Extent of reaction calculation

A heat-resistant polymer Nomex has a number-average molecular weight of 24,116. Hydrolysis of the polymer yields 39.31% by weight m-aminoaniline, 59.81% terephthalic acid, and 0.88% benzoic acid. Write the formula for this polymer. Calculate the degree of polymerization and the extent of reaction. Calculate the effect on the degree of polymerization if the polymerization had been carried out with twice the amount of benzoic acid. 

Figure 3. Changes in the degree of polymerization as a function of the extent of reaction calculated from equation 2 (a) changes in the ratio of phenol to formaldehyde reactive sites (r) for constant (f) and (p) (f=3, p=l), (b) changes in the functionality or number of reactive sites on a individual phenolic molecule (f) for constant (r) and (p) (r=l, p=l), and (c) changes in the amount of monofunctional phenolics (p) for constant (f) and (r) (fr=l, r=l).

To verify the method a 1.00-mL aliquot of a standard solution of 40.0-ppm glucose was added to 1.00 ml of the combined reagents, requiring 34.6 s to produce the same extent of reaction. Determine the calculated concentration of glucose in the standard and the percent error for the analysis. 

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

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 ... 

At 270°C adipic acid decomposesf to the extent of 0.31 mol % after 1.5 hr. Suppose an initially equimolar mixture of adipic acid and diol achieves a value of p = 0.990 after 1.5 hr. Compare the expected and observed values of n in this experiment. Criticize or defend the following proposition The difference between the observed and expected values would be even greater than calculated above if, instead of the extent of reaction being measured analytically, the value of p expected (neglecting decomposition) after 1.5 hr were calculated by an appropriate kinetic equation. 

Continuous esterification of acetic acid in an excess of -butyl alcohol with sulfuric acid catalyst using a four-plate single bubblecap column with reboiler has been studied (55). The rate constant and the theoretical extent of reaction were calculated for each plate, based on plate composition and on the total incoming material to the plate. Good agreement with the analytical data was obtained. 

Zavitsas et al. account for the effects of water in their calculations. Water promotes depolymerization of the paraformaldehyde as well as the hemiformals. Their modifications correct for the apparent reduction in methylolation rate as the extent of reaction proceeds, in that the hemiformals remove formaldehyde reactivity from the reaction mixture. Their rate constants look large because they are written for phenate concentrations rather than phenol and because of the formaldehyde equilibrium adjustments. They note that unsalted phenol is a by-... 

That is, (Aq — A ) is proportional to the entire extent of reaction, and (A, — Aoo) is proportional to the concentration unreacted at time t. Obviously these quantities can be separated, and the plots made without knowledge of Aq however, as noted above, Aq (whose knowledge is equivalent to knowing < ) is needed to calculate a zero-order or second-order rate constant. 

In general, if K is a very small number, the equilibrium mixture will contain mostly unreacted starting materials for all practical purposes, the forward reaction does not go. Conversely, a large K implies a reaction that, at least in principle, is feasible products should be formed in high yield. Frequently, K has an intermediate value, in which case you must make quantitative calculations concerning the direction or extent of reaction. 

The results of the experiment depicted in Fig. 62 and others similarly obtained are summarized in Table XXXI. In every case the observed gel point is reached at higher than the theoretical extent of reaction. The discrepancies between the observed and calculated ojc s appear to be due to the failure of the theory to take into account a minor degree of intramolecular condensation. Since some of the interunit linkages... 

Fig. 70.—Weight fractions of various finite species and of gel in a simple trifunctional condensation as a function of a, which in this case equals the extent of reaction p. Curves have been calculated from Eqs. (36) and (45). ...

The two time constants x and tV2 define time intervals in which a specific extent of reaction has been completed. In some applications one may wish to define a time point associated with a certain other extent of reaction completion. That is, how much time is required for the reaction to go to, say, 75% or 90% completion. This can be calculated using rearranged forms of Equations (A.16) through (A.21). For convenience, in Table Al.l we tabulate the extent of reaction completion for different time intervals, as multiples of x and ty2. 

The agreement between the experimental and calculated values of Ce, is excellent. The data shown in Figure 2 are for a constant bake time of 17 minutes. The upper and lower limits on define a cure window. The cure window for the low solids coating is 50 C. The model was further tested by measuring extents of reaction and temperature profiles for samples attached to different parts of a car body which passed through a pilot plant oven. This simulation tested the model under conditions where the substrate temperatures were far from constant. As shown in Table II, the agreement between the experimental and calculated values of Ce is again excellent. 

The science of chemical kinetics is concerned primarily with chemical changes and the energy and mass fluxes associated therewith. Thermodynamics, on the other hand, is concerned with equilibrium systems. .. systems that are undergoing no net change with time. This chapter will remind the student of the key thermodynamic principles with which he should be familiar. Emphasis is placed on calculations of equilibrium extents of reaction and enthalpy changes accompanying chemical reactions. 

This equation is extremely useful for calculating the equilibrium composition of the reaction mixture. The mole numbers of the various species at equilibrium may be related to their values at time zero using the extent of reaction. When these values are substituted into equation 2.6.9, one has a single equation in a single unknown, the equilibrium extent of reaction. This technique is utilized in Illustration 2.1. If more than one independent reaction is occurring in a given system, one needs as many equations of the form of equation 2.6.9 as there are independent reactions. These equations are then written in terms of the various extents of reaction to obtain a set of independent equations equal to the number of unknowns. Such a system is considered in Illustration 2.2. 

The conclusions reached are valid qualitatively if the amount of monohydroxy PPO is less than that obtained from the chemical analyses of the PPG. In fact, if no monohydroxy PPO were present, then the calculated values of vcRT and G ax for the LHT-240 elastomer become 0.13 MPa and 0.48 MPa, respectively. Such results because, to obtain the observed sol fraction (0.041), the extent of reaction must be 0.9728 instead of 0.9859 (Table III). Similarly, if the true values of the sol fraction are somewhat larger than those found, calculations then show that vcRT is less and G J13 is larger than those reported in Table III. 

Calculations Equilibrium Dissolved gases Rates of reaction Chemical potential and AG with the extent of reaction Henry s Law and the pH of the oceans Temperature dependence of chemistry and the analysis of chemical networks in prebiotic environments... 

Activation Energy. The gel times, determined by dynamic rheological tests, can also be utilized to calculate an apparent activation energy. We can obtain the gel times over the temperature range of interest and if the extent of reaction at these temperatures are constant, an apparent activation energy can be determined. First, the polymerization reaction can be represented by a generalized kinetic expression of the type (24)... 

Figure 7. IR spectra of the trimethylolpropane tris(2-mercaptoacetate)/ trimethylolpropane diallyl ether system for three different UV exposure times (0 s, 713 s, 8995 s) showing S-H stretching (2570 cm 1), C=C stretching (1646 cm 1), and aromatic out-of-phase C-H deformation (830 cm 1) peaks. The thiol peak is monitored to calculate the extent of reaction while the C-H deformation peak is used as an internal standard.

In light of the small solubilities of many minerals, the extent of reaction predicted by this type of calculation may be smaller than expected. Considerable amounts of diagenetic cements are commonly observed, for example, in sedimentary rocks, and crystalline rocks can be highly altered by weathering or hydrothermal fluids. A titration model may predict that the proper cements or alteration products form, but explaining the quantities of these minerals observed in nature will probably require that the rock react repeatedly as its pore fluid is replaced. Local equilibrium models of this nature are described later in this section. 

---