Question

A student wrote the formula for an ionic compound of titanium as \(\mathrm{Ti}_{2} \mathrm{O}_{4}\). What is wrong with this formula? What should the formula be?

Short answer

The original formula Ti2O4 is incorrect because it doesn't reflect the simplest ratio of ions. The correct formula should be TiO2, indicating one titanium ion for every two oxygen ions.

Step-by-step solution

- Identify the Ions and Their Charges

The first step is to identify the ions that make up the compound and their respective charges. Titanium typically has a charge of +4 (as it is in the +4 oxidation state in TiO2), and oxygen has a charge of -2.

- Determine the Correct Ratio of Ions

To create a neutral compound, the total charge from the positively-charged titanium ions must balance the total charge from the negatively-charged oxygen ions. The simplest ratio of Ti to O that accomplishes this is 1 Ti to 2 O.

- Write the Correct Formula

Using the simplest whole number ratio, the correct chemical formula for titanium oxide is TiO2. This reflects a single titanium ion, Ti4+, for every two oxygen ions, O2-.

Key concepts

Ionic Compound Nomenclature

Understanding the nomenclature of ionic compounds is essential for clear communication in chemistry. It involves naming compounds based on the ions that make them up. The positive ion, or cation, is always named first, followed by the negative ion, the anion. In cases where the metal cation can have different possible charges — that is, it is a transition metal like titanium — the specific charge is indicated in parentheses using Roman numerals immediately following the cation's name.
For example, in the given exercise solution, titanium has a +4 charge, so the correct name for TiO₂ would be titanium(IV) oxide. This distinguishes it from other potential compounds of titanium and oxygen that may have different oxidation states of titanium. Ionic compound names do not indicate the number of ions in the formula; instead, they simply provide information about which ions are present and their oxidation states if multiple oxidation states are possible.
An effective strategy to ensure proper nomenclature is to become familiar with the common charges of ions and to always check if the metal has more than one possible charge. Using the stock system of nomenclature can help in accurately naming compounds with transition metals.

Oxidation States

Oxidation states, also known as oxidation numbers, are used to describe the degree of oxidation of an atom in a chemical compound. They provide insight into the electronic structure of the compound and are essential for balancing chemical equations. The oxidation state is represented as a number, which can be positive, negative, or zero, and it indicates the hypothetical charge an atom would have if the compound was composed entirely of ions.
In ionic compounds, the oxidation state of an element is simply the charge on its ion. For instance, titanium in TiO₂ has an oxidation state of +4, and oxygen has an oxidation state of -2. When determining the correct formula for an ionic compound, the total sum of the oxidation states must equal zero, as ionic compounds are electrically neutral. This principle was used in step 1 and step 2 of the original exercise to identify that the student’s formula Ti₂O₄ did not correctly represent the charges of titanium and oxygen, leading to the revised and correct formula, TiO₂.

Chemical Formula Balancing

Balancing the chemical formula of an ionic compound is a methodical process of ensuring that the charges on the ions sum up to zero, which indicates a neutral compound. In the exercise, the student initially wrote the formula Ti₂O₄, which did not reflect the correct charge balance between titanium and oxygen ions. To correct this, one must apply the rule that the total positive charge from the cations must equal the total negative charge from the anions.

Simple Ratio Calculation

To balance the formula, start by writing the charge of each ion above its symbol. Then, find the simplest whole number ratio of ions that balances these charges, similar to step 2 in the provided solution. For TiO₂, a single titanium ion with a charge of +4 is balanced by two oxygen ions each with a charge of -2 (+[Ti⁴⁺] and 2[O^2-]).

Checking the Formula

Finally, to check if the formula is balanced, multiply the subscripts (the small numbers after each element) by the ions' charges and sum them. If the sum is zero, the formula is correctly balanced. Remember, the formula should be in the most reduced form, meaning the subscripts should be the smallest possible whole numbers that maintain the charge balance, which is also demonstrated in step 3 of the solution. This concept is vital in all areas of chemistry, as it ensures the correct stoichiometry in reactions.