Parallel first-order reaction mechanism 2026-10-18
A parallel first-order reaction mechanism consumes the same reactant through competing routes. Extend the product-split idea in catalytic selectivity by following both reaction products over time. Stipulate irreversible first-order reactions and in a uniformly mixed closed system of fixed volume and temperature. Initially only A is present, with concentration . With ,Here abbreviates a sum of rate constants, not an equilibrium constant. The rate equations are , , and . Integrating the last two after solving the first proves the expressions and their conserved total .
Choose two alternative models: model U has ; model V has . Both have , so every measurement of A alone is identical, even with no measurement error. Yet their P-to-Q concentration ratios at any are and , respectively. This is a precise failure of identifiability from that one observable. A calibrated measurement distinguishing P from Q resolves it within the stipulated two-route model.
At , both models give . Model U gives ; model V exchanges these. Measuring only the summed reaction product concentration would also fail to distinguish them. Product-specific observations therefore answer a question that total conversion cannot. As with any reaction mechanism, fitting these observables still does not rule out a more elaborate untested route.
Reaction mechanism Created 2026-10-13 Updated 2026-10-18
A reaction mechanism describes how reactants become reaction products through specified elementary reactions. Adding the steps must recover the overall chemical equation; intermediate chemical species cancel. That accounting is necessary, but the proposed steps must also predict a rate law compatible with experiment. Several reaction mechanisms can pass the same test.[ref]
12.6 Reaction Mechanisms. Chemistry 2e by Paul Flowers and others; §12.6, opening discussion and Relating Reaction Mechanisms to Rate Laws: net equations, elementary steps, and experimental constraints
For example, the stipulated steps and sum to . I is a reaction intermediate: it is formed and then consumed. The catalyst C in the existing catalytic cycle instead starts available, participates, and is regenerated; its bound form can be a reaction intermediate. Both can disappear from the summed chemical equation, so cancellation alone does not distinguish their roles. Cancellation is algebraic bookkeeping, not an assertion that every step finishes instantaneously.
The net chemical equation supplies consumption ratios, not a clock. For the stipulated two-step example, directional reaction rates and give and . Initially can mean zero reaction product formation while A already disappears. In particular, requires negligible intermediate accumulation here. A single elementary reaction with the same net chemical equation would instead predict immediate formation at . Measuring both sides can reveal a distinction hidden by the net equation.
This makes reaction mechanisms useful for designing observations: follow a candidate reaction intermediate, measure individual reaction products, or vary one starting concentration at a time. The consecutive first-order reaction mechanism quantifies an intermediate's rise and fall; the parallel first-order reaction mechanism shows how identical reactant traces can conceal different reaction products. The acetone iodination rate-law experiment connects such reasoning to a real laboratory protocol. The existing reaction coordinate, potential energy surface, and energy profile describe configurations and barriers along a route; a concentration plotted against time describes a different observable.
