equilibrium and critical loci for mixtures containing polar or quadrupolar constituents. Two applications of the theory are then considered. In the first, the relation between intermolecular forces and the type of phase behavior is explored for binary mixtures in which one component is either polar or quadrupolar. Such systems are shown to give rise to five of the six classes of binary phase diagrams found in nature. The second application Involves comr-parison of theory and experiment for binary and ternary mixtures. 

Crystalline solid, 505 Intermolecular forces, 494 Phase diagram, 524 X-ray diflraction, 510... 

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