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Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
Calculating Equilibrium Concentrations02:05

Calculating Equilibrium Concentrations

Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more...
The Small x Assumption02:20

The Small x Assumption

If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may occur if the initial concentrations of reactants are high and the Kc value is small. In such circumstances, the equilibrium concentration is approximately equal to its initial concentration. This estimation can be used to simplify the equilibrium calculations by assuming that some equilibrium concentrations are equal to the initial...
Calculating the Equilibrium Constant02:46

Calculating the Equilibrium Constant

The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
The Equilibrium Constant03:10

The Equilibrium Constant

Consider the oxidation of sulfur dioxide:
Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:

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Related Experiment Video

Updated: Jun 28, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Machine computation of equilibrium concentrations-some practical considerations.

D J Leggett1

  • 1University of Toronto, Erindale College, Mississauga, Ontario, Canada.

Talanta
|September 1, 1977
PubMed
Summary
This summary is machine-generated.

This study evaluates seven computer programs for calculating solution equilibrium concentrations. A modified Newton-Raphson approach with Choleski factoring proved most efficient for solving these chemical equilibrium problems.

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Area of Science:

  • Computational Chemistry
  • Chemical Engineering
  • Numerical Analysis

Background:

  • Calculating equilibrium concentrations is crucial in various chemical and engineering applications.
  • Numerous computational programs exist, but their efficiency varies.
  • Understanding program performance is key for accurate and timely results.

Purpose of the Study:

  • To critically evaluate seven published computer programs for calculating equilibrium concentrations.
  • To compare the efficiency and performance of different algorithms for solving equilibrium systems.
  • To identify the most effective computational approach for these calculations.

Main Methods:

  • Evaluation of seven distinct computer programs designed for equilibrium calculations.
  • Selection of six diverse equilibrium systems to test program capabilities.
  • Comparative analysis of execution times and solution accuracy across programs.

Main Results:

  • Program efficiency is primarily determined by the chosen algorithm.
  • A modified Newton-Raphson approach demonstrated superior speed.
  • Choleski factoring within the Newton-Raphson method yielded the fastest solutions.

Conclusions:

  • The selection of an appropriate algorithm significantly impacts computational efficiency.
  • Modified Newton-Raphson with Choleski factoring is highly recommended for rapid equilibrium concentration calculations.
  • This finding aids in selecting optimal computational tools for chemical equilibrium studies.