Vapor pressure entropy

Enthalpy, entropy, vapor pressure SolubUity, osmotic pressure Surface tension Viscosity, rheology Condensation form at room conditions Polymorphic crystalline forms Hardness, mechanical strength Roiling and melting temperature... 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Values for many properties can be determined using reference substances, including density, surface tension, viscosity, partition coefficient, solubihty, diffusion coefficient, vapor pressure, latent heat, critical properties, entropies of vaporization, heats of solution, coUigative properties, and activity coefficients. Table 1 Hsts the equations needed for determining these properties. 

Treatment of Solutions by Statistical Mechanics. Since the vapor pressure is directly connected with the free energy, in the thermodynamic treatment the free energy is discussed first, and the entropy is derived from it. In the treatment by statistical mechanics, however, the entropy is discussed first, and the free energy is derived from it. Let us first consider an element that consists of a single isotope. When the particles share a certain total energy E, we are interested in the number of recog-... 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

Use the Third Law to calculate the standard entropy, S°nV of quinoline (g) p — 0.101325 MPa) at T= 298,15 K. (You may assume that the effects of pressure on all of the condensed phases are negligible, and that the vapor may be treated as an ideal gas at a pressure of 0.0112 kPa, the vapor pressure of quinoline at 298.15 K.) (c) Statistical mechanical calculations have been performed on this molecule and yield a value for 5 of quinoline gas at 298.15 K of 344 J K l mol 1. Assuming an uncertainty of about 1 j K 1-mol 1 for both your calculation in part (b) and the statistical calculation, discuss the agreement of the calorimetric value with the statistical... 

C. C. Stephenson and W. F. Giauque. "A Test of the Third Law of Thermodynamics by Means of Two Crystalline Forms of Phosphine. The Heat Capacity. Heat of Vaporization and Vapor Pressure of Phosphine. Entropy of the Gas". J. Chem. Phys.. 5. 149-158 (1937). 

R. H. Sherman and W. F. Giauque, "Arsine. Vapor Pressure, Heat Capacity, Heats of Transition, Fusion, and Vaporization. The Entropy from Calorimetric and from Molecular Data", J. Am. Chem. Soc., 77, 2154-2160 (1955). 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

Linear least squares treatments of plots of the logarithm of the vapor pressure versus the reciprocal temperature were performed. The second-law enthalpy and entropy of sublimation at the median temperature are proportioned to the slope and... 

Neither the enthalpy nor the entropy of vaporization varies much with temperature so, for a given substance, ASvap° and AHtl )° can both be treated as approximately constant. It follows that the vapor pressures P, and P2 at any two temperatures T, and T2 are related by writing this equation for two temperatures and subtracting one from the other. In the process, the entropy terms cancel ... 

Because the presence of a nonvolatile solute lowers the vapor pressure of the solvent, the boiling point of the solvent rises. This increase is called boiling-point elevation. The elevation of the boiling point has the same origin as vapor-pressure lowering and is also due to the effect of the solute on the entropy of the solvent. 

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. 

Calculate (a) the standard enthalpy of vaporization of trimethylphosphine (b) the standard entropy of vaporization of trimethylphosphine (c) the vapor pressure of trimethylphosphine at 15.0°C. 

We may now use Equations 7 and 12 for the vapor pressure of crystal and glass to calculate the change in entropy when we pass from crystal to glass at temperatures near the absolute zero. 

For convenience and in accordance with a familiar formulation of the third law of thermodynamics, let us take our starting point for entropy measurements such that the entropy of the crystal is zero at the extremely low temperature involved. Starting with the crystal let us then form by reversible evaporation one mole of vapor at the vapor pressure. The entropy of the gas thus formed will evidently be... 

Continuing the process we may now change the pressure on the gas to the vapor pressure of the glass as given by (12) and then carry out a reversible condensation. These steps will be seen to involve the entropy change... 

We apply the condensed form of the seven-step strategy. To calculate a vapor pressure, we need the enthalpy and entropy of vaporization. Then we can apply Equation. ... 

An attractive feature of K<)A is that it can replace the liquid or supercooled liquid vapor pressure in a correlation. K,-ja is an experimentally measurable or accessible quantity, whereas the supercooled liquid vapor pressure must be estimated from the solid vapor pressure, the melting point and the entropy of fusion. The use of KOA thus avoids the potentially erroneous estimation of the fugacity ratio, i.e., the ratio of solid and liquid vapor pressures. This is especially important for solutes with high melting points and, thus, low fugacity ratios. 

As was discussed earlier in Section 1.2.8 a complication arises in that two of these properties (solubility and vapor pressure) are dependent on whether the solute is in the liquid or solid state. Solid solutes have lower solubilities and vapor pressures than they would have if they had been liquids. The ratio of the (actual) solid to the (hypothetical supercooled) liquid solubility or vapor pressure is termed the fugacity ratio F and can be estimated from the melting point and the entropy of fusion. This correction eliminates the effect of melting point, which depends on the stability of the solid crystalline phase, which in turn is a function of molecular symmetry and other factors. For solid solutes, the correct property to plot is the calculated or extrapolated supercooled liquid solubility. This is calculated in this handbook using where possible a measured entropy of fusion, or in the absence of such data the Walden s Rule relationship suggested by Yalkowsky (1979) which implies an entropy of fusion of 56 J/mol-K or 13.5 cal/mol-K (e.u.)... 

Heats of fusion, AHfus, are generally expressed in kcal/mol or kJ/mol and entropies of fusion, ASlus in cal/mol-K (e.u. or entropy unit) or J/mol K. The fugacity ratio F, as discussed in Section 1.2.8, is used to calculate the supercooled liquid vapor pressure or solubility for correlation purposes. In the case of liquids such as benzene, it is 1.0. For solids it is a fraction representing the ratio of solid-to-liquid solubility or vapor pressure. 

Overberger, J.E., Steele, W.A., Aston, J.G. (1969) The vapor pressure of hexamethylbenzene. The standard entropy of hexamethyl-benzene vapor and the barrier to internal rotation. J. Chem. Thermodyn. 1, 535-542. 

Pitzer, K.S., Guttman, L., Westrum, Jr., E.F. (1946) The heat capacity, heats of fusion and vaporization, vapor pressure, entropy, vibration frequencies and barrier to internal rotation of styrene. J. Am. Chem. Soc. 68, 2209-2212. 

The printed data output step 4 lists the values for the constants A and B of the general vapor pressure equation and the enthalpy and entropy of vaporization or sublimation. 

Gross, K. D. Williamson, G. Waddington and H. M. Huffman Spiropentane Heat Capacity, Heats of Fusion and Vaporization, Vapor Pressure, Entropy and Thermodynamic Functions. J. Amer. chem. Soc. 72, 4664 (1950). 

The vapor pressure of germanic iodide. The entropies of germanic... 

Figure 11.6. Entropy of liquid He under its equilibrium vapor pressure. Data below 1.90 K from H. C. Kramers, J. D. Wasscber, and C. J. Gorter, Physica 18, 329 (1952). Data from 1.90 K to 4.00 K from R. W. Hill and O. V. Lounasmaa, Phil. Mag. Ser. 8, 2, 143 (1957).

At 42°C the enthalpy of mixing of 1 mole of water and 1 mole of ethanol is — 343.1 J. The vapor pressure of water above the solution is 0.821 p and that of ethanol is 0.509 P2, in which p is the vapor pressure of the corresponding pure liquid. Assume that the vapors behave as ideal gases. Compute the excess entropy of mixing. 

Jones, W.M. and Giauque, W.F. The entropy of nitromethane. Heat capacity of solid and liquid. Vapor pressure, heats of fusion and vaporization, / Am. Chem. Soc., 69(5) 983-987, 1947. 

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