Segments coefficients

The forward and reverse segment coefficients Aok and Ak0 of that pseudo-single step, however, are not in general concentration-independent. Given by eqns 6.5 and 6.6, they are functions of the true rate coefficients of all steps and of the concentrations of any co-reactants and co-products, but are independent of the concentrations of the intermediates. The problem of accounting for the effects of co-reactants and co-products has not been solved, but has been deferred to a time when it is more easily taken care of. 

Equations 6.5 and 6.6 for the segment coefficients look rather formidable, but are in fact quite simple and very easy to remember and apply. The numerator of Aok, the forward coefficient, is the product of all forward X coefficients similarly, the numerator of Ak0, the reverse coefficient, is the product of all reverse X coefficients. The denominator Z)0k, common to both segment coefficients, is easily obtained with the following recipe ... 

If any step in the sequence is irreversible, the equations apply with the respective reverse X coefficient equated to zero. Automatically, this also makes the reverse segment coefficient zero since the latter contains the zero X coefficient as a factor If one step is irreversible, the entire pathway is irreversible ... 

Table 7.3. Algebraic forms of segment coefficient Ay, of segment with stoichiometry Xk + B — P and different configurations (from Helfferich and Savage [7]).

In network I, paraffin is formed by hydrogenation of the tricarbonyl alkyl, X4. Here, the segment coefficients are... 

The yield ratio equations, obtained as ratios of the segment coefficients according to eqn 6.38, are shown with the respective networks in Table 7.4 (preceding page). For network I, the yield ratio is proportional to the partial pressure of H2. In the other three cases, the yield ratio is seen to depend only on the H2-to-CO ratio, not on total pressure at same H2-to-CO ratio. However, the dependence on that ratio differs. For network II it is of the form... 

In this example, the rates in the networks with and without by-product formation were found to be of same algebraic form and the yield ratio and selectivity to be concentration-independent. This is due to the concentration independence of the segment coefficients of the two parallel pathways, A2X and A2X and is not generally true even if the different pathways consist of strictly analogous steps. 

Ajk segment coefficient of pathway or linear network segment i—[eqns 6.5] t l... 

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