Question

A certain complex of metal \(\mathrm{M}\) is formulated as \(\mathrm{MCl}_{3} \cdot 3 \mathrm{H}_{2} \mathrm{O}\). The coordination number of the complex is not known but is expected to be 4 or 6. (a) Would conductivity measurements provide information about the coordination number? (b) In using conductivity measurements to test which ligands are bound to the metal ion, what assumption is made about the rate at which ligands enter or leave the coordination sphere of the metal? (c) Suppose you experimentally determine that this complex exists in aqueous solution as a single species. Suggest a likely coordination number and the number and type of each ligand.

Short answer

Conductivity measurements cannot directly determine the coordination number as they only provide information about the number of ions and their charges in a solution. Using these measurements to test ligands assumes that ligand exchange rates are fast, allowing for equilibrium in the solution. In this case, it is more likely that the coordination number is 6, with three chloride ligands and three water ligands, as this accounts for all the ions present in the compound's formula.

Step-by-step solution

(a) Analyzing conductivity measurements for coordination number determination

Conductivity measurements are useful for determining the number of ions in a solution, as well as the charge on the ions. In this case, since the formula of the compound is given as \(\mathrm{MCl}_{3} \cdot 3 \mathrm{H}_2 \mathrm{O}\), we know that there are three chloride ions and three water molecules in the compound. However, conductivity measurements cannot provide information about the arrangement of these ligands in the coordination sphere of the metal, so they cannot directly determine the coordination number.

(b) Assumptions about ligand exchange

When using conductivity measurements to test which ligands are bound to the metal ion, it is assumed that the rate at which ligands enter or leave the coordination sphere is relatively fast. This is because, in a conductivity measurement, we are looking at the overall charge of the ions in solution, and if ligands are exchanging rapidly, it means the complex is in equilibrium with its surroundings and we can get a reliable measurement. If ligands exchange slowly, it becomes difficult to determine the true composition of the complex as the overall solution may not have reached equilibrium.

(c) Suggesting a likely coordination number and ligand count

Given that the complex exists in aqueous solution as a single species and considering the formula of the compound \(\mathrm{MCl}_{3} \cdot 3 \mathrm{H}_2 \mathrm{O}\), it is more likely that the coordination number is 6, as this would account for all three chloride ions and three water molecules present in the formula. In this case, the metal ion would be bonded to three chloride ligands and three water molecules, with a coordination number of 6. Although coordination number 4 is also a possibility, it would require an explanation for the presence of the additional water molecules in the crystal structure. Therefore, the most likely coordination number is 6, with three chloride ligands and three water ligands.

Key concepts

Conductivity Measurements

Understanding the concept of conductivity measurements can be quite helpful when analyzing ionic compounds in solution. Conductivity, fundamentally, depends on the presence of ions capable of carrying an electrical current. More ions, or ions with higher charges, result in increased conductivity.

When examining a complex such as \(\mathrm{MCl}_{3} \cdot 3\mathrm{H}_{2}O\), conductivity measurements can reveal the number of ionizable chloride ligands because these contribute to the total charge in solution when dissociated from the metal. However, the arrangement or identity of non-ionizable ligands (like water in this case) won't influence conductivity significantly. Thus, the number of charged species released into the solution upon dissolution provides some insight but doesn't paint the full picture regarding coordination number.

For instance, students would learn that a complex releasing more ions into solution would demonstrate higher conductivity. This data, however, needs careful interpretation since various factors, including the geometry of the complex and the nature of its ligands, can affect the reading.

Ligand Exchange Rate

When dealing with complex ions, the rate at which ligands attach and detach from the metal ion at the center—the ligand exchange rate—is a crucial concept. In simple terms, this rate indicates how quickly a ligand can be replaced by another ligand in the complex ion's coordination sphere.

For conductivity measurements to accurately reflect the nature of a complex such as \(\mathrm{MCl}_{3} \cdot 3\mathrm{H}_{2}O\), we need to assume the ligands exchange at a rapid pace. This rapid exchange ensures that the observed conductivity is representative of a dynamic equilibrium in which the ions and the complex constantly interact. A slow exchange rate would mean that the solution doesn't truly reflect the real-time composition of the complex ion since it's not in equilibrium.

Students often wonder why equilibrium matters. If conductivity is measured when the complex ion hasn't fully released all possible ions into the solution, due to slow ligand exchange, the measurements won't accurately reflect the potential for conductivity of the entire system.

Complex Ions

Complex ions feature a central metal atom or ion surrounded by molecules or ions termed as ligands. The coordination number of a complex ion refers to the number of ligand attachment sites occupied on the metal ion, a concept crucial to understanding complex structures.

When a compound like \(\mathrm{MCl}_{3} \cdot 3\mathrm{H}_{2}O\) is dissolved in water, determining its coordination number entails figuring out how many of the ligands directly interact with the metal ion. If experimental findings suggest there exists only one species in solution, it implies all the ligands maintain a static relationship with the metal ion. Considering the stoichiometry of the given compound, it is most likely that the coordination number is six. This number not only explains the presence of all chloride and water ligands in the structure but also aligns with common geometric arrangements for complexes with coordination number six, like octahedral structures.

Understanding complex ions and their coordination is vital for appreciating why certain elements form particular types of complexes, how these complexes interact in solution, and why they demonstrate distinct physical and chemical properties. Knowing that three water molecules and three chloride ions are present assists students in visualizing a complete coordination sphere around the metal ion.