# 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 to solve a problem. For example, an analytical chemist who is 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.

The ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory. For the most part, the material in this text assumes you are familiar with topics covered in earlier courses; however, 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—likely 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 the 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.
• 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 how energy changes during a chemical reaction.
• 6.3: Manipulating Equilibrium Constants
We can take advantage of two useful relationships when we work with equilibrium constants. First, if we reverse a reaction’s direction, the equilibrium constant for the new reaction is the inverse of that for the original reaction. Second, if we add together two reactions to form 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 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 action by reequilibrating itself in a manner that diminishes that action, is formalized as Le Châtelier’s principle.
In this section we introduce the ladder diagram as a simple graphical tool for visualizing equilibrium chemistry. We will use ladder diagrams to determine what reactions occur when we combine several reagents, to estimate the approximate composition of a system at equilibrium, and to 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 and for providing a reasonable estimate 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; instead, we need to find an algebraic solution. In this section we will learn how to set‐up and solve equilibrium problems.
• 6.8: Buffer Solutions
Adding as little as 0.1 mL of concentrated HCl to a liter of $$\text{H}_2\text{O}$$ shifts the pH from 7.0 to 3.0. Adding the same amount of HCl to a liter of a solution that 0.1 M in acetic acid and 0.1 M in sodium acetate, however, results in a negligible change in pH. Why do these two solutions respond so differently to the addition of HCl? A mixture of acetic acid and sodium acetate is one example of an acid–base buffer.
• 6.9: Activity Effects
Careful measurements on the metal–ligand complex $$\text{Fe(SCN)}^{2+}$$ suggest its stability, and thus its equilibrium constant, decreases in the presence of inert ions. Understanding why this is so is critical to developing a complete understanding of equilibrium chemistry.
• 6.10: Using Excel and R to Solve Equilibrium Problems
In solving equilibrium problems we typically make 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 higher‐order equation that is more challenging to solve. Both Excel and R are useful tools for solving such equations.
• 6.11: Some Final Thoughts on Equilibrium Calculations
In this chapter we developed several tools to evaluate the composition of a system at equilibrium. These tools differ in how precisely they allow us to answer questions involving equilibrium chemistry. They also differ in how easy they are to use. An important part of having several tools to choose from is knowing when to each is most useful.
• 6.12: Problems
End-of-chapter problems to test your understanding of topics in this chapter.