Reaction single

A limiting reactant is a reactant whose concentration at the start of the reaction is the least of all reactants relative to the required stoichiometric amount needed for complete conversion. For instance, for the single reaction (7-12), A is the limiting reactant if the initial molar ratio of concentrations of A and B is less than the ratio of their stoichiometric coefficients  

Once the limiting reactant is depleted, the respective reaction stops even though other (nonlimiting) reactants may still be abundant. 

For eacn reaction or each step in a network of reactions, a unique extent of reaction t that relates the composition of components that participate in the reaction to each other can be defined. For instance, for the single reaction (7-1)  

The equilibrium constant (based on volumetric concentrations) is defined as the ratio of the forward and reverse rate constants and is related to the composition at equilibrium as follows  

can be calculated from the free energy change of the reaction. Using the van t Hoff relation, we obtain the dependence of K, on temperature  

When A is the limiting reactant as in Eq. (7-21), the maximum extent of reaction (with A fully converted) is 

For multiple reactions with reactants participating in more than one reaction, it is more difficult to determine the limiting reactant and often it is necessary to calculate the concentration as the reactions proceed to determine which reactant is consumed first. When the limiting reactant is depleted, all reactions that use this component as reactant stop, and the corresponding rates become zero. 

One-step reactions between stable molecules are rare since a stable molecule is by definition a quite unreactive entity. Rather, complicated rearrangements of chemical bonds are usually required to go from reactants to products. This implies that most reactions do not proceed in a single elementary step as illustrated below for NO formation from N2 and O2. 

Normally, a sequence of elementary steps is necessary to proceed from reactants to products through the formation and destruction of reactive intermediates (see Section 1.1). 

There are two types of sequences leading from reactants to products through reactive intermediates. The first type of sequence is one where a reactive intermediate 

Chain and catalytic reaction cycles provide energetically favorable pathways for reactant molecules to proceed to product molecules. This point is illustrated below for both types of cycles. Consider the reaction between dihydrogen and dichlorine to produce HCl that can be brought about in the gas phase by irradiating the reactants with light. It is known that over 10 molecules of HCl can be formed per absorbed photon. The reaction proceeds as follows  

Once chlorine atoms are produced (initiation), the propagation steps provide a closed cycle that can be repeated numerous times (e.g., 10 ) prior to the recombination of the chlorine atoms (termination). 

If both reaction steps are assumed to be of first order, the net rate of reaction of 

Rather than both adsorption and desorption constants, adsorption equilibrium constants are customarily used. 

The overall reaction is the sum of the individual steps so that the thermodynamic equilibrium constant for the reaction is 

This relation can be used to eliminate one of the other equilibrium constants, often the unknown of the surface reaction between adsorbed species. 

If the total concentration of sites, Q, is assumed constant, it must consist of the vacant plus occupied sites, so that 

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Single reactions. Most reaction systems involve multiple reactions. In practice, the secondary reactions can sometimes be neglected, leaving a single primary reaction to consider. Single reactions are of the type... 

Multiple reactions in parallel producing byproducts. Rather than a single reaction, a system may involve secondary reactions producing (additional) byproducts in parallel with the primary reaction. Multiple reactions in parallel are of the tj ie... 

Single reactions. Consider the single reaction from Eq. (2.1) ... 

In the preceding section, the choice of reactor type was made on the basis of which gave the most appropriate concentration profile as the reaction progressed in order to minimize volume for single reactions or maximize selectivity for multiple reactions for a given conversion. However, after making the decision to choose one type of reactor or another, there are still important concentration effects to be considered. 

In a single reaction (where selectivity is not a problem), the usual choice of excess reactant is to eliminate the component which is more difficult to separate in the downstream separation system. Alternatively, if one of the components is more hazardous (as is chlorine in this example), again we try to ensure complete conversion. 

Having considered reactor temperature and pressure, we are now in a position to judge whether the reactor phase will be gas, liquid, or multiphase. Given a free choice between gas- and liquid-phase reactions, operation in the liquid phase is usually preferred. Consider the single reaction system from Eq. (2.19) ... 

Single reactions. For single reactions, a good initial setting is 95 percent conversion for irreversible reactions and 95 percent of the equilibrium conversion for reversible reactions. Figure 2.9 summarizes the influence of feed mole ratio, inert concentration, temperature, and pressure on equilibrium conversion. ... 

Multiple reactions. For multiple reactions in which the byproduct is formed in parallel, the selectivity may increase or decrease as conversion increases. If the byproduct reaction is a higher order than the primary reaction, selectivity increases for increasing reactor conversion. In this case, the same initial setting as single reactions should be used. If the byproduct reaction of the parallel system is a... 

For multiple reactions in which the byproduct is formed in series, the selectivity decreases as conversion increases. In this case, lower conversion than that for single reactions is expected to be appropriate. Again, the best guess at this stage is to set the conversion to 50 percent for irreversible reactions or to 50 percent of the equilibrium conversion for reversible reactions. 

Reactor conversion. In Chap. 2 an initial choice was made of reactor type, operating conditions, and conversion. Only in extreme cases would the reactor be operated close to complete conversion. The initial setting for the conversion varies according to whether there are single reactions or multiple reactions producing byproducts and whether reactions are reversible. 

Reducing waste from multiple reactions producing waste byproducts. In addition to the losses described above for single reactions, multiple reaction systems lead to further waste through the formation of waste byproducts in secondary reactions. Let us briefly review from Chap. 2 what can be done to minimize byproduct formation. 

Figure 3-2. Two reaction equations showing two completely different uses for the (+) symbol a) giving a fully balanced single reaction, b) combining two parallel reactions into a single equation that is not stoichiometrically balanced.

A proper resolution of Che status of Che stoichiometric relations in the theory of steady states of catalyst pellets would be very desirable. Stewart s argument and the other fragmentary results presently available suggest they may always be satisfied for a single reaction when the boundary conditions correspond Co a uniform environment with no mass transfer resistance at the surface, regardless of the number of substances in Che mixture, the shape of the pellet, or the particular flux model used. However, this is no more than informed and perhaps wishful speculation. 

The procedure in the case of two independent reactions should be compared with that described earlier for a single reaction. When there is a single reaction, p, X2 ...,x are related to by solution of an... 

Single-reaction-step processes have been studied. However, higher selectivity is possible by optimizing catalyst composition and reaction conditions for each of these two steps (40,41). This more efficient utilization of raw material has led to two separate oxidation stages in all commercial faciUties. A two-step continuous process without isolation of the intermediate acrolein was first described by the Toyo Soda Company (42). A mixture of propylene, air, and steam is converted to acrolein in the first reactor. The effluent from the first reactor is then passed directiy to the second reactor where the acrolein is oxidized to acryUc acid. The products are absorbed in water to give about 30—60% aqueous acryUc acid in about 80—85% yield based on propylene. 

Derivatives of the natural product juglone [77189-69-6] eg (109), have been obtained ia 90% yield ia a single reaction involving halogenation and oxidation by A/-bromosucciniinide (115). 

A typical 20-MW, a-c furnace is fitted with three 45-in. (114.3-cm) prebaked amorphous carbon electrodes equdateraHy spaced, operating on a three-phase delta connection. The spacing of the electrodes is designed to provide a single reaction zone between the three electrodes. The furnace is rotated to give one revolution in two to four days or it may be oscillated only. Rotation of the furnace relative to the electrodes minimizes silicon carbide buildup in the furnace. 

For a specific single reaction, equation 231 may be written as foUows ... 

The general criterion of chemical-reaction equilibria is given by Eq. (4-274). For a system in which just a single reaction occurs, Eq. (4-33 becomes... 

Example 2 Single-Reaction Equilihrium Consider the eqiiilih-liiim state at 1,000 K and atmospheric pressure for the reaction... 

For the given conditions, the assumption of ideal gases is appropriate Eq. (4-345) written for a single reaction (subscript j omitted) with V = 0 becomes... 

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