Chemical Equilibria

Ionic strength describes the total electrolyte concentration in a solution. It is a quantitative measure of how many ions are present and how strongly they contribute to the solution. The concept was introduced in 1921 by Gilbert N. Lewis and Merle Randall while they were describing the activity coefficient of strong electrolytes.

To calculate ionic strength, written as I or μ, both cations and anions are included. The concentration of each ion matters, but the charge number z matters even...

Salt effect can change the solubility of a sparingly soluble salt in water. When an inert ionic compound is added, the dissolved salt may become more soluble. A common example is potassium nitrate added to a saturated calcium sulfate solution, which increases the amount of calcium sulfate that dissolves.

Le Châtelier’s principle does not explain this shift well. Instead, the change is described by the effective concentration of ions in solution. Each ion is surrounded by an ionic atmosphere,...

Chemical potential and activity describe how a species behaves in a solution. Activity is the effective concentration of a species. It accounts for the electrolytes near that species and depends on the ionic strength of the solution.

Activity is calculated as molar concentration multiplied by the activity coefficient. This makes it a more precise way to describe a species in solution than concentration alone. The thermodynamic equilibrium constant is also defined more accurately using activity...

Activity coefficient in ionic solutions describes how much a species behaves like its measured concentration. Activity is the effective concentration of a solute in solution. It equals the molar concentration multiplied by the activity coefficient, which is a unitless number.

The activity coefficient depends on the total ionic strength of the solution. It shows how far a solution is from ideal behavior. When ionic strength is very low, the activity coefficient of an ionic species is close to...

Salt effect changes how a sparingly soluble salt dissolves when an inert salt is added. The size of this effect depends on the ionic strength of the solution. Ionic strength reflects how strongly the ions in the solution interact.

In solution, the activity of a species is the product of its concentration and its activity coefficient. A redefined equilibrium constant must account for these activity effects when the ionic strength is moderately high. This form is also called the thermodynamic...

The activity coefficient of an ion in water depends on ionic strength, ion charge, and ion size. The extended Debye-Hückel equation describes these effects for aqueous solutions at 25°C. These three factors are partly linked, so changes in one can influence the others.

When a solution has almost zero ionic strength, the activity coefficient is close to one. That means the solution behaves almost ideally. As ionic strength rises from 0 to 0.1 mol/L, the activity coefficient usually drops.

Chemical equilibrium calculations become easier when they are organized around mass balance and charge balance. This approach is useful for systems with multiple equilibria, where several reactions must be considered together. It is especially helpful when finding the solubility of a sparingly soluble salt in water with a common ion present.

The first step is to identify every chemical reaction in the system. Next, write the equilibrium constant expression for each reaction. These expressions...

pH depends on hydrogen ion activity, not just hydrogen ion concentration. In an ideal solution, pH is the negative logarithm of the hydrogen ion concentration. In a non-ideal solution, a more accurate pH uses hydrogen ion activity, which combines concentration with an activity coefficient.

This difference matters most in very low ionic strength solutions, such as pure water. At first, the hydrogen ion activity coefficient is close to one. When an electrolyte that does not donate or accept a...

Ladder diagrams help show how acid-base equilibria change with pH. They are graphical tools that make the chemistry of a system easier to read during analysis. In a ladder diagram, the vertical axis shows pH. Horizontal bars, or steps, place the pKa values in the system.

Ladder diagrams show redox equilibrium using electrochemical potential, E, as the vertical scale. They help students see how changes in concentration affect which species is most stable. The areas of predominance are set with the Nernst equation.

A useful example is the Fe3+/Fe2+ half-reaction, which has a standard-state potential of +0.771 V. At potentials more positive than +0.771 V, Fe3+ predominates. At potentials more negative than +0.771 V, Fe2+ predominates.

Ladder diagrams also show...

Ladder diagrams help show equilibria in metal-ligand complexes. In these diagrams, the vertical scale shows pL, or the concentration of free ligand that has not reacted. The horizontal lines mark the log of formation constants and show which species is dominant in each region.

For the Cd and ammonia system, the formation constant K1 for Cd(NH3)2+ is 3.55 × 10^2. Its log value is 2.55, so pNH3 = 2.55 is the dividing line between Cd2+ and Cd(NH3)2+ dominance. Above 2.55, Cd2+ is the predominant...

Solubility equilibrium describes what happens when a sparingly soluble salt dissolves in water and then reaches a balance with the solid left over. In a saturated solution, dissolved ions and the undissolved solid are in dynamic equilibrium. The process is reversible, so this topic is also called precipitation equilibrium.

This balance matters in real life. Sugar-rich foods can produce organic acids that dissolve hydroxyapatite, the mineral in tooth enamel, which can lead to tooth decay. A...

Water ionization and the ionic product of water describe how pure water reaches equilibrium. Water is a weak electrolyte, so only a small amount breaks into hydrogen ions and hydroxide ions. At a fixed temperature, the amount of undissociated water stays almost constant.

Because of this, the ionic product of water is the product of the hydrogen ion concentration and the hydroxide ion concentration. It is written as K w . The square root of K w gives the concentration of each ion in pure water.

Stepwise metal-ligand complexation forms coordination compounds when metal ions and ligands share electrons through dative, or coordinate covalent, bonds. In these reactions, the metal ion binds to one or more ligands until its coordination number is reached. This number tells how many bonds form between the metal ion and the ligands.

In aqueous solution, many metal ions are already surrounded by water molecules. These species are called aqua complexes. Complexation reactions are described by...

Metal complexes form when metal atoms or cations interact with ligands in a complexation reaction. These donor-acceptor adducts are central to understanding how metal ions bind in chemistry.

Ligands can bind in different ways. A monodentate ligand uses one donor site. A bidentate ligand uses two donor sites, and a polydentate ligand uses more than two. Ethylene diamine is a bidentate ligand that binds through two nitrogen donor atoms and forms a five-membered ring.

Polydentate ligands can...

Complex ions form when a metal cation accepts electron pairs from ligands, which are the electron pair donors. The stability of these metal complexes depends mainly on the metal ion and on the ligands attached to it.

The metal ion’s size and charge play a major role in stability. As the size of the metal ion increases, complex stability usually decreases when the valency of the metal ion and the ligands stays the same. As the charge on the metal ion increases, complex stability increases.

Redox reactions involve the transfer of electrons from one species to another. In this type of reaction, electrons are not shared between atoms. They move from the species that loses them to the species that gains them.

The species that loses electrons is the reducing agent, also called the reductant. It is oxidized during the reaction. The species that gains electrons is the oxidizing agent, or oxidant, and it is reduced.

Redox reactions are often written as two half-reactions. One...

Titrimetric methods use a standard solution to measure the amount of an analyte in chemistry. The main categories are volumetric, gravimetric, and coulometric methods. Each one reaches the endpoint in a different way.

In volumetric titrations, the key measurement is the volume of a titrant with a known concentration. The titrant is added until it reacts completely with the analyte. In gravimetric titrations, the standard solution forms an insoluble precipitate with the analyte. That solid is...

Titrimetric analysis measures solution volume and is also called volumetric analysis. A standard solution with a known concentration is placed in the burette and is called the titrant. The solution with an unknown concentration in the flask is the analyte, or titrand.

Titrimetric analysis is grouped into four types based on the reaction between the titrant and the analyte. Acid-base titrations involve a neutralization reaction between an acid and a base. This reaction forms water molecules.