Stoichiometric table

A useful tool for dealing with reaction stoichiometry in chemical kinetics is a stoichiometric table. This is a spreadsheet device to account for changes in the amounts of species reacted for a basis amount of a closed system. It is also a systematic method of expressing the moles, or molar concentrations, or (in some cases) partial pressures of reactants and products, for a given reaction (or set of reactions) at any time or position, in terms of initial concentrations and fractional conversion. Its use is illustrated for a simple system in the following example. 

For the gas-phase oxidation of ethylene to ethylene oxide, construct a stoichiometric table in terms of moles on the basis that only the reactants are present initially, and ethylene is the limiting reactant. 

As indicated, it is suggested that the table be constructed in symbolic form first, and numerical values substituted afterwards. If molar amounts are used, as in the table above, the results are valid whether the density is constant or not. If density is constant, molar concentrations, C , may be used in a similar manner. If both density and temperature are constant, partial pressure, pt, may be used in a similar manner. 

The first column lists all the species involved (including inert species, if present). The second column lists the basis amount of each substance (in the feed, say) this is an arbitrary choice. The third column lists the change in the amount of each species from the basis or initial state to some final state in which the fractional conversion is fA. Each change is in terms of fA, based on the definition in equation 2.2-3, and takes the stoichiometry into account. The last column lists the amounts in the final state as the sum of the second and third columns. The total amount is given at the bottom of each column. 

2-1 The half-life (t 1/2) of a reactant is the time required for its concentration to decrease to one-half its initial value. The rate of hydration of ethylene oxide (A) to ethylene glycol (C2H4O + H2O - C2H6O2) in dilute aqueous solution is proportional to the concentration of A with a proportionality constant kA = 4.11 X 10-5 s-1 at 20°C for a certain catalyst (HCIO4) concentration (constant). Determine the half-life (ti/2), or equivalent space-time (T1/2), in s, of the oxide (A) at 20°C, if the reaction is carried out 

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For the system in problem 1-3, and the equations obtained for part (b), construct an appropriate stoichiometric table. Note the significance of there being more than one chemical equation (in comparison with the situation in problems 2-8 and 2-9). 

For a complex system, determination of the stoichiometry of a reacting system in the form of the maximum number (R) of linearly independent chemical equations is described in Examples 1-3 and 14. This can be a useful preliminary step in a kinetics study once all the reactants and products are known. It tells us the minimum number (usually) of species to be analyzed for, and enables us to obtain corresponding information about the remaining species. We can thus use it to construct a stoichiometric table corresponding to that for a simple system in Example 2-4. Since the set of equations is not unique, the individual chemical equations do not necessarily represent reactions, and the stoichiometric model does not provide a reaction network without further information obtained from kinetics. 

A stoichiometric table for keeping track of the amounts or flow rates of all species during reaction may be constructed in various ways, but here we illustrate, by means of an example, the use of , the extent of reaction variable. We divide the species into components and noncomponents, as determined by a stoichiometric analysis (Section 5.2.1), and assume experimental information is available for the noncomponents (at least). 

Using the chemical system and equations (1), (2), and (3) of Example 5-1, construct a stoichiometric table, based on the use of j, to show the molar flow rates of all six species. Assume experimental data are available for the flow rates (or equivalent) of CO, CO and HCHO as noncomponents. 

Since this is a gas-phase reaction, and the total number of moles changes, the volume changes as the reaction progresses. We use a stoichiometric table to determine the effect of fA on V. 

In equation (A), q and fA ate unknown, but may be determined fiom the given composition of the outlet stream, with the aid of a stoichiometric table. Far a feed consisting of Fao moles of A, this is constructed as follows ... 

Since kA depends on T, it remains inside the integral, and we must relate T to /A- Since the density (and hence q) changes during the reaction (because of changes in temperature and total moles), we relate q to fA and T with the aid of a stoichiometric table and the ideal-gas equation of state. 

A stoichiometric analysis based on the species expected to be present as reactants and products to determine, among other things, the maximum number of independent material balance (continuity) equations and kinetics rate laws required, and the means to take into account change of density, if appropriate. (A stoichiometric table or spreadsheet may be a useful aid to relate chosen process variables (Fj,ch etc.) to a minimum set of variables as determined by stoichiometry.)... 

We first develop an expression ior fm (D, and then plot values calculated from this expression. The expression comes from the form of K, which involves partial pressures, and which may be related to fEB,eq by means of the following stoichiometric table ... 

For use in (C), the partial pressures can be determined using a stoichiometric table as in Example 21-3, in conjunction with CgH10(EB) = C8H8(S) + H2 ... 

The partial pressures are functions of the species mole fractions, yt, which are, in turn, dependent upon the extent of conversion of the reactants. A stoichiometric table may be used to relate the number of moles of all species at equilibrium, with x representing the moles of H2 consumed. The moles of each species can thus be represented as follows ... 

Now that we have shown how the rate law can be expressed as a function of concentrations, we need only, express concentration as a function of conversion in order to carry out calculations similar to those presented in Chapter 2 to size reactors. If the rate law depends on more than one species, we must relate the concentrations of the different species to each other. This relationship is most easily established with the aid of a stoichiometric table. This table presents the stoichiometric relationships between reacting molecules for a single reaction. That is, it tells us how many molecules of one species will be formed during a chemical reaction when a given number of molecules of another species disappears, These relationships wil be developed for the general reaction... 

In formulating our stoichiometric table we shall take species A as our basis of calculation (i.e., limiting reactant) and then divide through by the stoichiometric coefficient of A,... 

The complete stoichiometric table for the reaction shown in Equation (2-2) taking place in a batch reactor is presented in Table 3-2. 

After writing similar equations for B, C, and D, we use the stoichiometric table to express the concentration of each component in terms of the conversion X ... 

Letting X represent the conversion of sodium hydroxide (the moles of sodium hydroxide reacted per mole of sodium hydroxide initially present), set up a stoichiometric table expressing the concentration of each species in terms of its initial concentration and the convetsdon X. 

The form of the stoichiometric table for a continuous-flow system (see Figure 3-2) is virtually identical to that for a batch system (Table 3-2) except that we replace by and by (Table 3-3). Taking A as the basis, divide Equation (2-1) through by Ihe stoichiometric coefficient of A to obtain... 

At the point where condensation begins, From die stoichiometric table. 

We must use the column in the stoichiometric table labeled after condensation in conjunction with Equation (E3-10.11) to determine and Cg. 

Set up a stoichiometric table for each of the following reactions and express the concentration of each species in the reaction as a function of conversion evaluating all constants (e.g., e, ). 

P3-21b The gas-phase reaction between cMotine and methane to form carbon tetrachloride and hydrochloric acid is to be carried out at 75 C and at 950 kPa in a continuous-flow reactor. The vapor pressure of carbon tetrachloiide at 75°C is approximately 95 kPa. Set up a stoichiometric table for this reaction with phase change. Calculate the conversion of methane at which condensation begins. Plot the concentrations and molar flow rates of each species as well as the total molar flow rate as a function of conversion for a stoichiometric feed, The volumetric flow rate is 0.4 dm /s. 

To determine the number of moles of each species remaining after moles of A have reacted, we form the stoichiometric table (Table 3-2). This stoichiometric table presents the following information ... 

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