Question

A student has prepared a cobalt complex that has one of the following three structures: \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}\), \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2},\) or \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right] \mathrm{Cl} .\) Explain how the student would distinguish between these possibilities by an electrical conductance experiment. At the student's disposal are three strong electrolytes \(-\mathrm{NaCl}, \mathrm{MgCl}_{2}\), and \(\mathrm{FeCl}_{3}-\) which may be used for comparison purposes.

Short answer

Compare conductance: if it matches NaCl's, it's Structure 3; MgCl2's, it's Structure 2; FeCl3's, it's Structure 1.

Step-by-step solution

Understanding the Question

We are tasked with determining the structure of a cobalt complex using electrical conductance experiments. The three possible complex structures are 1. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\mathrm{Cl}_{3}\),2. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5}\mathrm{Cl}\right] \mathrm{Cl}_{2},\)and 3. \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\mathrm{Cl} .\)}.

Concept of Electrical Conductance

Electrical conductance in a solution depends on the number of ions present. A strong electrolyte dissociates completely in water to form free ions, which increase the solution's electrical conductance.

Comparing with Standard Electrolytes

We have three standard electrolytes for comparison: NaCl (produces 2 ions), MgCl2 (produces 3 ions), and FeCl3 (produces 4 ions). Each cobalt complex will dissociate in solution, releasing a certain number of ions, similar to these standard electrolytes.

Analyzing Complex 1

For \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]\mathrm{Cl}_{3}\), the complex dissociates into 1 cation \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}\) and 3 chloride ions \(\mathrm{Cl}^-\), totalling 4 ions. Thus, it should have conductance similar to FeCl3.

Analyzing Complex 2

For \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right]\mathrm{Cl}_{2}\), it dissociates into 1 cation \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{Cl}\right]^{2+}\) and 2 chloride ions, also totalling 3 ions. Its conductance would match MgCl2.

Analyzing Complex 3

For \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\mathrm{Cl}\), it breaks down into 1 cation \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^+\) and 1 chloride ion \(\mathrm{Cl}^-\), totaling 2 ions. This should match conductance to NaCl.

Experimentation and Observation

The student can carry out an electrical conductance test on the prepared solution of the cobalt complex. By comparing the conductance with solutions of NaCl, MgCl2, and FeCl3, the student can determine which of the three structures the complex aligns with based on the number of ions released.

Key concepts

Electrical Conductance

Electrical conductance is important in understanding how well a solution can carry an electric current. It relies on free-moving charged particles, mainly ions, in the solution. The higher the number of ions, the greater the conductance.

In this experiment, electrical conductance serves as a helpful tool to determine the structure of a cobalt complex. Each different structure will dissociate to release a different number of ions, affecting the conductance. More ions mean higher conductance, while fewer ions mean lower conductance. Thus, by measuring how well the solution conducts electricity, we can infer the number of ions and relate it to the structure of the cobalt complex.

Electrolyte Dissociation

Electrolyte dissociation is the process by which a compound separates into its individual ions when dissolved in a solvent like water. Strong electrolytes disassociate completely, leading to a large number of free ions.

The dissociation process is crucial in determining the cobalt complex's structure through electrical conductance. Each of the possible cobalt complexes dissociates differently:

• The first complex, \([\mathrm{Co}(\mathrm{NH}_3)_6]\mathrm{Cl}_3\), breaks into four ions.
• The second, \([\mathrm{Co}(\mathrm{NH}_3)_5 \mathrm{Cl}]\mathrm{Cl}_2\), breaks into three ions.
• The third, \([\mathrm{Co}(\mathrm{NH}_3)_4 \mathrm{Cl}_2]\mathrm{Cl}\), breaks into two ions.

By understanding how these compounds dissociate, we can predict their electrical conductance and better ascertain the structure of the experiment's cobalt complex.

Coordination Compounds

Coordination compounds involve a central metal atom or ion surrounded by molecules or ions called ligands. These complexes are often characterized by their geometries and the number of ions that dissociate in solution.

In our exercise, cobalt serves as the central metal ion. The ammonia molecules (NH₃) and chloride ions (Cl^-) are the ligands that complete the coordination sphere. Understanding how these components fit together gives insight into their chemical behavior, especially regarding ionic dissociation and resulting electrical conductance. The different ligands impact stability and dissociation patterns, which in turn affect the number of ions in solution.

Ion Comparison

The experiment consists of comparing the dissociated ions from the cobalt complexes to known strong electrolytes: NaCl, MgCl₂, and FeCl₃. Each of these standard compounds dissociates into a specific number of ions:

• NaCl dissociates into 2 ions;
• MgCl₂ dissociates into 3 ions;
• FeCl₃ dissociates into 4 ions.

By comparing the electrical conductance of the unknown cobalt complex with these known standards, the student can determine how many ions are released, thus indicating which cobalt structure is present. Comparing conductance directly ties the number of ions released by a compound to its structural identity.

Complex Ion Formations

Complex ion formations involve how a central ion, such as cobalt, bonds with ligands to form a stable structure. The arrangement and charge of ligands like NH₃ and Cl^- influence how the complex dissociates within a solution.

For the cobalt complexes at hand, knowing the formation aids in predicting dissociation patterns and electrical conductance. Each structure's specific formation and ionic charge distribution result in unique dissociation paths. These paths ultimately dictate the number of ions released and aid in deducing the correct structure through conductance experiments.