Predict the number of vertices and faces on each closo-borane. a. B6 H6^2- b. B12 H12^2-

Name: Problem 29, Chapter 24: Chemistry A Molecular Approach
Uploaded: 2020-02-11T01:58:02-08:00
Duration: 3 min 29 s
Channel: Amy Jiang
Description: Predict the number of vertices and faces on each closo-borane. a. B6 H6^2- b. B12 H12^2-

step 1 Okay, so we have to predict the number of vertices and faces in our closed -o -boring. For part

Predict the number of vertices and faces on each...

Key Concepts

Vertex-Face Relationships in Polyhedra

The relationship between the vertices and faces of a polyhedron is governed by geometric principles and Euler's formula. For closo-boranes, knowing the number of vertices (which corresponds to the number of boron atoms) allows one to infer the number of faces by identifying the standard polyhedral shape (for example, an octahedron with 6 vertices has 8 faces and an icosahedron with 12 vertices has 20 faces). This connection is crucial for predicting and understanding the molecular structure of these compounds.

Wade’s Rules

Wade’s rules are guidelines used to predict the structures of electron-deficient clusters, particularly boranes. They relate the number of skeletal electrons to the type of polyhedral structure that will form. In closo-boranes, these rules indicate that a cluster with n boron atoms typically forms a closed polyhedron with n vertices, helping chemists determine not only the connectivity but also the overall geometry of the molecule.

Closo-Boranes

Closo-boranes are a family of boron-hydrogen clusters in which the boron atoms form a closed polyhedral framework. In these compounds, each boron atom is located at a vertex of the polyhedron, and the overall structure follows the criteria for closo structures, which are determined by the number of skeletal bonding electrons as outlined by Wade’s rules.

Polyhedral Geometry

Polyhedral geometry refers to the study of three?dimensional shapes with flat faces, straight edges, and sharp vertices. In the context of closo-boranes, each compound adopts a structure corresponding to a specific polyhedron, where the number of boron atoms equals the number of vertices of the polyhedron. Recognizing standard polyhedra, like the octahedron and the icosahedron, helps in predicting structural attributes such as the number of faces.

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