A transition metal compound contains a cobalt ion, chloride ions, and water molecules. The \(\mathrm{H}_{2} \mathrm{O}\) molecules are the ligands in the complex ion and the \(\mathrm{Cl}^{-}\) ions are the counterions. \(\mathrm{A}\) \(0.256-\mathrm{g}\) sample of the compound was dissolved in water, and excess silver nitrate was added. The silver chloride was filtered, dried, and weighed, and it had a mass of \(0.308 \mathrm{~g}\). A second sample of \(0.416 \mathrm{~g}\) of the compound was dissolved in water, and an excess of sodium hydroxide was added. The hydroxide salt was filtered and heated in a flame, forming cobalt(III) oxide. The mass of cobalt(III) oxide formed was \(0.145 \mathrm{~g}\). What is the oxidation state of cobalt in the complex ion and what is the formula of the compound?

Determining the oxidation state in a transition metal complex ion is a fundamental step in understanding its chemical properties. The oxidation state, often represented by a Roman numeral, describes the degree of oxidation of an atom within a molecule or ion. It is assessed based on a set of rules, including the assumption that the more electronegative atom will take the electrons.

For transition metal complexes, the oxidation state of the metal ion can be calculated by considering the overall charge of the complex and the known charges of any counterions or ligands. In the provided exercise, cobalt's oxidation state was deduced by analyzing the mole ratios derived from stoichiometric conversions and the assumption that chloride ions (Cl-) act as counterions. The 1:1 mole ratio of Co to Cl- suggested that cobalt's oxidation state is +3, assuming each chloride ion has a charge of -1 and that they balance the charge on the cobalt ion. This step in the problem highlights the importance of carefully considering each component's charge in the complex to determine the correct oxidation state.

Calculating the molar mass of a compound is a key skill in chemistry that allows us to convert between mass and mole quantities, a process essential for stoichiometry. Molar mass is defined as the mass in grams of one mole of a substance. Due to this significance, solving the given problem required calculating the molar masses of silver chloride (AgCl) and cobalt(III) oxide (Co2O3).

This is done by summing the molar masses of the individual elements, which are obtained from the periodic table, and multiplying by the number of atoms of each element in a molecule. As shown in the solution, for AgCl and Co2O3, the atomic masses of silver, chlorine, cobalt, and oxygen were used. Correct molar mass calculation is crucial for accurately determining the moles of a substance, a foundational step in further stoichiometric calculations.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to predict how much product will form from a given amount of reactant, or how much reactant is needed to produce a desired quantity of product. In the context of the provided exercise, stoichiometry was used to relate the masses of silver chloride and cobalt(III) oxide to the amount of Cobalt and Chloride ions in the original complex ion.

By understanding the concept of moles and the molar mass of substances involved, we were able to convert between mass and mole quantities, setting up a stoichiometric relationship to solve for unknown variables. For instance, knowing the mole ratio of Co2O3 to Co allowed us to determine the moles of cobalt ions. Stoichiometry is a powerful tool in chemistry that forms the basis for many quantitative analyses, including determining empirical formulas and understanding reaction yields.