Fugacity temperature variation

This reaction suggests that a decrease in H2S concentration, and increases in H+ concentration and (H2 fugacity) and temperature variations are important causes for the deposition of gold in electrum. 

Only the fugacity change with respect to pressure and temperature variation has been considered for the pure gases. For a mixed gas system, interactions between the different gas molecules and atoms must also be taken into account. The second virial coefficient, Bm(T), for a binary mixture between molecules 1 and 2 can be expressed as... 

In their correlation, Chao and Seader use the original Redlich-Kwong equation of state for vapor-phase fugacities. For the liquid phase, they use the symmetric convention of normalization for y and partial molar volumes which are independent of composition, depending only on temperature. For the variation of y with temperature and composition, Chao and Seader use the equation of Scatchard and Hildebrand for a multicomponent solution ... 

The C02 fugacity decreases sharply during cooling (Fig. 23.3), as would be expected, since gas solubility increases as temperature decreases. In the calculation, the fugacity decrease results almost entirely from variation in the equilibrium con-... 

In our kinetic calculations, we refer to the directly observed partial pressure of propylene, rather than to its fugacity, because over the temperature and pressure range examined, we can assume that partial pressures and fugacities are practically proportional. In fact, from the literature data, the variation in propylene fugacity coefficient, in the range of our kinetic tests, is small (about 0.97 at 30° and 2700 mm. Hg about 0.99 at 70° and 450 mm. Hg of propylene partial pressure). 

Table 2 Model high-temperature and low-temperature equilibria demonstrating the effects of oxidation and variation of H2S fugacity, as well as the contrasting stoichiometric effects of changing pH, upon gold solubility.

As a first approximation, Cp may be treated as independent of the pressure, and if MJ.T. is expressed as a function of the pressure, it is posnble to carry out the integration in equation (29.24) alternatively, the integral may be evaluated graphically. It is thus posdble to determine the variation of the fugacity with temperature. 

By following the procedure given in 29f, with / representing the fugacity of pure liquid or solid, an equation exactly analogous to (29.22) is obtained for the variation of the fugacity with temperature at constant pressure. As before, H is the molar heat content of the gas, i.e., vapor, at low pressure, but H is now the molar heat content of the pure liquid or solid at the pressure P. The difference — H has been called the ideal heat of vaporization, for it is the heat absorbed, per mole, when a very small quantity of liquid or solid vaporizes into a vacuum. The pressure of the vapor is not the equilibrium value, but rather an extremely small pressure where it behaves as an ideal gas. 

This equation also gives the dependence of the activity Op on the temperature, since this activity is equal to the fugacity. Further, since Op is equal to ypP, where yp is the activity coefficient, the same equation represents the variation of the activity coefficient with temperature, p being constant. 

The equations derived in 30c, 30d thus also give the variation with pressure and temperature of the fugacity of a constituent of a liquid (or solid) solution. In equation (30.17), Vi is now the partial molar volume of the particular constituent in the solution, and in (30.21), i is the corresponding partial molar heat content. The numerator — fti thus represents the change in heat content, per mole, when the constituent is vaporized from the solution into a vacuum (cf. 29g), and so it is the ideal" heat of vaporization of the constituent i from the given solution, at the specified temperature and total pressure. 

Heterogeneous physical equilibria, e.g., between a pure solid and its vapor or a pure liquid and its vapor, can be treated in a manner similar to that just described. If the total pressure of the system is 1 atm., the fugacity of the vapor is here also equivalent to the equilibrium constant. The variation of In/ with temperature is again given by equation (33.16), where MP is now the ideal molar heat of vaporization of the liquid (or of sublimation of the solid) at the temperature T and a pressure of 1 atm. If the total pressure is not 1 atm., but is maintained constant at some other value, the dependence of the fugacity on the temperature can be expressed by equation (29.22), since the solid or liquid is in the pure state thus,... 

The use of the foregoing definition of an ideal solution implies certain properties of such a solution. The variation of the fugacity / of a pure liquid i with temperature, at constant pressure and composition, is given by equation (29.22), viz.. 

Most approximations of this class involve the relative magnitudes of the partial derivatives of the activity coefficients, fugacities, and the departure function Q with respect to temperature. If, for example, the Q is independent of temperature or its variation with temperature is small, then the approximation dQ/dT = 0 may be made. 

A formula for computing the variation of the fugacity of pure component i in the liquid phase with pressure at a given temperature is found by first restating Eq. (14-26) in the following form... 

Normally of course the expression for the variation of K with P is simpler than this, perhaps because all three states of matter may not be present, but also because it is quite unusual to use a variable pressure standard state for constituents whose fugacities are known or sought, (because this adds complexities rather than simplifying matters), and the In Qig) term is therefore essentially never required. To take a real example, let s consider the brucite-periclase reaction again. We have discussed the variation of the equilibrium constant for the brucite-periclase-water reaction with temperature at one bar, and showed that the equilibrium temperature for the reaction at one bar is about 265°C. Calculation of the equilibrium temperature of dehydration reactions such as this one at higher pressures was discussed briefly in 13.2.2. Here we will discuss the reaction in different terms to demonstrate the relationships between activities, standard states and equilibrium constants. 

The variation of fugacity with the temperature can be found by examining the derivative of the equation (5.93) ... 

Equation (9-177) describes the variation of vapor fugacity with temperature when the liquid composition is held constant and the total pressure is adjusted so as to preserve equilibrium. The quantity dpjdT) can be obtained from the slope of a pressure-temperature diagram. When p is small,... 

Determine the equilibrium composition that is achieved at 300 bar and 700 K when the initial mole ratio of hydrogen to carbon monoxide is 2. You may use standard enthalpy and Gibbs free energy of formation data. For purposes of this problem you should not neglect the variation of the standard heat of reaction with temperature. You may assume ideal solution behavior but not ideal gas behavior. You may also use a generalized fugacity coefficient chart based on the principle of corresponding states as well as the heat capacity data listed below. 

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