Equilibrium constant mole fraction

In an investigation the isotope ratio 0/ 0 was found to be 2.045 x 10 for fresh water and 2.127 x 10 for carbon dioxide in the atmosphere. Calculate the equilibrium constant (mole fractions ) for the reaction... 

The phase rule permits only two variables to be specified arbitrarily in a binary two-phase mixture at equilibrium. Consequently, the curves in Fig. 13-18 can be plotted at either constant temperature or constant pressure but not both. The latter is more common, and data in Table 13-1 correspond to that case. The y-x diagram can be plotted in mole, weight, or volume fractions. The units used later for the phase flow rates must, of course, agree with those used for the equilibrium data. Mole fractions, which are almost always used, are applied here. 

D15. We wish to batch distill 100 kmol of a mixture of n-butanol and water. The system consists of a batch still pot plus 1 equilibrium stage. The system is at one atmosphere. The feed is 48 mol% water and 52 mol% butanol. The distillate vapor is condensed and sent to a liquid-liquid settler. The water rich product (0.975 mole fraction water) is taken as the distillate product and the butanol rich layer (0.573 mole fraction water) is refluxed to the column. We desire a final still pot mole fraction of 0.08 water. Energy is added at a constant rate to the still pot thus, V = constant. Note that the distillate product is a constant mole fraction. The reflux ratio increases as the distillate vapor mole fraction decreases during the course of the batch distillation. Equilibrium data are given in Table 8-2. 

Then, when the dependence of the ceiling temperature is computed for any feed the composition of the equilibrium copolymer (mole fraction of 1,3-dioxane units, fr(B)) can be calculated on the basis of the computed equilibrium constants of homopropagation (the equation easily derivable from relationships [45] and [46] assuming the infinite X ) ... 

InFig. 9, aplotofEq. (114) results in predicted adsorption as a function of pH with total cation and surface-site mole fraction held constant. For the Gibbs plot in Fig. 10 of equation (115), adsorption is plotted as the areal surface concentration, Tg, as a function of increasing total cation mole fraction [or equilibrium solution mole fraction with Eq. (102)] at constant pH and total surface-site concentration. 

The solubilization of diverse solutes in micelles is most often examined in tenns of partitioning equilibria, where an equilibrium constant K defines the ratio of the mole fraction of solute in the micelle (X and the mole fraction of solute in the aqueous pseudophase. This ratio serves to define the free energy of solubilization -RT In K). 

Since in most practical circumstances at temperatures where vapour transport is used and at around one atmosphere pressure, die atomic species play a minor role in the distribution of atoms, it is simpler to cast the distribution equations in terms of the elemental molecular species, H2, O2 and S2, tire base molecules, and the derived molecules H2O, H2S, SO2 and SO3, and eliminate any consideration of the atomic species. In this case, let X, be tire initial mole fraction of each atomic species in the original total of atoms, aird the variables Xi represent the equilibrium number of each molecular species in the final number of molecules, N/. Introducing tire equilibrium constants for the formation of each molecule from tire elemental atomic species, with a total pressure of one aurros, we can write... 

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

Substituting the expressions for the mole fractions of Hj, Nj, and NH3, respectively, for the equilibrium constant gives... 

The solution then follows along the same lines as for TCR if the temperature and pressure are known then 7, S and the resulting mole fractions can be determined from the equilibrium constants. The temperature change between inlet and outlet is now likely to be higher than in the TCR reactions, so the determination of the A, s as functions of a single mean temperature for the reaction is more difficult. 

Many equilibrium calculations are accomplished using tlie plrase equilibrium constant K,. Tliis constant has been referred to in industry as a coiiiponential split factor, since it provides the ratio of the mole fractions of a component in two equilibrium pluises. The defining equation is... 

The liquid line and vapor line together constitute a binary (vapor + liquid) phase diagram, in which the equilibrium (vapor) pressure is expressed as a function of mole fraction at constant temperature. At pressures less than the vapor (lower) curve, the mixture is all vapor. Two degrees of freedom are present in that region so that p and y2 can be varied independently. At pressures above the liquid (upper) curve, the mixture is all liquid. Again, two degrees of freedom are present so that p and. v can be varied independently/... 

The thermodynamic activity equilibrium constant (Ka) is expressed in terms of mole fraction (X) and activity coefficient (y) by the following equation ... 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

Solution The kinetic equilibrium constant is 50mol/m. It is converted to mole fraction form using... 

Each gas establishes its own dynamic equilibrium with water. The concentration depends on the partial pressure of the gas in the atmosphere and on the value of its Henry s law constant at 25 °C. Recall from Chapter 5 that the partial pressure of any gas in a mixture is given by the mole fraction (X multiplied by total pressure. 

Even in relatively concentrated solutions, the mole fraction of water remains close to 1.00. At a solute concentration of 0.50 M, for example, H2 O = 0.99, only 1% different from 1.00. Equilibrium calculations are seldom accurate to better than 5%, so this small deviation from 1.00 can be neglected. Consequently, we treat solvent water just like a pure substance its concentration is essentially invariant, so it is omitted from the equilibrium constant expression. 

Please note that the correction corresponds to introducing a corrected equilibrium constant K(T)/X . The correction has hardly any influence on the mole fraction of ammonia in the mixture at low pressures, but for ptot = 100 bar and higher the correction becomes significant. The results are presented in the last column of Tab. 2.4 and in Fig. 2.1. It should be noted that correction procedures exist for cases where the mixture does not behave ideally, but this goes beyond the scope of the present treatment. 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

Air needs to be dissolved in water under pressure at 20°C for use in a dissolved-air flotation process (see Chapter 8). The vapor-liquid equilibrium between air and water can be predicted by Henry s Law with a constant of 6.7 x 104 bar. Estimate the mole fraction of air that can be dissolved at 20°C, at a pressure of 10 bar. 

Kx Equilibrium constant of reaction based on mole fraction in the liquid phase (-)... 

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