Verified Answer :

  • Cobalt (III) indicates a cobalt cation with a charge of \(+3\) (\(\text{Co}^{3+}\)).
  • Chloride indicates an anion with a charge of \(-1\) (\(\text{Cl}^{-}\)).
  • For the compound to be electrically neutral, the charge balance equation \(3x - 1y = 0\) requires a ratio of \(1\) cobalt ion to \(3\) chloride ions.
  • The resulting chemical formula is \(\boxed{\text{CoCl}_3}\).

Explanation

  1. Identifying Ion Charges

Cobalt (III) chloride is a chemical compound consisting of cobalt ions and chloride ions. To determine the correct formula, we must identify the charges of each constituent ion and ensure that the final compound is electrically neutral.

The name "Cobalt (III)" indicates that the cobalt ion has an oxidation state of +3, written as \(\text{Co}^{3+}\). The term "chloride" refers to the anion formed by chlorine, which typically has an oxidation state of -1, written as \(\text{Cl}^{-}\).

  1. Achieving Electrical Neutrality

In any ionic compound, the total positive charge must be equal to the total negative charge to ensure the compound is electrically neutral. Let \(x\) be the number of \(\text{Co}^{3+}\) ions and \(y\) be the number of \(\text{Cl}^{-}\) ions in the formula. The neutrality condition can be expressed as:
\[x \times (+3) + y \times (-1) = 0\]
Rearranging this equation gives:
\[3x = y\]
To find the simplest empirical formula, we look for the smallest integer values of \(x\) and \(y\). If we let \(x = 1\), then \(y = 3\). This indicates that we need one \(\text{Co}^{3+}\) ion for every three \(\text{Cl}^{-}\) ions.

  1. Conclusion and Final Formula

Based on the ion ratio derived, the formula for the compound is \(\text{Co}_1\text{Cl}_3\), which is standardly written as \(\text{CoCl}_3\). Comparing this to the given options (\(\text{CoCl}\), \(\text{CoCl}_3\), \(\text{Co}_2\text{Cl}_3\)), we confirm that \(\text{CoCl}_3\) is the correct chemical formula.

Examples

In chemical manufacturing and laboratory settings, understanding the correct chemical formula is crucial for stoichiometry, which allows chemists to calculate the precise amounts of reactants needed to synthesize a substance or analyze the products of a reaction. For example, when synthesizing Cobalt (III) chloride for industrial applications like battery production or catalysis, knowing that it requires a ratio of one Cobalt atom to three Chlorine atoms ensures the reaction produces the intended material rather than an unwanted byproduct. This principle of balancing charges applies to all ionic compounds, providing a consistent method for predicting the composition of salts and complexes.

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