Fugacity of nitrogen

Problem Utilize the following data to calculate the fugacities of nitrogen gas at the various pressures at 0° C. 

Determine by the graphical method the fugacity of nitrogen in the mixture at the various total pressures, and compare the results with those obtained for the pure gases hence, test the Lewis-Randall rule for the fugacity of a gas in a mixture [cf. Merz and Whittaker, J, Am. Chem, Soc., 50, 1522 (1928)]. 

Figaie 1.2-2 shows the fugacity of nitrogen at 100 K. as computed from Eqs. (1.2-30), (1.2-32), and (1.2-33). Also shown are several oommonly employed approximations. The dashed line/f = P is the ideal-gas approximation to the vapor fugacity it is a special case of Eq. (1.2-26) and Is a consequance of the definition, Eq. (1.2-28). Note that the idenl-gas approximation becomes asymptotically valid as P approaches zero. 

Foam fractionation Fractional extraction Fractionation, seeDistillation Free-volume theory of diffusion Freezing-point determination Fugacity of nitrogen standard state Fugacity coefficient composition dependence of acetic acid vapor... 

FIGURE 1.2-2 Pressure dependence of fugacity /of nitrogen at 100 K. Dashed and dotted lines represent approximations to real behavior. 

To illustrate how fugacity varies with pressure. Table 4.1 lists the fugacities of nitrogen gas. Note how the fugacity almost equals the pressure at p = 1 atm, but by the time p = 1000 atm, the fugacity is almost twice the pressure. 

Using the data in the table, compute the pure component fugacity of nitrogen at 0°C, 25°C, and 50°C. Since the data are not equally spaced, use of the trapezoidal rule is suggested to perform the numerical integration. 

Fio. 10. Solubility of nitrogen in water at high pressures. Fugacity is in atmospheres. 

The feed stream consists of 60 mole percent hydrogen, 20% nitrogen, and 20% argon. Calculate the composition of the exit gases, assuming equilibrium is achieved in the reactor. Make sure that you take deviations from the ideal gas law into account. The equilibrium constant expressed in terms of activities relative to standard states at 1 atm may be assumed to be equal to 8.75 x 10 3. The fugacity of pure H2 at 450 °C and 101.3 MPa may be assumed to be equal to 136.8 MPa. 

If the gas mixture is considered to be an ideal gas mixture then all fugacity coefficients are 1 and since K is a constant, the effect of increasing pressure is an increase of the equilibrium mole fraction of ammonia and a decrease of the mole fractions of nitrogen and hydrogen. However, since the ammonia synthesis is a high pressure process the gas mixture is not an ideal gas and the fugacity coefficients have to be taken into account. 

Indeed, the constant k in (296) and (297) characterizes only the rates of adsorption and desorption of nitrogen and is thus one and the same for both reactions. The difference in the rates of these reactions results only from the nonidentity of the fugacities of adsorbed nitrogen pNl and pf,2, the last being determined for reaction (314), instead of (298) by the equation... 

The three seminal ideas in this early work of Temkin are quite general. The first is that adsorption of nitrogen is rate determining. The second is the virtual pressure or fugacity of adsorbed nitrogen, a concept of great importance to the understanding of catalytic cycles at the steady state. The third idea is the kinetic description of the catalytic surface as a nonuniform one. The last was systematized later by Temkin s school, both in theory and in application, to a... 

N (g), we obtain A H = -153.69 0.75 kcal mol" at unit fugacities of oxygen and nitrogen. When this value is combined... 

It can be shown that the maximum conversion of nitrogen and hydrogen into ammonia occurs when the gases are mixed with the stoichiometric ratio. (See Problem PI5.1.) hSee Section 11.3a of Chapter 11 for a discussion of the effect of pressure on the fugacity, including the Lewis and Randall rule. 

When liquid water is equihbrated with nitrogen at 298.15 K and 1 bar, the partial pressure of H2O in the gas phase is pa = 0.03185bar. Use the given values of Baa. bb. and Bab to calculate the fugacity of the gaseous H2O in this binary mixture. Compare this fugacity with the fugacity calculated with the value of Bab predicted by the rule of Lewis and Randall. 

To illustrate this thermodynamic consistency test, Figs. 15, 16, and 17 show plots of the appropriate functions needed to calculate Areas I, II, and III, respectively, for the nitrogen-carbon dioxide system at 0°C the data are taken from Muirbrook (M5). Fugacity coffiecients were calculated with the modified Redlich-Kwong equation (R4). 

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