Question

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?

Short answer

The oxidation state of cobalt in the complex ion is +3, and the formula of the compound is \(\mathrm{[Co(H_2O)_6]Cl_3}\).

Step-by-step solution

Calculate the number of moles of silver chloride, AgCl, in the first sample

In order to determine the number of moles of \(\mathrm{AgCl}\), we need to use the mass of the silver chloride, \(0.308\ \mathrm{g}\), along with its molar mass, which can be found by adding the molar mass of silver (\(107.87\ \mathrm{g/mol}\)) and the molar mass of chlorine (\(35.45\ \mathrm{g/mol}\)): Molar mass of \(\mathrm{AgCl} = 107.87 + 35.45 = 143.32\ \mathrm{g/mol}\) Then, we can calculate the moles of \(\mathrm{AgCl}\) as follows: Moles of \(\mathrm{AgCl} = \frac{\text{mass of }\mathrm{AgCl}}{\text{molar mass of }\mathrm{AgCl}} = \frac{0.308\ \mathrm{g}}{143.32\ \mathrm{g/mol}} = 0.00215\ \mathrm{mol}\)

Calculate the number of moles of chloride ion, Cl-, in the compound

In this step, we will find the number of moles of \(\mathrm{Cl}^{-}\) in the compound. Since there is a 1:1 ratio between \(\mathrm{AgCl}\) and \(\mathrm{Cl}^{-}\), the moles of \(\mathrm{Cl}^{-}\) will be the same as the moles of \(\mathrm{AgCl}\): Moles of \(\mathrm{Cl}^{-} = 0.00215\ \mathrm{mol}\)

Calculate the number of moles of cobalt(III) oxide, Co2O3, in the second sample

We are given that the mass of cobalt(III) oxide formed is \(0.145\ \mathrm{g}\). In order to get the moles of \(\mathrm{Co}_{2}\mathrm{O}_{3}\), we need to divide the mass of \(\mathrm{Co}_{2}\mathrm{O}_{3}\) by its molar mass. The molar mass of \(\mathrm{Co}_{2}\mathrm{O}_{3}\) can be calculated as follows: Molar mass of \(\mathrm{Co}_{2}\mathrm{O}_{3} = 2 \times (\text{molar mass of Co}) + 3 \times (\text{molar mass of O}) = 2 \times 58.93 + 3 \times 16 = 137.86\ \mathrm{g/mol}\) Moles of \(\mathrm{Co}_{2}\mathrm{O}_{3} = \frac{\text{mass of }\mathrm{Co}_{2}\mathrm{O}_{3}}{\text{molar mass of }\mathrm{Co}_{2}\mathrm{O}_{3}} = \frac{0.145\ \mathrm{g}}{137.86\ \mathrm{g/mol}} = 0.00105\ \mathrm{mol}\)

Calculate the number of moles of cobalt ion, Co^(n+), in the compound

Since there is a 2:1 ratio between cobalt ions, \(\mathrm{Co}^{n+}\), and \(\mathrm{Co}_{2}\mathrm{O}_{3}\), we can find the moles of cobalt ions using this relationship: Moles of \(\mathrm{Co}^{n+} = 2 \times (\text{moles of }\mathrm{Co}_{2}\mathrm{O}_{3}) = 2 \times 0.00105\ \mathrm{mol} = 0.00210\ \mathrm{mol}\)

Determine the oxidation state of cobalt and the formula of the compound

Now that we have the moles of all the components, we can set up a ratio to find the oxidation state of cobalt: \(\frac{\text{moles of }\mathrm{Co}^{n+}}{\text{moles of }\mathrm{Cl}^{-}} = \frac{0.00210}{0.00215} = 0.9767\) Since this ratio is approximately 1, it means the oxidation state of cobalt is +3. Now that we know the oxidation state of cobalt, we can find the formula of the compound. Since the moles of \(\mathrm{Co}^{3+}\) and \(\mathrm{Cl}^{-}\) are approximately equal, with a 1:1 ratio, and each \(\mathrm{Co}^{3+}\) is complexed with six \(\mathrm{H}_{2}\mathrm{O}\) molecules: The formula of the compound is \(\mathrm{[Co(H_2O)_6]Cl_3}\)

Key concepts

Oxidation State Determination

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.

Molar Mass Calculation

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

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.