Energy of vaporization

Use Eq. Ill-15 and related equations to calculate and the energy of vaporization of argon. Take m to be eo of Problem 6, and assume argon to have a close-packed structure of spheres 3.4 A in diameter. 

The calculation of the surface energy of metals has been along two rather different lines. The first has been that of Skapski, outlined in Section III-IB. In its simplest form, the procedure involves simply prorating the surface energy to the energy of vaporization on the basis of the ratio of the number of nearest neighbors for a surface atom to that for an interior atom. The effect is to bypass the theoretical question of the exact calculation of the cohesional forces of a metal and, of course, to ignore the matter of surface distortion. 

Calculate the surface energy at 0 K of (100) planes of radon, given that its energy of vaporization is 35 x 10 erg/atom and that the crystal radius of the radon atom is 2.5 A. The crystal structure may be taken to be the same as for other rare gases. You may draw on the results of calculations for other rare gases. 

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... 

Physically, is a measure of the difference in the energies of vaporization of the two species (roughly a difference in nomial boiling point), and L is a measure of the energy of mixing. With these definitions equation (A2.5.8) can be rewritten as... 

The quantity AU JV° is the internal energy of vaporization per unit volume and is called the cohesive energy density (CED) of component i. The square root of the CED is generally given the symbol 6j for component i. 

The calculation method can be selected by application of the decision tree in Figure 9.2. The liquid temperature is believed to be about 339 K, which is the temperature equivalent to the relief valve set pressure. The superheat limit temperatures of propane and butane, the constituents of LPG, can be found in Table 6.1. For propane, T, = 326 K, and for butane, T i = 377 K. The figure specifies that, if the liquid is above its critical superheat limit temperature, the explosively flashing liquid method must be chosen. However, because the temperature of the LPG is below the superheat limit temperature (T i) for butane and above it for propane, it is uncertain whether the liquid will flash. Therefore, the calculation will first be performed with the inclusion of vapor energy only, then with the combined energy of vapor and liquid. 

In Eq. (8-35), Afvap is the molar energy of vaporization, and AH p is the molar heat of vaporization. In effect, -it is a measure of the energy required to break some of the solvent-solvent forces, whereas ced is a measure of the energy required to... 

Physical properties are summarized in Table 9.1 (see also p. 373). Silicon is notably more volatile than C and has a substantially lower energy of vaporization, thus reflecting the smaller... 

The Eq for the free energy of vaporization of nitric acid for the temp range 275-305°K has been obtained from vapor pressure measurements (Ref 30)... 

The vapor pressure of chlorine dioxide, Cl02, is 155 Torr at —22.75°C and 485 Torr at ().()0°C. Calculate (a) the standard enthalpy of vaporization (b) the standard entropy of vaporization (c) the standard Gibbs free energy of vaporization (d) the normal boiling point of C102. 

Sodium atoms must be removed from the solid to form sodium gas. Energy must be supplied to do this because, as we describe in Chapter 11. interatomic forces hold the atoms together in the solid metal. The tabulated value for the enthalpy of vaporization of Na is 107.5 kJ/mol. As described in Chapter 6, at 298 K the energy of vaporization is 2.5 kJ/mol less than this ... 

All the energy changes for the cycle are found among the data, except for the electron affinity of O, which E A2 We need to subtract 2.48 kJ/mol from the enthalpy of vaporization to convert it into an energy of vaporization. Then we set up the sum of the individual energy changes and solve for E A2. ... 

Molecules have forces of attraction between them, and these intermolecular forces are responsible for many of the properties of liquids. There is a cohesion energy that holds the molecules together. The energy necessary to overcome these forces to vaporize a mole of liquid is known as the cohesion energy of the liquid or the energy of vaporization. It is related to the enthalpy of vaporization by the equation... 

Molecular weight and Gibbs free energy of vaporization AGV (Burkhard et al. 1985a) ... 

The parameters a and p indicate the capacity of a solvent to donate or accept a hydrogen bond from a solute, i.e., the solvent s hydrogen bond acidity or basicity. % is intended to reflect van der Waals-type solute-solvent interactions (dipolar, dispersion, exchange-repulsion, etc.). Equation (43) was subsequently expanded to include a term representing the need to create a cavity for the solute (and thus to interrupt solvent-solvent interactions).188 For this purpose was used the Hildebrand solubility parameter, 5, which is defined as the square root of the solvent s energy of vaporization per unit volume.189 Thus Eq. (43) becomes,190... 

The cohesive pressure (c) of a solvent, otherwise known as cohesive energy density (CED), is a measure of the attractive forces acting in a liquid, including dispersive, dipolar and H-bonding contributions, and is related to the energy of vaporization and the molar volume (Equation 1.1) ... 

In Fig. 5.1 we see that the intermolecular interactions accounting for VCIE (upper curve) and VPIE (lower curve) differ not in kind, only in degree. The well depth for gas-gas interaction is available from analysis of the virial coefficient of the parent isotopomer, that for the condensed phase can be obtained by combining the energy of vaporization and the zero point energies of the condensed and ideal vapor phases. 

As an alternative to the use of Fiery s interaction parameter, we intend to express AH based on the solubiHty parameter, 6, being slightly hmited in accuracy but superior in simpHcity, needing only pen and paper. According to its definition, 6 is equal to the square root of the molar energy of vaporization, AE per unit molar volume, thus [79]... 

The three kinds of forces described above, collectively known as the cohesive forces that keep the molecules of liquids together, are responsible for various properties of the liquids. In particular, they are responsible for the work that has to be invested to remove molecules from the liquid, that is, to vaporize it. The energy of vaporization of a mole of liquid equals its molar heat of vaporization, Ay//, minus the pressure-volume work involved, which can be approximated well by Rr, where R is the gas constant [8.3143 J K" mol" ] and T is the absolute temperamre. The ratio of this quantity to the molar volume of the liquid is its cohesive energy density. The square root of the cohesive energy density is called the (Hildebrand) solubility parameter of the liquid, 8 ... 

Physical properties of polymers, including solubility, are related to the strength of covalent bonds, stiffness of the segments in the polymer backbone, amount of crystallinity or amorphousness, and intermolecular forces between the polymer chains. The strength of the intermolecular forces is directly related to the CED, which is the molar energy of vaporization per unit volume. Since intermolecular attractions of solvent and solute must be overcome when a solute (here the polymer) dissolves, CED values may be used to predict solubility. 

At the critical temperature, Tc, and critical pressure, Pc, a liquid and its vapor are identical, and the surface tension, y, and total surface energy, as in the case of the energy of vaporization, must be zero (Birdi, 1997). At temperatures below the boiling point, which is 2/3 Tc, the total surface energy and the energy of evaporation are nearly constant. The variation in surface tension, y, with temperature is given in Figure A.l for different liquids. 

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