Question

What is the empirical formula of a potassium silicate in which the silicate tetrahedra share (a) two \(\mathrm{O}\) atoms and form a chain or (b) three \(\mathrm{O}\) atoms and form a sheet? In each case, there are single negative charges on the unshared \(\mathrm{O}\) atoms.

Short answer

The empirical formula for the potassium silicate where tetrahedra share two O atoms forming a chain is K2SiO3, and where they share three O atoms forming a sheet is KSi2O5.

Step-by-step solution

Determine the empirical formula for the chain structure

For a chain structure where two oxygen atoms are shared, each silicate tetrahedron (SiO4) will share two oxygen atoms with its neighbors, effectively contributing two oxygens to the structure. Since there are four oxygen atoms in the SiO4 unit, two are shared and two are unshared. Each unshared oxygen carries a single negative charge. As a result, one silicon atom contributes two negative charges which requires two potassium (K) atoms to balance the charge, leading to an empirical formulaof K2SiO3.

Determine the empirical formula for the sheet structure

For a sheet structure where three oxygen atoms are shared, each silicate tetrahedron (SiO4) will share three oxygen atoms with its neighbors, effectively contributing one and a half (1.5) oxygens to the structure. Since there is normally four oxygen atoms in the SiO4 unit, three are shared (1.5 contributed to the formula) and one is unshared and carries a single negative charge. Therefore, one silicon atom contributes one negative charge which requires one potassium (K) atom to balance the charge, leading to an empirical formula of KSi2O5.

Key concepts

Silicate Tetrahedra

Silicate tetrahedra are the fundamental building blocks of a variety of silicate minerals which form the majority of the Earth's crust. Each tetrahedron consists of a central silicon atom covalently bonded to four oxygen atoms, effectively forming a three-dimensional shape resembling a pyramid with a triangular base. This structure can be denoted as SiO₄ because it consists of one silicon (Si) and four oxygen (O) atoms.

In different silicate minerals, these tetrahedra can be arranged in diverse ways, leading to variations in mineral properties and compositions. Some of the arrangements include isolated tetrahedra, chains, sheets, and frameworks. In our textbook example, the tetrahedra share oxygen atoms to form either chains or sheets. When they share two oxygens, forming a chain structure, or three oxygens, constructing a sheet, the way they bond significantly affects the resulting empirical formula of the silicate mineral.

Potassium Silicate

Potassium silicate is an inorganic compound composed of potassium, silicon, and oxygen. In our exercise, we're examining different empirical formulas of potassium silicate that arise from the way silicate tetrahedra share oxygen atoms. In chemical terms, an empirical formula represents the simplest whole-number ratio of the elements in a compound.

In the case of a chain structure, where each silicate tetrahedron shares two oxygen atoms with its neighbors, the resulting empirical formula is K₂SiO₃. For the sheet structure, with each tetrahedron sharing three oxygen atoms, the empirical formula becomes KSi₂O₅. The difference in sharing oxygen atoms directly influences the number of potassium ions required to maintain electrical neutrality in the compound. Potassium balances the charge because each unshared oxygen atom has a single negative charge. Understanding the correlation between the structure of silicate tetrahedra and the potassium ions needed offers students a concrete example of how chemical structures determine chemical formulas.

Chemical Principles

The chemical principles underlying the determination of empirical formulas are based on the law of conservation of mass and the law of definite proportions. Each element in a chemical compound is present in a certain definite proportion by mass, and during chemical reactions, the total mass of the products equals the total mass of the reactants.

To compute an empirical formula, one must account for the ratios in which different atoms combine and the charges of ions in ionic compounds. For instance, in the potassium silicate example, the SiO₄ tetrahedra share oxygen atoms, altering the number of atoms contributed to the overall structure. This sharing of oxygen atoms affects the charge balance, which leads to variation in the potassium to silicon ratio. By applying these chemical principles, students can make sense of the relationship between the structure of silicate compounds and their empirical formulas, an essential skill in the study of chemistry.