Starting with separate feeds of reactant \(A\) and \(B\) of given concentration (no dilution with inerts permitted), for the competitive-consecutive reactions with stoichiometry and rate as shown $$\begin{array}{l} \mathrm{A}+\mathrm{B} \rightarrow \mathrm{R}_{\text {desired }} \cdots r_{1} \\\ \mathrm{R}+\mathrm{B} \rightarrow \mathrm{S}_{\text {unwanted }} \cdots r_{2} \end{array}$$ sketch the best contacting patterns for both continuous and noncontinuous operations: (a) \(r_{1}=k_{1} C_{\mathrm{A}} C_{\mathrm{B}}^{2}\) \(r_{2}=k_{2} C_{\mathrm{R}} C_{\mathrm{B}}\) (b) \(r_{1}=k_{1} C_{\mathrm{A}} C_{\mathrm{B}}\) \(r_{2}=k_{2} C_{\mathrm{R}} C_{\mathrm{B}}^{2}\) (c) \(r_{1}=k_{1} C_{\mathrm{A}} C_{\mathrm{B}}\) \(r_{2}=k_{2} C_{\mathrm{R}}^{2} C_{\mathrm{B}}\) (d) \(r_{1}=k_{1} C_{\mathrm{A}}^{2} C_{\mathrm{B}}\) \(r_{2}=k_{2} C_{\mathrm{R}} C_{\mathrm{B}}\)

Chemical reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. By understanding the proportions in which chemicals react, one can predict the amount of product formed from a given quantity of reactants. In the competitive-consecutive reactions described in the exercise, A and B react to form the desired product R, and then R further reacts with B to form the unwanted product S. The stoichiometry of the reaction dictates that to maximize the yield of R, the concentration of B should be managed carefully because it participates in both the desired and the unwanted reactions.

For instance, in scenario (a), where the rate of reaction for the production of R depends quadratically on B's concentration, controlling the amount of B becomes crucial. By adding B slowly in a continuous process or by having an excess of A in noncontinuous operations, the formation of the unwanted product S may be minimized, as the stoichiometry suggests a higher propensity for B to create R under these conditions.

Reaction rate laws express the speed at which a chemical reaction proceeds in terms of the concentrations of the reactants. The rate laws for the competitive-consecutive reactions indicate the dependence of the reaction rates on the concentrations of A, B, and R. For example, in scenario (b), the rate law for the formation of the desired product is proportional to the concentrations of both A and B, whereas the unwanted reaction rate is proportionally higher with increasing B's concentration squared.

This knowledge helps to design a reactor system—such as a continuous stirred-tank reactor (CSTR) for continuous operations—that maintains low B concentrations to favor the desired reaction while suppressing the second reaction. Understandably, in noncontinuous operations, similar logic applies: maintain a low concentration of B while ensuring there is enough A to drive the desired reaction forward.

Continuous and noncontinuous operations represent two different approaches to carrying out chemical processes. In continuous operations, reactants are added and products removed simultaneously during the runtime of the reaction, while in noncontinuous (or batch) operations, all reactants are added at the beginning, and products are removed at the end of the reaction period.

As observed in the exercise solutions, selecting the appropriate operation-type is pivotal based on the rate laws. For consecutive reactions that form an undesired byproduct, continuous operations such as a Plug Flow Reactor (PFR) or CSTR may optimize the yield by managing reactant feeds and product removals. Conversely, noncontinuous operations are often easier to control and can be tailored to handle particular stages of reaction by limiting reactant availability, which is especially useful in scenarios where we seek to minimize consecutive reactions.

Reactor design significantly influences the outcome of chemical reactions. The right reactor can improve yield, maximize efficiency, and reduce the formation of undesired products. Each reaction sequence demands a specific type of reactor to optimize conditions according to the kinetics and stoichiometry. For example, in scenario (c), a Plug Flow Reactor (PFR) is preferable for continuous operations because it allows the desired product R to form and exit the reaction zone promptly before excess R can react to form S. In contrast, batch reactors are usually chosen for noncontinuous operations where the precise control over the reactant addition rate can avert the build-up of intermediate products that give rise to unwanted reactions.

Maximizing product yield in competitive-consecutive reactions is all about controlling the conditions to favor the desired reaction over undesired pathways. Both the selection of the reactor and the operation mode play crucial roles in this aspect. Strategies include maintaining certain reactant concentrations at optimal levels, controlling the reaction temperature and time, and choosing a reactor type that matches the reaction’s kinetic profile. For instance, keeping the concentration of B low can tilt the balance toward the production of R instead of S in our exercise scenarios.

By understanding how the concentrations of reactants and reaction intermediates influence the rate of product formation, as well as decomposition or side reactions, the reactor can be designed or operated to provide the conditions favorable for maximizing the yield of the desired product.