Mole fraction in the vapor phase

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

Since the partial pressure is the mole fraction in the vapor phase multiplied by the total pressure, (i.e., Pi = Yi P), the equilibrium... 

The limits of the Lewis fugacity rule are not determined by pressure but by composition the Lewis rule becomes exact at any pressure in the limit as y( - 1, and therefore it always provides a good approximation for any component i which is present in excess. However, for a component with small mole fraction in the vapor phase, the Lewis rule can sometimes lead to very large errors (P5, R3, RIO). 

P7.1 Vapor pressure data for ethanol (1) + 1,4-dioxane (2) at T = 323.15 K is given in the following table, where. vq is the mole fraction in the liquid phase and y is the mole fraction in the vapor phase. 

Because C-C6H12 has a higher vapor pressure than c-CsHuCHj, the vapor phase above the liquid mixture is richer in C-C6H12 than is the liquid phase. Thus, if 2 is the mole fraction of c-C6H 2 in the liquid phase and >2 is the corresponding mole fraction in the vapor phase, then yz > 2. 

These are both pressure fractions, as calculated, and also are the mole fractions in the vapor phase. 

Estimated relative errors are 0.2% for temperature, 5% for pressure, 4% for carbon dioxide mole fraction in the liquid phase, and 10% for lemon oil mole fraction in the vapor phase. Relative error is defined as experimental error divided by sample average val ue. 

Since the partial pressure is the mole fraction in the vapor phase multiplied by the total pressure, (i.e., p, = y, P), the equilibrium constant Keq is expressed as Keq = Ky PAn, where An = (2 - 1 - 3), the difference between the gaseous moles of the products and the reactants in the ammonia synthesis reaction. 

Three streams enter the volume, including air, water, and the chemical substance whose hazard we are trying to control. When n is defined as the number of moles, y is defined as the mole fraction in the vapor phase, and x is defined as the mole fraction in the liquid phase. The subscripts C, a, and w correspond to the chemical in question, air, and water, respectively. The individual molar flow rates of these three species are... 

Calculate the mole fraction in the vapor phase. When the components of the system are soluble in each other in the liquid state (as is the case for benzene and toluene), so that there is only one liquid phase, then the moles of vapor V per total moles can be calculated from the equation... 

Figure 9. Mole fraction in the adsorbed phase, X a

In both Figs. 22, A and B the uppermost curve gives the total vapor pressure as a function of the composition of the liquid. The corresponding curve as a function of the vapor composition will lie below it in each case, so that the vapor contains more of the constituent the addition of which causes an increase in the total vapor pressure. If an expression for the partial vapor pressure in terms of the mole-fraction composition of the liquid is available (of. 35d), an analogous expression for the vapor composition can be derived by utilizing the relationship based on the postulated ideal behavior of the vapor, i.e., that nJ/n2 is equal to pi/p2 ( 34e), where nJI and N2 refer to the respective mole fractions in the vapor phase. 

Figure 15.17. Mole fractions in the vapor phase as a function of condenser length for condensation of a mixture of normal paraffins (propane to /i-octane) in the presence of hydrogen.

In the gas phase, the activity is the fugacity, since the activity is the fugacity divided by the fugacity of the standard state, which is one atmosphere. In turn, you can write the fugacity as the product of the fugacity coefficient (providing a correction from ideal gas behavior) times the total pressure times the mole fraction in the vapor phase ... 

For the case in which the solute mole fraction in the vapor phase 73 cannot be neglected, the S-L-V equilibrium calculations also include the S-V equilibrium for the solid solute in addition to Eqs. (51) to as follows ... 

A mixture of ethanol and 1-propanol behaves ideally at 36°C and is in equilibrium with its vapor. If the mole fraction of ethanol in the solution is 0.62, calculate its mole fraction in the vapor phase at this temperature. (The vapor pressures of pure ethanol and 1-propanol at 36°C are 108 mmHg and 40.0 mmHg, respectively.)... 

When the equilibrium-based model is applied to multicomponent mixtures, a number of problems arise. Values of EMG differ from component to component and vary from stage to stage. But at each stage, the number of independent values of EMG must be determined so as to force the mole fractions in the vapor phase to sum to 1. This introduces the possibility that negative values of EMG can result. This is in contrast to binary mixtures for which the values of EMG are always positive and are identical for the two components. 

In this equation, N is the number of data points in the experimental data set and y is the congener mole fraction in the vapor phase. 

From Antoine s equation, we first calculate the vapor pressure of ethanol from which we can then derive its initial mole fraction in the vapor phase (at 25 C) ... 

Fig. 2.1-18 Saturation temperature in dependence of the mole fraction at constant pressure (above) and mole fraction in the vapor phase in dependence of the mole fraction in the liquid phase for a constant pressure...

Using these values obtained for phase or phase directly the corresponding pressure and mole fraction in the vapor phase can be calculated. 

With the help of the activity coefficients and the given vapor pressures, the partial pressures, the total pressure, and the mole fraction in the vapor phase at 70 C can be calculated ... 

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