A numerical method to calculate equilibrium concentrations for single-equation systems

Abstract

126. Bits and pieces, 46. A numerical method to calculate equilibrium concentrations for single-equation systems.

Calculating Equilibrium Concentrations by Iteration: Recycle Your Approximations

“…As a consequence the iteration defined by yi+i = F(yi) (7) has a fixed point at the desired equilibrium value ye. Otherwise, two consecutive iterates establish an upper and lower bound toye-If y;+i = y, or the absolute value of the difference is less than a convergence criterion, then a solution of the problem has been found.…”

“…If acceptable convergence2 is not reached in a small number, say four or five iteration steps, a change of method is indicated. For the best available y,, evaluate y;+i = F(y;) and yi+2 = /''(y.+i), and calculate the next y by the expres-sion3 ynext yti -yffM 2yl-i~yi~yi+2 (7) For typical chemical problems, the convergence by this method is fast and assured.…”

Spreadsheet Tools for Solving One-Equation Chemical Equilibrium Problems

“…Figure 6 presents a special example of hi nary-mixture analysis as the spectrophotometric determination of equilibrium constants possible when the conjugate variables each have characteristically different spectra. By this technique, it is possible to determine the pifa spectrophotometrically with far greater reliability than that obtained using most potentiometric methods; it also provides a means of calibrating glass electrodes accurately (2). Literature Cited Given the equilibrium constant for a reaction as written and the initial concentrations or partial pressures of all the species involved, what will be the concentrations or partial pressures of various species once the reaction reaches its equilibrium position?…”

“…The equilibrium concentrations of various species are governed by the extent of the of papers Weltin has demonstrated that the extent of a reaction and the equilibrium concentrations are uniquely de-termined by initial concentrations (1)(2)(3). He has suggested the bisection method for calculating the equilibrium extent of a reaction (2). A BASIC program for the bisection method has recently been published by Campanario and Ballesteros (4).…”

Oxidation Number Rules: A Program to Test the Effect of Various Rules on the Assignment of Oxidation Numbers

“…The program works by minimizing the Gibbs Free Energy as a function of the extent of reaction using an iterative algorithm. This method for single step equilibria (5,6) has been extended to competing and coupled reactions (7).…”