Question

Two silicate anions are known in which the linking of the tetrahedra forms a closed ring. One of these cyclic silicate anions contains three silicate tetrahedra, linked into a ring. The other contains six silicate tetrahedra. (a) Sketch these cyclic silicate anions. (b) Determine the formula and charge of each of the anions.

Short answer

The cyclic silicate anions containing three and six silicate tetrahedra have the empirical formulas Si3O3(O)3 and Si6O6(O)6, respectively. Considering the charges of the silicon (+4) and oxygen (-2) atoms and accounting for shared oxygen atoms, the anions have formulae and charges of [Si3O9]^3- and [Si6O18]^6-, respectively.

Step-by-step solution

Understanding the structure of silicate anions

Silicate anions are formed by linking silicon-oxygen tetrahedra together. Each tetrahedron consists of a silicon atom (Si) in the center, surrounded by four oxygen atoms (O) at the vertices. The oxygen atoms can be shared between two tetrahedra, creating a bond. The more oxygen atoms are shared, the more condensed the structure of the anion becomes.

Sketching cyclic silicate anions with three tetrahedra

In a cyclic structure with three silicate tetrahedra, two oxygen atoms from each tetrahedron are shared with neighboring tetrahedra to form a closed ring. This leaves one unshared oxygen atom at the outside of each tetrahedron, giving Si3O3(O)3 as the empirical formula.

Sketching cyclic silicate anions with six tetrahedra

In a cyclic structure with six silicate tetrahedra, two oxygen atoms from each tetrahedron are shared with neighboring tetrahedra to form a closed ring. This leaves one unshared oxygen atom at the outside of each tetrahedron, giving Si6O6(O)6 as the empirical formula.

Determining the formula and charge of the anions

To find the overall formula and charge of each anion, we need to take into account the charges of the individual atoms in the tetrahedra and the shared oxygen atoms. A silicon atom carries a charge of +4, and an oxygen atom carries a charge of -2. For the three-tetrahedra ring: Three silicon atoms (Si) contribute a total charge of 3(+4) = +12. Three unshared oxygen atoms (O) contribute a total charge of 3(-2) = -6. Three shared oxygen atoms (O) each contribute a charge of -2, but they are shared between two tetrahedra, so their net charge contribution to the anion is 3(-1) = -3. The total charge of the three-tetrahedra anion is +12 - 6 - 3 = +3. Therefore, the formula and charge of this cyclic silicate anion are [Si3O9]^3-. For the six-tetrahedra ring: Six silicon atoms (Si) contribute a total charge of 6(+4) = +24. Six unshared oxygen atoms (O) contribute a total charge of 6(-2) = -12. Six shared oxygen atoms (O) each contribute a charge of -2, but they are shared between two tetrahedra, so their net charge contribution to the anion is 6(-1) = -6. The total charge of the six-tetrahedra anion is +24 - 12 - 6 = +6. Therefore, the formula and charge of this cyclic silicate anion are [Si6O18]^6-.

Key concepts

Silicon-Oxygen Tetrahedra

At the heart of silicate mineralogy is the silicon-oxygen tetrahedron, a unit that plays a pivotal role in the formation of silicate anions. Imagine it as a pyramid with a silicon atom nestled in the center and four oxygen atoms occupying the corners. These tetrahedra are remarkable for their ability to link up in various ways, creatingsophisticated structures which are the backbone of many minerals.

By sharing one or more oxygen atoms with adjacent tetrahedra, they form different silicate structures, including chains, sheets, and even three-dimensional frameworks. The manner in which these tetrahedra share oxygen atoms has a direct impact on the properties of the minerals formed. For instance, sharing fewer oxygen atoms results in a less condensed structure, often yielding minerals with different cleavage and stability characteristics.

Silicate Anion Structure

Silicate anions are an integral part of silicate minerals and can exhibit various structures, from isolated tetrahedra to complex frameworks. The structural diversity arises from how the silicon-oxygen tetrahedra bind together. In cyclic silicate anions, these tetrahedra connect in a ring formation, sharing two oxygen atoms with their neighbors, which creates a stable, closed-loop structure.

These rings can contain different numbers of tetrahedra. In our example, one type of cyclic silicate anion includes three tetrahedra, while another contains six. The beauty of these cyclic structures is their symmetry and the tight-knit binding which imparts considerable strength to the resulting mineral. Understanding the structure is key to mastering the concepts of mineralogy and harnessing the properties of such materials for various applications in science and industry.

Empirical Formula of Silicates

Diving into the simplicity of nature's complexity, the empirical formula of silicates provides a snapshot of the composition of these minerals. It is determined by considering the number of silicon and oxygen atoms present, as well as their ratios and the connectivity between tetrahedra. For cyclic silicates with three and six tetrahedra, the formulas are derived by balancing the number of shared and unshared oxygen atoms to reflect the real structure of these anions.

For instance, in a three-tetrahedra ring, each tetrahedron has two shared and one unshared oxygen, resulting in the empirical formula Si3O9. Similarly, in a six-tetrahedra ring, the formula becomes Si6O18. These formulas provide a fundamental understanding of the mineral’s composition and are crucial for anyone studying geology or materials science to grasp.

Charge of Silicate Anions

The charge of silicate anions culminates from the balance between the positively charged silicon atoms and the negatively charged oxygen atoms within the silicon-oxygen tetrahedra. Silicon typically has a +4 charge, while oxygen has a -2 charge. In a closed cyclic silicate structure, the charges must be accounted for to understand the anion's overall charge.

This is significant in predicting how these anions will interact with other elements and molecules, a key factor in the formation of silicate minerals. For cyclic silicate anions that we've explored, each compound comes out with a net charge of +3 and +6, respectively, for the three- and six-tetrahedra rings. These charges are notable in the formula by notation such as [Si3O9]^3- and [Si6O18]^6-, indicating their ability to bond with other positively charged ions in forming complex minerals.