Equilibrium Ratio Plots

Here we shift our attention from the concentration of each species in equilibrium to the ratio of acid to conjugate base at equilibrium, since this ratio fixes the pH. From the Kg expression, 

This equilibrium ratio must not be confused with the buffer ratio of equation (3-7), which is CJC, the ratio of the analytical concentrations, which may or may not be close to the ratio of the species at equilibrium. The equilibrium ratio is given by H/Kg. A material balance expression for this ratio can be found from the complete 

The OH is negligible here, and the log Rg is thus near 3. To have pH 1, all the HX must form ions and Rg is zero, logR — — oc. We have taken ionic strength 0.1 M throughout this section, so that pX , is 13.80. Thus, a neutral solution occurs at pH 6.9 where H = OH = 10-6.90 jg yyhere denominator of our Rg fraction goes to zero for the pure acid case and logRg— oo. 

For the base, a mirror image of the acid plot is found. For the buffers, H and OH are negligible in the central region, where these are both small, and Rg is effectively the same as the buffer ratio CJC. The curved portions show the behavior of rather strong acid or base, where equation (3-7) is not valid. 

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The equilibrium ratios of hydrogen-to-hydrogen sulfide for the reaction, derived (34) from available thermodynamic data (35), are plotted in Figure 10 as a function of temperature. When Ph2/Ph2s over the catalyst is less than the equilibrium value, the nickel can be sulfided and hence poisoned. Conversely, when this ratio is greater than the equi-... 

Steam. Steam is a potential poison of nickel catalysts under extremely high steam concentrations and low hydrogen concentrations. This is apparent in Figure 11 where the equilibrium ratio of Ph2/Fh2o over Ni and over Ni(active) is plotted as a function of temperature for the following reactions ... 

The culprit is the phenomenon of retrograde condensation, which wa6 previously discussed In connection with hydrocarbon dewpoints. This can best be understood by looking at a graph of equilibrium ratios, commonly called K-values, as shown in Figure 2. We have cross-plotted a limited number of curves, to avoid confusion while Illustrating our point. 

Figure 9-7 A shows the rate of exchange of isotopi-cally labeled glucose (glucose ) with glucose 6-phosphate as catalyzed by the enzyme hexokinase (Chapter 12). The exchange rate is plotted against the concentration of glucose 6-phosphate with the ratio [glucose] / [glucose 6-phosphate] constant at 1 /19, such that an equilibrium ratio for reactants and products is always...

Experimentally determined K-factors normally are plotted against pressure on a log-log scale. Figures 14-1 and 14-2 show equilibrium ratios of two typical petroleum mixtures for several temperatures. 

Identify mislocated feed. For binary distillation the feed point should be where the q-line intersects the equilibrium curve. For multicomponent distillation this may or may not be the case. So for multicomponent distillation feed location, key ratio plots and d/b plots are preferred and discussed next. 

From the mole-ratio plot, we see that m = 0. Values for 8ml ml, can be obtained from the two straight-line portions of the curve. With one or more measurements of A in the curved region of the plot, sufficient data are available to calculate the three equilibrium concentrations and thus the formation constant. 

HNOj concentration of the aqueous phase must be over 0.00004 M. At equilibrium, neptunium in the aqueous phase is then divided between the hexavalent and pentavalent states. The ratio of hexavalent to pentavalent neptunium is given by Eq, (10.27), obtained from the equilibrium ratio /lnp defined by Eq. (10.24), and plotted in Fig. 10.30. 

The rate at which the steam-carbon reaction proceeds depends greatly on temperature (9), requiring heat above 2000°F. to approach equilibrium (II). Since hydrogasification tests are conducted at less than 2000°F. to preserve the methane formed, the carbon-steam reaction is expected to be substantially removed from equilibrium. This is shown by Figure 6 where calculated equilibrium ratios are plotted against maximum bed temperature. The curve represents true equilibrium for comparison. 

Methane equilibrium ratios calculated from effluent gas compositions for 10 runs at 2.5 atm. range from about 0.14 to about 0.19, while ratios calculated for two runs at 8 atm. are about 0.075 and 0.095. The two respective ranges are indicated by the two vertical arrows in Figure 1, which is a plot of methane equilibrium ratio vs. reciprocal of absolute temperature. (Ratios for two runs at 5 atm. are about 0.082 and 0.11.)... 

Wen and Huebler (8) reported batch-system measurements of bituminous coal-char-hydrogen equilibrium at 1300°F. and 137 atm. Typically, about 20 hours were required for the system to reach an apparent equilibrium (the maximum in a plot of the methane equilibrium ratio vs. time). The results are reproduced in a plot of pseudo-equilibrium vs. bum-off in Figure 4 of Wen, Abraham, and Talwalkar s chapter in this volume. The open Maltese cross plotted in Figure 1 of this discussion shows Wen and Huebler s value for zero bum-off, and the closed cross shows the value for 25% bum-off. Since these pseudo-equilibria were not measured for an on-going reaction, they do not represent quasiequilibria in Squires sense. 

We introduced the monoprotic ratio methods in Chapter 4. We shall treat only the equilibrium condition ratio here. While the a s of Figure 5-1 show the variations of species in a most clear way, they are tedious to plot unless programmed for computer calculation and automatic plotter. The log ratio diagrams are composed entirely of straight lines and can be plotted in a few minutes. They contain all the information of the a diagrams, though in less clear display. We shall show how to derive the a diagrams from these log ratio plots. Let us do this for citric acid. 

For V-L-L equilibrium calculations, one can select the light liquid phase as the reference phase and then estimate the initial equilibrium ratios according to the procedure of Example 4.2. Figure 4.12 plots the calculated results for a C02 reservoir oil system at various pressures at fixed composition and 307.6 K. The compositions of oil B and CO2 mixtures investigated by Shelton and Yarborough (1977) are used. Note that up to a pressure of 78.8 bar, two phases, a vapor phase and a hydrocarbon-rich liquid phase, coexist. From P = 78,8 to 81.2 bar, three phases exist and above P = 81.2 bar, the vapor phase disappears and two liquid phases are present. Details of various parameters can... 

This parameter is called the stripping factor, S, and its reciprocal, Ltf/rnGM. is called the absorption factor, A. The absorption factor is used in a number of popular techniques for the design of both packed and tray absorbers. It can be considered ro be the ratio of Lm Gm, the sl( of the operating line, to m, the slope of the equilibrium line. Plots of equation 1-17,... 

Use the molecular weight ratio to calculate the apparent extent of reaction of the caprolactam in these systems. Is the variation in p qualitatively consistent with your expectations of the effect of increased water content in the system Plot p versus moisture content and estimate by extrapolation the equilibrium moisture content of nylon-6 at 255 C. Does the apparent equilibrium moisture content of this polymer seem consistent with the value given in Sec. 5.6 for nylon-6,6 at 290°C ... 

Now let us refer to the right-hand side of the above expression. The mean driving force varies with the specified design temperatures and also the ratio of water/air loading (L/G). If we take a low airflow, the air soon rises in temperature and tends to reach equilibrium conditions with the boundary layer. Thus the driving force is reduced. On the other hand, excess air is unnecessary. Therefore, one must adjust the airflow that supply just meets demand. A plot of L/G versus AT MDF is shown in Figure 34.17. This is known as a demand curve. 

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