Equilibrium constant fugacity ratio

At 900 °F the equilibrium constant for this reaction is 5.62 when the standard states for all species are taken as unit fugacity. If the reaction is carried out at 75 atm, what molal ratio of steam to carbon monoxide is required to produce a product mixture in which 90% of the inlet CO is converted to C02 ... 

For every initial H20/C0 ratio, the mixture mole fractions, hence the critical temperature and volume, are determined by the reaction extent e. The equilibrium constant is calculated at the critical temperature. The fugacities are calculated also at the critical condition for the given e. The function F, defined as... 

Figures 1 to 3 present calculated equilibrium molar ratios of products to reactants as a function of temperature and total pressure of 1 and 100 atm. for the gas-carbon reactions (4), (7), and (5), (6), (4), (7), respectively. Up to 100 atm. over the temperature range involved, the fugacity coefficients of the gases are close to 1 therefore, pressures can be calculated directly from the equilibrium constant. From Fig. 1, it is seen that at temperatures above 1200°K. and at atmospheric pressure, the conversion of carbon dioxide to carbon monoxide by the reaction C - - COj 2CO essentially is unrestricted by equilibrium considerations. At elevated pressures, the possible conversion markedly decreases hence, high pressure has little utility for this reaction, since increased reaction rate can easily be obtained by increasing reaction temperature. On the other hand, for the reaction C -t- 2H2 CH4, the production of methane is seriously limited at one atmosphere pressure and practical operating temperatures, as seen in Fig. 2. Obviously, this reaction must be conducted at elevated pressures to realize a satisfactory yield of methane. For the carbon-steam reaction.

When equilibrium is attained, the concentration of the compound in the SPMD is equal to the concentration in water multiplied by ratio of compound uptake and release rate constants. The ratio describes partition coefficient between SPMD and water, Ksw. Equilibrium for some chemicals with high fugacities may occur in less than one month. 

Equations (1.3-14) and (1.3-15) thus give the prediction from transition-state theory for the rate of a reaction in terms appropriate for an SCF. The rate is seen to depend on (i) the pressure, the temperature and some universal constants (ii) the equilibrium constant for the activated-complex formation in an ideal gas and (iii) a ratio of fugacity coefficients, which express the effect of the supercritical medium. Equation (1.3-15) can therefore be used to calcu-late the rate coefficient, if Kp is known from the gas-phase reaction or calculated from statistical mechanics, and the ratio (0a 0b/0cO estimated from an equation of state. Such calculations are rare an early example is the modeling of the dimerization of pure chlorotrifluoroethene = 105.8 °C) to 1,2-dichlor-ohexafluorocyclobutane (Scheme 1.3-2) and comparison with experimental results at 120 °C, 135 °C and 150 °C and at pressures up to 100 bar [15]. 

The equilibrium constant from thermodynamics is defined as follows in terms of fugacity ratios ... 

The equilibrium constant is then the ratio of the fugacity capacities. The magnitude of Z will depend on temperature and the properties of the compound as they relate to the characteristics of a given phase. Compounds will accumulate in compartments with a high value of Z. The next step is to define Z for environmental compartments air, water, soil, sediments, and biota. 

At equilibrium the gas pressure is equal to the fugacity p=P and the rate in the reverse direction is equal to the rate in the forward direction r =r+ giving the ratio of rate constants on each site... 

C = constant in Equation 5 EW = universal constants in Equation 3 K = equilibrium ratio = y/x M = index for Equation 3 N = index for Equation 3 N = mole fraction R = universal gas constant T = absolute temperature V = volume f = fugacity... 

Equation (1.114) relates the vapor-liquid equilibrium ratio, Ki, to the ratio of fugacity coefficients. The fugacity coefficients can be obtained from the volumetric properties given by an EOS. However, as Eq. (1.109) demands, the volumetric data are required from zero pressure to pressure P of the system at constant temperature and composition. Therefore, the EOS should represent the volumetric behavior over the whole range. 

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