Write the chemical equilibria and equilibrium laws that correspond to \(K_{\text {form }}\) for the following complexes: (a) \(\mathrm{Ag}\left(\mathrm{S}_{2} \mathrm{O}_{3}\right)_{2}^{3-},\) (b) \(\mathrm{Zn}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\) (c) \(\mathrm{SnS}_{3}^{2-}\).

Understanding equilibrium laws is essential when studying chemical equilibria. These laws relate to the dynamic balance that occurs in a reversible reaction, where the rate of the forward reaction equals the rate of the backward reaction. At this point, although the individual molecules continue to react, the macroscopic concentrations of reactants and products remain constant. An essential law to consider is the Law of Mass Action, which states that the rate of a reaction is proportional to the product of the concentrations of the reactants raised to the power of their stoichiometric coefficients.

This law serves as the foundation for writing equilibrium expressions. The expression itself, called the equilibrium constant, encompasses the concentrations of the products over the reactants, each raised to the power of their coefficients in the balanced chemical equation. To ensure that students fully grasp this concept, it's helpful to work with actual chemical equations and write out the corresponding equilibrium expressions—as seen in the steps for forming silver thiosulfate, zinc tetraammine, and tin trisulfide complexes.

Every chemical equilibrium can be described by its equilibrium constant (\(K\text{eq}\) or often simply represented by 'K'). This dimensionless value quantifies the ratio of the concentrations of products and reactants at equilibrium, each raised to the power of their respective stoichiometric coefficients. It essentially captures the extent to which a reaction proceeds before reaching equilibrium.

For instance, a larger equilibrium constant indicates a greater concentration of products at equilibrium, suggesting the reaction favors the products side. Conversely, a smaller constant implies a reaction favoring the reactants. It’s important for students to understand that the equilibrium constant depends solely on the temperature, and any change in temperature may alter its value. Illustrating this through calculation, as shown in the step-by-step solutions for the formation of different complex ions, helps reinforce the concept.

Complex ion formation is a classic example of chemical equilibria and involves the union of a central metal ion with molecules or anions, referred to as ligands, resulting in a charged species. Students can visualize it as a metal ion at the center surrounded by several ligands that have donated electron pairs to form coordinate covalent bonds.

These complex ions exhibit dynamic equilibria, where ligands associate and dissociate; their formations can be distinctively represented via equilibrium equations. As shown in the exercise solutions, understanding the stoichiometry of a complex ion, including the number of ligands and their charges, is crucial for writing accurate expressions for the equilibrium constant, relevant to the complex’s formation. Each complex ion detailed (e.g., silver thiosulfate, zinc tetraammine, tin trisulfide) illustrates a different ligand-metal combination, offering practice in determining corresponding equilibria.

Stoichiometry, from the Greek words 'stoicheion' (element) and 'metron' (measure), is the quantitative aspect of chemistry that involves the calculation of the reactants and products in a chemical reaction. It plays a vital role in understanding chemical equilibria as it dictates the proportions of reactants that combine and the amounts of products formed.

Stoichiometric coefficients become exponents in the equilibrium constant expressions, underlying their significance. For example, the stoichiometry of the chemical equation depicting the formation of the zinc tetraammine complex tells us that each zinc ion reacts with four ammonia molecules, leading to the exponent four in the equilibrium expression. Clarifying stoichiometry in chemical equations helps students link the abstract concept of balanced reactions with the concrete numbers used in equilibrium calculations.