Enthalpy-composition data

The simplifying assumptions that are necessary for the Y-X solution method are then relaxed to include enthalpy balances. A graphical solution of this more rigorous model, which requires enthalpy-composition data, is presented. 

The surface-catalyst composition data for the silica-supported Ru-Rh cuid Ru-Ir catalyst are shown in Figure 1. A similcir plot for the series of silica-supported Pt-Ru bimetallic catalysts taken from ref. P) is included for comparison purposes. Enthalpies of sublimation for Pt, Ru, Rh and Ir are 552, 627, 543, and 648 KJ/mole. Differences in enthalpies of sublimation (a<75 KJ/mole) between Pt and Ru cind between Rh and Ru are virtually identical, with Pt euid Rh having the lower enthalpies of sublimation. For this reason surface enrichment in Pt for the case of the Pt-Ru/Si02 bimetallic clusters cannot be attributed solely to the lower heat of sublimation of Pt. Other possibilities must also be considered. 

Although the thermal demands of crystallization processes are small compared with those of possibly competitive separation processes such as distillation or adsorption nevertheless, they must be known. For some important systems, enthalpy-composition diagrams have been prepared, like those of Figure 16.4, for instance. Calculations also may be performed with the more widely available data of heat capacities and heats of solution. The latter are most often recorded for infinite dilution, so that their utilization will result in a conservative heat balance. For the case of Example 16.3, calculations with the enthalpy-concentration diagram and with heat of solution and heat capacity data are not far apart. 

Inversion of composite isotherms and enthalpy curves have been made using the constructed database, and assuming a lognormal form for the pore size distribution. The symmetrical distribution underlying the composite data is reproduced well Significantly however, the isotherm data underestimate the proportion of ultramicropores in the composite on the other hand, the enthalpy data do not entirely account for the fraction of wider pores present. This initial study suggests that prospects exist for a more precise characterisation of micropore distributions using a combination of enthalpy and isotherm experimental data. 

The figure-that follows for the ethanol + water sy.s-tem is an unusual one in that it shows both vapor-liquid equilibrium and the enthalpy concentration diagrams on a single plot. This is done as follows. The lower collection of heavy lines give the enthalpy concentration data for the liquid at various temperatures and the upper collection of lines is the enthalpy-concentration data for the vapor, each at two pressures, 0.1013 and 1 013 bar. (There are also enthalpy-concentration lines for several other temperatures.) The middle collection of lines connect the equilibrium compositions of liquid and vapor. For example, at a pressure of 1.013 bar, a saturated-vapor containing 71 wt % ethanol with an enthalpy of 1535 kJ/kg is in equilibrium with a liquid containing 29 wt % ethanol with an enthalpy of 315 kJ/kg at a temperature of 85°C. Note also that the azeotropes that form in the ethanol -f water system are indicated at each pressure. 

The heat effects accompanying a crystallization operation may be determined by making heat balances over the system, although many calculations may be necessary, involving knowledge of specific heat capacities, heats of crystallization, heats of dilution, heats of vaporization, and so on. Much of the calculation burden can be eased, however, by the use of a graphical technique in which enthalpy data, solubilities and phase equilibria are represented on an enthalpy-composition H x) diagram, sometimes known as a Merkel chart. 

Enthalpy-concentration data. An enthalpy-concentration diagram for a binary vapor-liquid mixture of A and B takes into account latent heats, heats of solution or mixing, and sensible heats of the components of the mixture. The following data are needed to construct such a diagram at a constant pressure (1) heat capacity of the liquid as a function of temperature, composition, and pressure (2) heat of solution as a function of temperature and composition (3) latent heats of vaporization as a function of composition and pressure or temperature and (4) boiling point as a function of pressure, composition, and temperature. 

Integral thermodynamic values are derived for the a-phase by Allen (1991). The pressure-composition data are unanticipated and raise questions about the nature of the solution. Enthalpies of formation for the solid and liquid solutions are comparable with changes of about — 84 J for each 0.01 mol of H dissolved in the metal. As evidenced by the absence of a resolvable temperature dependence for the InP versus H/Pu isotherms, the derived entropies of formatiom for the solutions are essentially zero. This result is inconsistent with a ASf value near — 130 + 20 J/mol K Hj observed for condensed hydride phases (see tables 4a, 7 and 8) and implies that the disorder of H atoms in solution with plutonium is comparable to that for gaseous H2. 

With the formalism presented in section II it is possible to calculate the pressure-composition isotherms, the chemical potential the partial molar enthalpy H and entropy S j provided the density-of-sites function g(e ), the molar volume Vjj, the phonon spectrum o)(e ), and the function f(y) which contains all the concentration dependence of the site energies and interaction energies are known. This large number of input parameters makes it impossible to determine g(e ), V, m(e ), f(y) directly from a fit to experimental data (which in most cases are in the form of pressure-composition data or calorimetric data). There is thus a serious need for reliable approximate values of these various parameters. 

Theoretically the enthalpy-composition method is more exact than the use of the modified latent heats of vaporization, but in most cases the two agree within the accuracy of the calculation. For binary mixtures, if the necessary enthalpy data are already available, the enthalpy-composition method is the easier to apply if the data are not available and must be calculated, then the other method is the more convenient. For multicomponent mixtures the modified latent heat method is more convenient even if the complete enthalpy data are available. 

The temperature-composition data for a liquid in equilibrium with one of the pure solid components 1 can be generally expressed in terms of the mole fraction A i, the activity coefficient 71, and the enthalpy of fusion AHf° of component 1 by... 

Solution First, we must construct the balanced composite curves using the complete set of data from Table 7.1. Figure 7.5 shows the balanced composite curves. Note that the steam has been incorporated within the construction of the hot composite curve to maintain the monotonic nature of composite curves. The same is true of the cooling water in the cold composite curve. Figure 7.5 also shows the curves divided into enthalpy intervals where there is either a... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Some quantities associated with the rates and mechanism of a reaction are determined. They include the reaction rate under given conditions, the rate constant, and the activation enthalpy. Others are deduced reasonably directly from experimental data, such as the transition state composition and the nature of the rate-controlling step. Still others are inferred, on grounds whose soundness depends on the circumstances. Here we find certain features of the transition state, such as its polarity, its stereochemical arrangement of atoms, and the extent to which bond breaking and bond making have progressed. 

Suppose that the actual behavior of temperature versus enthalpy is known and is highly nonlinear, as shown in Figure 19.4. How can the nonlinear data be linearized so that the construction of composite curves and the problem table algorithm can be performed Figure 19.4 shows the nonlinear streams being represented by a series of linear segments. The linearization of the hot streams should... 

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