Question

Predict the chemical formula for each of the following binary ionic compounds given the formula of titanium oxide, \(\mathrm{TiO}_{2}\) : (a) zirconium oxide (b) titanium sulfide

Short answer

(a) \(\mathrm{ZrO}_2\); (b) \(\mathrm{TiS}_2\).

Step-by-step solution

Understanding the Given Formula

We start by understanding the chemical formula of titanium oxide, which is \(\mathrm{TiO}_{2}\). This implies that one titanium atom combines with two oxygen atoms to form titanium oxide.

Identifying Ionic Charges for Zirconium Oxide

Zirconium (Zr) is in the same group as titanium (Ti) in the periodic table, and usually forms a similar charge. Since titanium is typically in a +4 oxidation state in \(\mathrm{TiO}_2\), zirconium will generally also form a +4 cation, denoted as \(\mathrm{Zr}^{4+}\). Oxygen, being in group 16, typically forms \(\mathrm{O}^{2-}\) ions.

Formulating Zirconium Oxide

To balance the charges, we need two oxygen anions (each \(\mathrm{O}^{2-}\)) to balance one zirconium cation (\(\mathrm{Zr}^{4+}\)), leading to the formula \(\mathrm{ZrO}_2\).

Identifying Ionic Charges for Titanium Sulfide

In titanium sulfide, titanium (Ti) also typically forms a +4 cation (\(\mathrm{Ti}^{4+}\)), while sulfur, similar to oxygen, is in group 16 and typically forms \(\mathrm{S}^{2-}\) ions.

Formulating Titanium Sulfide

To balance the charges in titanium sulfide, similar to the process with zirconium oxide, two sulfur anions (each \(\mathrm{S}^{2-}\)) are required to balance one titanium cation (\(\mathrm{Ti}^{4+}\)), resulting in the formula \(\mathrm{TiS}_2\).

Key concepts

Understanding Chemical Formulas

Chemical formulas represent a shorthand way to denote the composition of chemical compounds. These formulas show the elements involved and the number of atoms of each element in a single molecule of the compound. For example, the formula \( \mathrm{TiO}_2 \) for titanium oxide indicates that each molecule consists of one titanium atom and two oxygen atoms.
This is crucial in understanding how compounds combine and react, which is particularly important for binary ionic compounds. Binary compounds, like titanium oxide, contain two different elements. The arrangement of these elements is determined by their ionic charges. Understanding the chemical formula gives us insight into the ratio in which elements combine to form a stable compound.

Ionic Charges Explained

Ionic charges play a key role in the formation of binary ionic compounds. Each element has a typical charge, or oxidation state, that it adopts when it forms ions. These charges are crucial for determining how different elements combine to form compounds. In ionic compounds, metals typically form positive ions, known as cations, while non-metals form negative ions, called anions.
Taking titanium oxide as an example, titanium usually forms a \( \mathrm{Ti}^{4+} \) cation, while oxygen becomes \( \mathrm{O}^{2-} \). These charges dictate how many ions of each element are needed to create a neutral compound. In the case of \( \mathrm{TiO}_2 \), it takes two oxygen ions to balance the charge of one titanium ion.

Exploring Periodic Table Groups

The periodic table is an invaluable tool for understanding the properties of elements, including their ionic charges. Elements are organized into groups or columns, with all members of a group typically exhibiting similar properties. Titanium and zirconium, for example, are in the same group. This means they often form ions with the same charge, in this case, a +4 oxidation state.
The periodic table helps predict the behavior of elements in chemical reactions. Oxygen and sulfur are in group 16, meaning they often form \( 2- \) charges. This is why these elements can substitute for each other in forming compounds, as seen with titanium oxide and titanium sulfide.

Understanding Oxidation State

The oxidation state, often synonymous with the oxidation number, indicates the degree of oxidation or the number of electrons an atom gains or loses when forming a compound. It's essential to know the oxidation state to predict the chemical formulas of compounds.
For instance, titanium in \( \mathrm{TiO}_2 \) is commonly in a +4 oxidation state, while oxygen is typically in a -2 state. When these states combine, they must balance the total charge to zero, resulting in the formation of stable compounds with specific formulas.
This understanding helps in predicting new compounds, such as inferring that zirconium in zirconium oxide will also prefer a +4 oxidation state. Understanding oxidation states is fundamental for predicting not just stability but also the reactivity of compounds.