# 6: Equilibrium Chemistry

Regardless of the problem on which an analytical chemist is working, its solution requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know, or know where to find, the chemical differences between p‑hydroxybenzoic acid and p‑hydroxyacetophenone, two common phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory. The material in this text assumes your familiarity with topics from earlier courses. Because of its importance to analytical chemistry, this chapter provides a review of equilibrium chemistry. Much of the material in this chapter should be familiar to you, although some topics—ladder diagrams and activity, for example—afford you with new ways to look at equilibrium chemistry.

• 6.1: Reversible Reactions and Chemical Equilibria
Although a system at equilibrium appears static on a macroscopic level, it is important to remember that the forward and reverse reactions continue to occur. A reaction at equilibrium exists in a steady-state, in which the rate at which a species forms equals the rate at which it is consumed. Hence, there is no further change in the amounts of these species.
• 6.2: Thermodynamics and Equilibrium Chemistry
Thermodynamics is the study of thermal, electrical, chemical, and mechanical forms of energy. The study of thermodynamics crosses many disciplines, including physics, engineering, and chemistry. Of the various branches of thermodynamics, the most important to chemistry is the study of the change in energy during a chemical reaction.
• 6.3: Manipulating Equilibrium Constants
We will take advantage of two useful relationships when working with equilibrium constants. First, if we reverse a reaction’s direction, the equilibrium constant for the new reaction is simply the inverse of that for the original reaction. Second, if we add together two reactions to obtain a new reaction, the equilibrium constant for the new reaction is the product of the equilibrium constants for the original reactions.
• 6.4: Equilibrium Constants for Chemical Reactions
Several types of chemical reactions are important in analytical chemistry, either in preparing a sample for analysis or during the analysis. The most significant of these are: precipitation reactions, acid–base reactions, complexation reactions, and oxidation–reduction (redox) reactions. In this section we review these reactions and their equilibrium constant expressions.
• 6.5: Le Châtelier’s Principle
The observation that a system at equilibrium responds to an external stress by reequilibrating in a manner that diminishes the stress, is formalized as Le Châtelier’s principle. One of the most common stresses to a system at equilibrium is to change the concentration of a reactant or product.
In this section we introduce the ladder diagram as a simple graphical tool for evaluating the equilibrium chemistry. Using ladder diagrams we will be able to determine what reactions occur when combining several reagents, estimate the approximate composition of a system at equilibrium, and evaluate how a change to solution conditions might affect an analytical method.
• 6.7: Solving Equilibrium Problems
Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system’s composition at equilibrium. If we need a more exact quantitative description of the equilibrium condition, then a ladder diagram is insufficient. In this case we need to find an algebraic solution. In this section we will learn how to set-up and solve equilibrium problems. We will start with a simple problem and work toward more complex problems.
• 6.8: Buffer Solutions
As outlined below, the Henderson–Hasselbalch approximation provides a simple way to calculate the pH of a buffer, and to determine the change in pH upon adding a strong acid or strong base.
• 6.9: Activity Effects
The activity coefficient for a species corrects for any deviation between its physical and ideal concentration. For a gas, a pure solid, a pure liquid, or a non-ionic solute, the activity coefficient is approximately one under reasonable experimental conditions. For reactions involving only these species, the difference between activity and concentration is negligible. The activity coefficient for an ion, however, depends on the solution’s ionic strength, the ion’s charge, and the ion’s size.
• 6.10: Using Excel and R to Solve Equilibrium Problems
In solving equilibrium problems we typically make one or more assumptions to simplify the algebra. These assumptions are important because they allow us to reduce the problem to an equation in x that we can solve by simply taking a square-root, a cube-root, or by using the quadratic equation. Without these assumptions, most equilibrium problems result in a cubic equation (or a higher-order equation) that is harder to solve. Both Excel and R are useful tools for solving such equations.
• 6.11: Some Final Thoughts on Equilibrium Calculations
Several tools for evaluating the composition of a system at equilibrium were discussed; they differ in both accuracy and ease in answering questions involving equilibrium chemistry. If you need to know whether a reaction if favorable, or to estimate the pH of a solution, then a ladder diagram will meet your needs. On the other hand, if you require a more accurate estimate of a compound’s solubility, then a rigorous calculation that includes activity coefficients is necessary.
• 6.E: Equilibrium Chemistry (Exercises)
These are homework exercises to accompany "Chapter 6: Equilibrium Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.
• 6.S: Equilibrium Chemistry (Summary)
This is a summary to accompany "Chapter 6: Equilibrium Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

Thumbnail: The $$N_2O_{(g)} \rightleftharpoons 2NO_{2(g)}$$ system at Different Temperatures. Nitrogen dioxide ($$NO_2$$) gas converts to the colorless gas dinitrogen tetroxide ($$N_2O_4$$) at low temperatures, and converts back to $$NO_2$$ at higher temperatures. The bottles in this photograph contain equal amounts of gas at different temperatures. Figure used with permission from Wikipedia (CC BY-SA 3.0).