The closo-borane with the formula B6 H6 ^2- has the six B atoms at vertices, forming an octahedr

step 1 The class of borane with the formula B6 S6 to negative has the 6 B atoms at vertices forming oct

The closo-borane with the formula B6 H6 ^2- has the six B...

The closo-borane with the formula $\mathrm{B}_{6} \mathrm{H}_{6}{ }^{2-}$ has the six $\mathrm{B}$ atoms at vertices, forming an octahedron structure with eight faces. The formula for the number of sides is $2 n-4,$ where $n$ is the number of boron atoms. Determine the number of vertices and faces for each closo-borane. a. $\mathrm{B}_{4} \mathrm{H}_{4}^{2-}$ b. $\mathrm{B}_{12} \mathrm{H}_{12}^{2-}$

The closo-borane with the formula $\mathrm{B}_{6} \mathrm{H}_{6}{ }^{2-}$ has the six $\mathrm{B}$ atoms at vertices, forming an octahedron structure with eight faces. The formula for the number of sides is $2 n-4,$ where $n$ is the number of boron atoms. Determine the number of vertices and faces for each closo-borane.
a. $\mathrm{B}_{4} \mathrm{H}_{4}^{2-}$
b. $\mathrm{B}_{12} \mathrm{H}_{12}^{2-}$

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Key Concepts

Polyhedral Geometry in Chemical Clusters

The geometry of closo-boranes is based on polyhedra, where the boron atoms form the vertices and the hydrogen atoms are attached externally. Understanding these polyhedral shapes involves recognizing important features like vertices (points of the polyhedron), edges (line segments connecting vertices), and faces (the flat surfaces enclosed by edges).

Relationship Between Number of Vertices and Faces

In closo-boranes, there is a direct relationship between the number of boron atoms (vertices) and the number of faces on the polyhedron. Specifically, for an n-vertex closo-borane, the number of faces is given by the formula 2n – 4, linking the molecular formula directly to the topological count of the polyhedral structure.

Closo-Boranes

Closo-boranes are a class of boron hydride clusters characterized by a closed polyhedral structure in which boron atoms occupy the vertices of a convex polyhedron. These compounds follow specific rules, such as Wade's rules, which relate the number of boron atoms to the electronic requirements and overall geometric structure of the compound.

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