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 ohm \(^{-1}\), respectively. $$ \begin{array}{ll} \hline \text { Complex } & \begin{array}{l} \text { Molar Conductance (ohm }^{-1} \text { ) }^{*} \\ \text { of } \mathbf{0 . 0 5 0 M \text { Solution }} \end{array} \\ \hline \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4} & 523 \\ \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{4} & 228 \\ \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{4} & 97 \\ \mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{4} & 0 \\ \mathrm{KPt}\left(\mathrm{NH}_{3}\right) \mathrm{Cl}_{5} & 108 \\ \hline \end{array} $$

Short answer

The final formulas for the platinum(IV) complexes showing the ligands in the coordination sphere of the metal are: 1. \([Pt(NH_3)_6]^{4+}(Cl^-)_4\) 2. \([Pt(NH_3)_4Cl_2]^{2+}(Cl^-)_2\) 3. \([Pt(NH_3)_3Cl]^{+}(Cl^-)\) 4. \((Pt(NH_3)_2Cl_4)\) 5. \((K^+)([Pt(NH_3)Cl_5]^{-})\)

Step-by-step solution

Identifying the number of ions for the given reference compounds

First, we need to find out how many ions are produced by the given reference compounds (NaCl and BaCl₂) when they dissociate in the solution. NaCl dissociates into one sodium ion (Na⁺) and one chloride ion (Cl⁻), producing a total of 2 ions. BaCl₂ dissociates into one barium ion (Ba²⁺) and two chloride ions (2 Cl⁻), producing a total of 3 ions.

Calculate the molar conductance per ion for the reference compounds

Now, we need to calculate the molar conductance of the reference compounds per ion. For NaCl (molar conductance = 107 ohm⁻¹), it would be: \[ \frac{107 \, \text{ohm}^{-1}}{2 \, \text{ions}} = 53.5 \, \frac{\text{ohm}^{-1}}{\text{ion}} \] For BaCl₂ (molar conductance = 197 ohm⁻¹), it would be: \[ \frac{197 \, \text{ohm}^{-1}}{3 \, \text{ions}} = 65.7 \, \frac{\text{ohm}^{-1}}{\text{ion}} \]

Calculate the number of dissociated ions for each platinum(IV) complex

Using the molar conductance per ion values from step 2, we can determine the number of ions produced by each platinum(IV) complex: 1. Pt(NH₃)₆Cl₄: \[ \frac{523 \, \text{ohm}^{-1}}{53.5 \, \frac{\text{ohm}^{-1}}{\mathrm{ion}}} \approx 10 \, \text{ions} \] 2. Pt(NH₃)₄Cl₄: \[ \frac{228 \, \text{ohm}^{-1}}{53.5 \, \frac{\text{ohm}^{-1}}{\mathrm{ion}}} \approx 4 \, \text{ions} \] 3. Pt(NH₃)₃Cl₄: \[ \frac{97 \, \text{ohm}^{-1}}{53.5 \, \frac{\text{ohm}^{-1}}{\mathrm{ion}}} \approx 2 \, \text{ions} \] 4. Pt(NH₃)₂Cl₄: \[ \frac{0 \, \text{ohm}^{-1}}{53.5 \, \frac{\text{ohm}^{-1}}{\mathrm{ion}}} = 0 \, \text{ions} \] 5. KPt(NH₃)Cl₅: \[ \frac{108 \, \text{ohm}^{-1}}{53.5 \, \frac{\text{ohm}^{-1}}{\mathrm{ion}}} \approx 2 \, \text{ions} \]

Assign the dissociated ions to find the correct formula of each complex

Based on the number of ions dissociated from each platinum complex, we can now assign the correct formula for each complex: 1. Pt(NH₃)₆Cl₄: \(([Pt(NH_3)_6]^{4+})(Cl^-)_4\) 2. Pt(NH₃)₄Cl₄: \(([Pt(NH_3)_4Cl_2]^{2+})(Cl^-)_2\) 3. Pt(NH₃)₃Cl₄: \(([Pt(NH_3)_3Cl]^{+})(Cl^-)\) 4. Pt(NH₃)₂Cl₄: \((Pt(NH_3)_2Cl_4)\) 5. KPt(NH₃)Cl₅: \((K^+)([Pt(NH_3)Cl_5]^{-})\) The final formulas for the platinum(IV) complexes showing the ligands in the coordination sphere of the metal are: 1. \([Pt(NH_3)_6]^{4+}(Cl^-)_4\) 2. \([Pt(NH_3)_4Cl_2]^{2+}(Cl^-)_2\) 3. \([Pt(NH_3)_3Cl]^{+}(Cl^-)\) 4. \((Pt(NH_3)_2Cl_4)\) 5. \((K^+)([Pt(NH_3)Cl_5]^{-})\)

Key concepts

Molar Conductance

Molar conductance is a measure of how well a solution can conduct electricity. It depends on both the concentration of ions in the solution and their mobility.
To calculate molar conductance, we divide the conductance of the solution by its concentration. The unit is usually ohm^-1 cm² mol^-1. Higher values indicate better conductivity.
Molar conductance increases as the number of ions in solution increases. This makes it a useful tool for understanding the structure of complex ions.
In the exercise, we used molar conductance to determine how many ions dissociate from platinum complexes in solution. By comparing these values with those of reference compounds like NaCl and BaCl₂, we can infer the number of ions each complex produces.
Such calculations help us determine which ligands are actually bonded to the central metal ion, providing insights into the coordination sphere.

Complex Ions

Complex ions consist of a central metal atom or ion, surrounded by molecules or ions known as ligands. These ligands can be either neutral or charged.
The arrangement of these ligands around the metal ion is what we refer to as the coordination sphere.
Understanding complex ions involves exploring the types of bonds present, the geometry around the central ion, and the electron configuration, which influence their chemical properties.
In coordination chemistry, we often use conventions to denote the oxidation state of the metal and the numbers of ions present in the complex.

• For example, in the complex \([Pt(NH_3)_6]^{4+}(Cl^-)_{4}\), Pt is the central metal ion.
• The NH₃ units are ligands attached to Pt, making up the coordination sphere.
• While the Cl^- ions balance the charge from the ion not within the coordination sphere.

Complex ions are fundamental to understanding many reactions in inorganic chemistry, as they can readily form under various conditions and have unique properties due to the interplay of their components.

Platinum Complexes

Platinum complexes are an important category in coordination chemistry due to their role in catalysis, medicine, and materials science.
The central atom in these complexes is platinum, and it is known for forming strong, stable bonds with ligands.
Platinum can exist in multiple oxidation states, which influences the geometry and electronic configuration of the complex.
In the platinum(IV) complexes discussed, we saw examples of different formulas, such as \([Pt(NH_3)_4Cl_2]^{2+}(Cl^-)_2\).

• Here, platinum is in a +4 oxidation state.
• The ligands attached to it are ammonia (NH₃) and chloride ions (Cl^-).
• The formula indicates which ligands are inside the coordination sphere, affecting the properties of the compounds.

These complexes can have diverse applications, including in chemotherapy for the treatment of cancer, due to their ability to interact specifically with biological molecules.
Studying these compounds helps us develop new technologies and therapeutic agents. Understanding the nature of bonding and the behavior of such complexes is crucial for progress in the field of coordination chemistry.