Question

Based on the molar conductance values listed here for the series of platinum(IV) complexes, write the formula for each complex so as to show which ligands are in the coordination sphere of the metal. By way of example, the molar conductances of \(0.050 \mathrm{M} \mathrm{NaCl}\) and \(\mathrm{BaCl}_{2}\) are \(107 \mathrm{ohm}^{-1}\) and \(197 \mathrm{ohm}^{-1}\), respectively. \begin{tabular}{lc} \hline Complex & Molar Conductance \(\left(o \text { ohm }^{-1}\right)^{*}\) of \(0.050\) M Solution \\ \hline \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}\) & 523 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{4}\) & 228 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{4}\) & 97 \\ \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4}\) & 0 \\ \(\left.\mathrm{KPt}_{4}\right) \mathrm{NH}_{5}\) & 108 \\ \hline \end{tabular} "The ohm is a unit of resistance; conductance is the inverse of resistance.

Short answer

The correct formulas for the platinum(IV) complexes are: 1. [Pt(NH₃)₆Cl₂]Cl₂ 2. [Pt(NH₃)₄Cl₄] 3. [Pt(NH₃)₃Cl₃]Cl 4. [Pt(NH₃)₂Cl₄] 5. K[Pt₄(NH₅)]

Step-by-step solution

Understanding Molar Conductance and Ions' Contribution

Molar conductance is the measure of the ease with which ions can move through a solution and is linked to the number of ions produced in a solution. In our case, the higher the conductance, the more ions are formed and vice versa. Given that: 1 mole of NaCl produces 1 mole of Na+ and 1 mole of Cl- i.e., 2 moles of ions 1 mole of BaCl2 produces 1 mole of Ba2+ and 2 moles of Cl- i.e., 3 moles of ions We'll use the molar conductance values for NaCl (107 ohm⁻¹) and BaCl₂ (197 ohm⁻¹) as reference points to help deduce ions' contributions in other complexes.

Determine Moles of Ions Produced by Each Complex

We will use the ratios of molar conductances to estimate the number of ions produced by each complex, which will in turn give an insight into the ligands inside coordination sphere. For Pt(NH₃)₆Cl₄ with a molar conductance of 523 ohm⁻¹, we first compare with NaCl: Ratio₁ = 523 / 107 ≈ 4.9 The ratio is close to 5, meaning the complex produces around 5 moles of ions. Now, compare with BaCl₂: Ratio₂ = 523 / 197 ≈ 2.7 In this case, the ratio is close to 3, suggesting the complex produces about 3 moles of ions. Since the first ratio (comparing with NaCl) gives a closer value to a whole number, we believe the complex produces 5 moles of ions. We can repeat this process for all platinum complexes: - For Pt(NH₃)₄Cl₄: 228 / 107 ≈ 2.1 (using NaCl) 228 / 197 ≈ 1.2 (using BaCl₂) The complex produces around 2 moles of ions. - For Pt(NH₃)₃Cl₄: 97 / 107 ≈ 0.9 (using NaCl) 97 / 197 ≈ 0.5 (using BaCl₂) The complex produces around 1 mole of ions. - For Pt(NH₃)₂Cl₄: 0 / 107 ≈ 0 (using NaCl) 0 / 197 ≈ 0 (using BaCl₂) The complex seems to produce no ions, indicating that all Cl⁻ ions are inside the coordination sphere. - For KPt₄):NH₅: 108 / 107 ≈ 1 (using NaCl) 108 / 197 ≈ 0.5 (using BaCl₂) The complex produces approximately 1 mole of ions.

Rewrite the Complex Formulas

Now that we have an estimate of the number of ions produced, we can rewrite the formulas for each complex: - For Pt(NH₃)₆Cl₄ producing 5 moles of ions, we deduce that 2 moles of Cl⁻ ions are inside the coordination sphere and 3 moles Cl⁻ are outside the sphere (counter ions). The formula would be [Pt(NH₃)₆Cl₂]Cl₂. - For Pt(NH₃)₄Cl₄ producing 2 moles of ions, all the Cl⁻ ions are inside the coordination sphere. The formula would be [Pt(NH₃)₄Cl₄]. - For Pt(NH₃)₃Cl₄ producing 1 mole of ions, 3 moles of Cl⁻ ions are inside the coordination sphere and 1 mole outside the sphere (counter ions). The formula would be [Pt(NH₃)₃Cl₃]Cl. - For Pt(NH₃)₂Cl₄, no ions are produced, which means all the Cl⁻ ions are inside the coordination sphere. The formula would be [Pt(NH₃)₂Cl₄]. - For (KPt₄):NH₅ producing 1 mole of ions, the only ion present must be K⁺, as there are no other ions in the formula. Thus, the formula would be K[Pt₄(NH₅)]. In summary, the correct formulas for the complexes are: 1. [Pt(NH₃)₆Cl₂]Cl₂ 2. [Pt(NH₃)₄Cl₄] 3. [Pt(NH₃)₃Cl₃]Cl 4. [Pt(NH₃)₂Cl₄] 5. K[Pt₄(NH₅)]

Key concepts

Coordination Compounds

Coordination compounds are a distinct class of compounds in which metal atoms or ions are surrounded by various molecules or anions, known as ligands. These ligands donate electron pairs to form coordinate covalent bonds with the metal center. The entire assembly of the central ion and its attached ligands is referred to as a coordination complex.

The formula of a coordination compound illustrates the arrangement of ligands in the coordination sphere of the metal. For example, the complex [Pt(NH₃)₄Cl₂] has the platinum metal at its center with four ammonia (NH₃) molecules and two chloride (Cl⁻) ions as ligands directly bonded to it. This complex structure has critical implications on its chemical reactivity, the color it might exhibit due to d-orbital electron transitions, and its magnetic properties.

Electrolyte Conductance

Electrolyte conductance refers to the ability of an electrolyte solution to carry an electric current. This property is central to understanding how dissolved substances, such as salts, acids, and bases, dissociate into ions when in solution. The degree of dissociation determines the number of charge carriers available, which in turn dictates the solution's conductivity.

Electrolytes can be strong or weak, depending on their capacity to dissociate in solution. Strong electrolytes, such as sodium chloride (NaCl), dissociate completely, resulting in a higher molar conductance. This is compared to weak electrolytes, which partially dissociate, creating fewer ions and lower conductance. Coordination compounds often show varying degrees of electrolytic conductance depending on the nature of their constituent ligands and the metal center.

Platinum Complexes

Platinum complexes are a group of coordination compounds that have a platinum ion as their metal center. Their conductive properties are of particular interest in electrolyte conductance studies. The conductance depends on the number of ions produced when these compounds dissociate in solution, which is associated with the nature of the platinum complexes and the ligands involved.

For instance, a platinum complex such as [Pt(NH₃)₆Cl₄] sees the chloride ions dissociate in solution, contributing to its high molar conductance. Meanwhile, a complex like [Pt(NH₃)₂Cl₄], which does not dissociate into ions, shows no conductivity. Understanding these relationships is crucial in applications such as catalysis, material science, and medicinal chemistry, where platinum complexes play a significant role.