Frequently, one may encounter a reaction that is not favored by Ka, and manipulation of temperature or pressure or feed composition provides only limited benefit for the desired conversion. In these cases, it may be possible to couple the reaction to another, more favorable, reaction to drive the overall production forward. Biological systems use coupling extensively. The building of sugars and biological tissue from CO2 and water is thermodynamically unfavorable. Carbon is fully oxidized and it must be reduced to create carbohydrates, and the reactions are endergonic at room temperature. These reactions are achieved by coupling an unfavorable carbon reduction with a strongly exergonic reaction.
To illustrate the principles of chemical coupling with a simple set of reactions, let us consider the production of butadiene from butene dehydrogenation at 900 K. We have investigated this reaction in Example 17.3 where we showed that the reaction is endergonic: Ka = 0.242 is small. The example showed that conversion is improved by diluting with steam. Consider instead if CO2 is fed to the reactor and a catalyst is provided for the water-gas shift reaction (c.f. Eqn. 17.32). The CO2 could then react with H2 product of the dehydrogenation, inducing higher conversion for the dehydrogenation. The hydrogen product is removed by Le Châtelier’s principle and the dehydrogenation reaction is pulled forward.
Example 17.8. Chemical coupling to induce conversion
Example 17.3(a) considered use of steam as a diluent where the conversion was found to be 78% using 10 moles of steam as diluent and only 44% without the diluent. Consider the conversion by inducing higher conversion by replacing the 10 mole steam with 10 mole CO2 which adds the water-gas shift reaction. For the water-gas shift written as 
, Ka2 = 0.441 at 900 K. What is the conversion of 1-butene at 900 K and 1 bar?
Solution
The butadiene reaction has been written in Example 17.3(a) and ξ1 will be used for that 1-butene reaction and ξ2 will be used for the water-gas shift reaction. The stoichiometry table is,
Physical limits for the reaction coordinates are 0 ≤ ξ1 ≤ 1 and 0 ≤ ξ2 ≤ ξ1. Solving Eqns. 17.41 and 17.42 simultaneously, we find ξ1 = 0.949 and ξ2 = 0.792. Reviewing previous examples, the conversion at 1 bar was only 44% without an inert, increased to 78% with an inert, and increased to 95% using CO2 to induce conversion by reaction coupling. Note that even though the water-gas shift equilibrium constant is not very large, it makes a significant difference in the conversion of 1-butene. Whether this is implemented depends on the feasibility of economically separating the products.
Chemical coupling can be classified in three ways: (1) induction, where a second reaction “pulls” a desired reaction by removing a product as in Example 17.8; (2) pumping, where the second reaction creates additional reactant for the desired reaction to “pump”; or (3) complex, where both induction and pumping are operative.3 An example of chemical pumping starts with the reaction of methyl chloride and water to form methanol and hydrochloric acid.
By adding the methyl chloride synthesis reaction,
This overall reaction becomes (adding the reactions, and take the product of the Kas):
The large equilibrium constant of 17.44 forms CH3Cl(g) readily, to pump reaction 17.43 via Le Châtelier’s principle. Through chemical coupling, the prospects of developing a feasible reaction network are virtually endless
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