Getting More out of a Job Plot: Determination of Reactant to Product Stoichiometry in Cases of Displacement Reactions and n:n Complex Formation

Abstract

The method of continuous variation (often referred to as Job's method) is an easy and common method for the determination of the reactant stoichiometry of chemical equilibria. The traditional interpretation of Job plots has been limited to complex association equilibria of the type nA + mB ⇌ A(n)B(m), while little focus has been placed upon displacement type reactions (e.g., A + B ⇌ C + D), which can give Job plots that look quite similar. We developed a novel method that allows the user to accurately distinguish between 1:1 complex association, 2:2 complex association, and displacement reactions using nothing more than a pocket calculator. This method involves preparing a Job plot of the system under investigation (using regularly spaced mole fractions), normalizing the measured quantities (such as the concentration of A(n)B(m) or C for the above reactions) to their maximum value (i.e., at mole fraction 0.5), and determining the sum of the normalized values. This sum is then compared with theoretically predicted normalized sum values that depend on the nature of the equilibrium. The relationship between, on the one hand, the sum of the normalized values and, on the other hand, the reaction equilibrium constant and the concentration of the stock solutions used for the preparation of the Job plot is also explored. The use of this new technique for the interpretation of Job plots permits users to readily determine information that can be obtained otherwise only with laborious additional experiments, as illustrated by the analysis of four Job plots taken from the literature.

Biochemical and Biophysical Methods for Analysis of Poly(ADP-Ribose) Polymerase 1 and Its Interactions with Chromatin

“…HIFI-FRET can be paired with Job plot continuous variation measurements to elucidate the stoichiometries ((14), and applied to PARP-1 in (3)). Here, the amount of donor labeled PARP-1 is increased in incremental titration steps while the acceptor labeled ligand (e.g.…”

Methode der kontinuierlichen Variation: Verwendung von Job‐Plots zur Untersuchung molekularer Assoziationen in der metallorganischen Chemie

“…(2) und (3)], die ohne die Hilfe von Kurvenangleichsprotokollen leicht übersehen werden kçnnten (Abbildung 4). [25] Die zugrundeliegende Mathematik und Datenverarbeitung ist relativ speziell. (6)] unterschieden, bei denen die Komplexierung neben AB ein Nebenprodukt D ergibt.…”

“…Ein täuschend einfacher Ausdruck wird durch Gleichung (8) beschrieben. [25] Jedoch schließen wir diesen Abschnitt mit der Bemerkung, dass keine dieser detaillierten mathematischen Analysen zwingend erforderlich ist, um sich die enormen Vorteile der MCV zu Nutze zu machen: Wer will, kann einfach Punkte auftragen. [32] Die Schwierigkeit mit Gleichung (8) rührt daher, dass eine Anreicherung von A m B n zur Folge hat, dass die Konzentrationen von A und B nicht mehr bekannt sind.…”

“…[3,[25][26][27][28][29]33] Insgesamt kann festgestellt werden, dass relativ wenige Forscher die Daten an ein Modell anpassen, und diejenigen, die es tun, tun es auf keine sehr eingängige Weise. [3,[25][26][27][28][29]33] Insgesamt kann festgestellt werden, dass relativ wenige Forscher die Daten an ein Modell anpassen, und diejenigen, die es tun, tun es auf keine sehr eingängige Weise.…”

Thiophosphoramide‐Based Cooperative Catalysts for Brønsted Acid Promoted Ionic Diels–Alder Reactions

“…[14] The stoichiometry of the resultant complex between 11 and 7 e was determined by 1 H NMR titration and resulted in the Job plot depicted in Figure 3 B. [15] The stoichiometry of binding is consistent with the formation of 1:1 complex between 11 and 7 e. WinEQNMR [16] was used to establish the association constant of this complex (K a = 7.3 10 4 m À1 in CDCl 3 ). Based on the value of K a , we conclude that 7 e strongly binds the tosylate anion of 11 in chloroform.…”