A \(0.01 \mathrm{M}\) complex of \(\mathrm{CoCl}_{2}\) and \(\mathrm{NH}_{3}\) (molar ratio \(1: 4\) ) is found to have effective molarity of \(0.02 \mathrm{M}\) (evaluated from colligative property). What is the formula of the complex? (a) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl}\) (b) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]\) (c) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{3}\) (d) \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}\)

Colligative properties are physical properties of solutions that depend solely on the number of solute particles present, and not on the chemical identity of those particles. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.
For instance, when a non-volatile solute is added to a solvent, the boiling point of the solution increases, whereas the freezing point decreases. The increase in boiling point and the decrease in freezing point are proportional to the molality (moles of solute per kilogram of solvent) of the solution. In the context of our exercise, understanding colligative properties helped deduce the number of ions released from the complex because these ions affected the effective molarity of the solution.

Complex ion formation is a dynamic and fundamental concept within coordination chemistry where central metal atoms or ions bond with a number of other molecules or ions. These surrounding entities, called ligands, donate electron pairs to the metal center, resulting in coordinate covalent bonds.
In our textbook problem, the complex ion consists of a cobalt(II) ion surrounded by ammonia molecules and chloride ions as ligands. The formation of the complex affects the solution's molarity, indicating the displacement of some chloride ions into the solution. These displaced ions influence the colligative properties and help us to identify the correct structure of the complex ion based on the increase in molarity.

Coordination chemistry delves into the study of compounds that feature one or more central atoms, usually metals, surrounded by molecules or anions, often referred to as ligands. These complexes can vary greatly in structure, properties, and color, among other characteristics.

Ligands and Complex Stability

The ligands that coordinate to the metal atom can be neutral or charged, and one ligand can form multiple bonds with the metal. The number of ligands attached to the central metal atom typically corresponds to its coordination number, which is 6 in the case of most cobalt complexes. Coordination compounds are pervasive in nature, playing critical roles in a wide array of biological systems and industrial applications.

Molarity is a measurement of concentration, representing the number of moles of solute per liter of solution (mol/L). Moles quantify the amount of a substance based on the number of particles, with one mole equivalent to Avogadro's number of particles (approximately 6.022 x 10^23).
In the given exercise, we used the concepts of molarity and moles to understand that the initial molarity of the solution (0.01 M) indicates that there are 0.01 moles of the complex per liter of solution. When the effective molarity is found to be 0.02 M due to the presence of free chloride ions in solution, it suggests that for each mole of the complex formed, an additional mole of ions must be present, allowing the determination of the complex's structure.