Initiating compositions

Latex Initial composition (styrene/comonomer) (M/M) Size (/xm) Reference... 

The initial compositions were calculated based on the reported amounts of the ingredients. 

Compound Initial composition and temperature, °C Gaseous components... 

It was assumed that fluoride-containing precursors undergo partial hydrolysis by atmospheric moisture. For instance, for an initial composition corresponding to x = 0.05, the final composition was found, using mass loss and chemical analyses, to be Lio.goCMgo.osoTao 9s)02.79sF0.o9o(OH)o.o6o. 

Fig. 95 shows the change in cell parameters, density and Curie temperature for ceramics with initial compositions of Li(Tai xMgx)03.3xF3x (where 0 < x < 0.2) versus x value. It should also be mentioned that the pyroelectric coefficient for x = 0.05 was found to be 4.0 nC cm 2 K l. 

The preceeding discussion was confined mostly to the carbon deposition curves as a function of temperature, pressure, and initial composition. Also of interest, especially for methane synthesis, is the composition and heating value of the equilibrium gas mixture. It is desirable to produce a gas with a high heating value which implies a high concentration of CH4 and low concentrations of the other species. Of particular interest are the concentrations of H2 and CO since these are generally the valuable raw materials. Also, by custom it is desirable to maintain a CO concentration of less than 0.1%. The calculated heating values are reported as is customary in the gas industry on the basis of one cubic foot at 30 in. Hg and 15.6°C (60°F) when saturated with water vapor (II). Furthermore, calculations are made and reported for a C02- and H20-free gas since these components may be removed from the mixture after the final chemical reaction. Concentrations of CH4, CO, and H2 are also reported on a C02 and H20-free basis. 

The carbon monoxide concentration contours for 50 atm and 700 °K (Figure 9) indicate that the equilibrium CO leakage will not be high if equilibrium is reached when the initial composition is near the stoichiometric line. 

Pyrolyses of formates, oxalates and mellitates yield CO and C02 (H2, H20 etc.) as the predominant volatile products and metal or oxide as residue. It is sometimes possible to predict the initial compositions from thermodynamic considerations [94], though secondary reactions, perhaps catalyzed by the solids present, may result in a final product mixture that is very different. The complex mixtures of products (hydrocarbons, aldehydes, ketones, acids and acid anhydrides) given [1109] by reactants containing larger organic groupings makes the collection of meaningful kinetic data more difficult, and this is one reason why there are relatively few rate studies available for the decompositions of these substances. 

The work of Higbie laid the basis of the penetration theory in which it is assumed that the eddies in the fluid bring an element of fluid to the interface where it is exposed to the second phase for a definite interval of time, after which the surface element is mixed with the bulk again. Thus, fluid whose initial composition corresponds with that of the bulk fluid remote from the interface is suddenly exposed to the second phase. It is assumed that equilibrium is immediately attained by the surface layers, that a process... 

In the experiments reported in Table 9.1, five mixtures with different initial compositions of the three gases were prepared and allowed to reach equilibrium at 1000. I<. The compositions of the equilibrium mixtures and the total pressure P were then determined. At first, there seemed to be no pattern in the data. However, Guldberg and Waage noticed an extraordinary relation the value of the quantity... 

Within experimental error, Guldberg and Waage obtained the same value of K whatever the initial composition of the reaction mixture. This remarkable result shows that K is characteristic of the composition of the reaction mixture at equilibrium at a given temperature. It is known as the equilibrium constant for the reaction. The law of mass action summarizes this result it states that, at equilibrium, the composition of the reaction mixture can be expressed in terms of an equilibrium constant where, for any reaction between gases that can be treated as ideal,... 

Each reaction has its own characteristic equilibrium constant, with a value that can be changed only by varying the temperature (Table 9.2). The extraordinary empirical result, which we justify in the next section, is that, regardless of the initial composition of a reaction mixture, the composition tends to adjust until the... 

The equilibrium constant of a reaction contains information about the equilibrium composition at the given temperature. However, in many cases, we know only the initial composition of the reaction mixture and are given apparently incomplete information about the equilibrium composition. In fact, the missing information can usually be inferred by using the reaction stoichiometry. The easiest way to proceed is to draw up an equilibrium table, a table showing the initial composition, the changes needed to reach equilibrium in terms of some unknown quantity x, and the final equilibrium composition. The procedure is summarized in Toolbox 9.1 and illustrated in the examples that follow. 

Step 1 Write the balanced chemical equation for the equilibrium and the corresponding expression for the equilibrium constant. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. In the first row, show the initial composition (molar concentration or partial pressure) of each species... 

Now consider the simultaneous evolution of and c)D. Suppose an air mass having initial compositions 3, = 0 cools and precipitates, always as an equilibrium process. According to the preceding analysis, measurements of both isotopic ratios in precipitation will plot on a curve with a slope approximately given by... 

The initial composition is Imol each of ethylbenzene and styrene and 0.5 mol of hydrogen. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

Formal verification that this result actually satisfies Equation (14.13) is an exercise in partial differentiation, but a physical interpretation will confirm its validity. Consider a small group of molecules that are in the reactor at position z at time t. They entered the reactor at time i = t — (zju) and had initial composition a t, z) = ai (t ) = ai (t — z/u). Their composition has subsequently evolved according to batch reaction kinetics as indicated by the right-hand side of Equation (14.14). Molecules leaving the reactor at time t entered it at time t — t. Thus,... 

Thus, the elementary cellular structure could be regarded as an intrinsic characteristic of fhe detonation in a mixture at given initial composition, temperature, and pressure. The dimension of X is of fhe order of magnitude of millimeters or less for gaseous mixfures with oxygen, but several centimeters for less sensitive mixtures (even larger, for methane/air af afmospheric pressure). It decreases when the initial pressure increases. Its variation with the initial temperature is more complicated and depends on the value of fhe reduced activation energy of fhe chemical reactions. The value of... 

For any initial composition of the two solntions, an equilibrium distribution of the species between the membrane, any initial composition of the two solutions, an equi-librinm distribntion of the species between the membrane, and hence also between the two solntions is attained after some time. 

Figure 1.29. Calculated changes in the S 0 values of volcanic rocks (5 0 = +7.0%c) as a result of equilibrium oxygen isotope exchange with waters of different initial compositions. The dotted areas represent the ranges of rocks in the zeolite and the sericite-chlorite zones (Green et al., 1983).

Change the initial composition by varying the mole X02. fractions >... 

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