Some of the first complexes discovered by Werner in the 1890...

Some of the first complexes discovered by Werner in the 1890 s had the empirical formulas given below. Also given are the number of chloride ions per formula unit precipitated by the addition of $\mathrm{Ag}^{+}(a q) .$ Explain these observations. $$ \begin{array}{lc} \hline \begin{array}{l} \text { Empirical } \\ \text { formula } \end{array} & \begin{array}{l} \text { Number of Cl }^{-} \text {per formula } \\ \text { unit precipitated by } \mathbf{A g}^{+}(a q) \end{array} \\ \hline \mathrm{PtCl}_{2} \cdot 4 \mathrm{NH}_{3} & 2 \\ \mathrm{PtCl}_{2} \cdot 3 \mathrm{NH}_{3} & 1 \\ \mathrm{PtCl}_{2} \cdot 2 \mathrm{NH}_{3} & 0 \end{array} $$

Some of the first complexes discovered by Werner in the 1890 s had the empirical formulas given below. Also given are the number of chloride ions per formula unit precipitated by the addition of $\mathrm{Ag}^{+}(a q) .$ Explain these observations.
$$
\begin{array}{lc}
\hline \begin{array}{l}
\text { Empirical } \\
\text { formula }
\end{array} & \begin{array}{l}
\text { Number of Cl }^{-} \text {per formula } \\
\text { unit precipitated by } \mathbf{A g}^{+}(a q)
\end{array} \\
\hline \mathrm{PtCl}_{2} \cdot 4 \mathrm{NH}_{3} & 2 \\
\mathrm{PtCl}_{2} \cdot 3 \mathrm{NH}_{3} & 1 \\
\mathrm{PtCl}_{2} \cdot 2 \mathrm{NH}_{3} & 0
\end{array}
$$

Key Concepts

Werner’s Coordination Theory

This theory was the foundation for modern coordination chemistry. It proposed that metal complexes consist of a metal ion surrounded by a fixed number of ligands in the inner sphere, with other ions present as counterions in the outer sphere. This distinction explains how compounds with similar empirical formulas can have different numbers of free ions, depending on which anions are directly coordinated to the metal center.

Inner and Outer Sphere Ligands

In coordination compounds, ligands that are directly bonded to the central metal ion form the inner coordination sphere, while ions present to balance overall charge but not directly bound to the metal constitute the outer sphere. Observations from precipitation reactions, such as the reaction with silver ions forming AgCl from free chloride ions, confirm which chloride ions are in the outer sphere.

Coordination Geometry and Number

The number of ligands attached directly to the metal ion (the coordination number) and the spatial arrangement (coordination geometry) determine the structure of the complex. In these examples, changing the number of ammonia ligands forces a corresponding change in the number of chloride ions bound in the coordination sphere, thus altering the number of chloride counterions available for precipitation.

Precipitation Reaction with Silver Ion

Silver ion reacts with free chloride ions to form insoluble silver chloride. This precipitation test is crucial in experimentally distinguishing between chloride ions that are coordinated to the metal (and thus not available to react with Ag+) and those that serve as counterions in the outer coordination sphere.

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