Question

What is the oxidation number of (a) phosphorus in \(\mathrm{Li}_{7} \mathrm{P}_{3} \mathrm{~S}_{11}\), which forms in some ceramic electrolytes; (b) titanium in \(\mathrm{BaTiO}_{3}\) ?

Short answer

The oxidation number of phosphorus in \(\mathrm{Li}_{7}\mathrm{P}_{3} \mathrm{~S}_{11}\) is +5, and the oxidation number of titanium in \(\mathrm{BaTiO}_{3}\) is +4.

Step-by-step solution

Understanding the Concept of Oxidation Number

The oxidation number of an element in a compound is the charge that atom would have if the compound was composed of ions. It is determined based on certain rules, the most important being that the sum of the oxidation numbers of all atoms in a neutral compound must be zero.

Determining the Oxidation Number of Phosphorus in \(\mathrm{Li}_{7}\mathrm{P}_{3} \mathrm{~S}_{11}\)

We start by assigning known oxidation numbers to each element except for phosphorus. Lithium (Li) has a +1 oxidation number in compounds. Sulfur (S) usually has a -2 oxidation number when it is not in a peroxide or other special compounds. There are 7 lithium atoms and 11 sulfur atoms. Using the formula \(x \times 3 + 7 \times +1 + 11 \times -2 = 0\) we can solve for the oxidation number of phosphorus (P).

Solving for the Oxidation Number of Phosphorus

Substitute the known quantities into the equation and solve for \(x\), the oxidation number of phosphorus: \(x \times 3 + 7 \times +1 + 11 \times -2 = 0 \Rightarrow 3x + 7 - 22 = 0 \Rightarrow 3x - 15 = 0 \Rightarrow 3x = 15 \Rightarrow x = +5\). The oxidation number of phosphorus in \(\mathrm{Li}_{7}\mathrm{P}_{3} \mathrm{~S}_{11}\) is +5.

Identifying the Known Oxidation Numbers in \(\mathrm{BaTiO}_{3}\)

For the compound \(\mathrm{BaTiO}_{3}\), barium (Ba) usually has a +2 oxidation number, and oxygen (O) has a -2 oxidation number.

Calculating the Oxidation Number of Titanium in \(\mathrm{BaTiO}_{3}\)

Since the compound is neutral overall, the oxidation numbers must add up to zero. Let \(y\) represent the oxidation number of titanium (Ti). The equation is: \(+2 + y + 3 \times -2 = 0\). Solve for \(y\): \(2 + y - 6 = 0 \Rightarrow y = 6 - 2 \Rightarrow y = +4\). Therefore, the oxidation number of titanium in \(\mathrm{BaTiO}_{3}\) is +4.

Key concepts

Understanding Chemical Principles

Chemical principles form the foundation for understanding the behavior of elements and compounds. One key principle is the concept of oxidation numbers, which helps us predict how different atoms will combine and interact.

Oxidation numbers are not actual charges but are useful for balancing chemical reactions, especially redox (reduction-oxidation) reactions. They are determined using a set of rules. For instance, the oxidation number of an element in its elemental form is always 0. In compounds, Group 1 metals have an oxidation number of +1, Group 2 metals have +2, and oxygen typically has an oxidation number of -2, except in peroxides.

In the provided exercise, we utilized these principles to determine the oxidation numbers of phosphorus in a lithium phosphorus sulfide compound and titanium in barium titanate. These values give insight into the electron transfer processes within the compounds.

Electron Configuration and Oxidation States

The oxidation state of an element in a compound is closely related to its electron configuration. Electrons are arranged in an atom's orbitals according to the principle of lowest energy, with specific patterns of shells and subshells.

The electron configuration determines how atoms bond with each other. Atoms with fewer electrons than needed to fill their outer shell tend to lose those electrons, adopting a positive oxidation state. Conversely, atoms that are close to filling their outer shell will gain electrons, adopting a negative oxidation state.

For example, in the exercise, lithium, a Group 1 element, has a single electron in its outer shell, which it can easily lose to achieve a noble gas configuration, resulting in a +1 oxidation state. Phosphorus, on the other hand, seeks to complete its outer shell, which leads to a higher positive oxidation state when in combination with lithium and sulfur.

Compound Neutrality in Chemical Reactions

Compound neutrality is the concept that a chemical compound, despite being made up of ions (charged particles), is electrically neutral overall. This principle is epitomized by the rule that the sum of oxidation numbers for all atoms in a neutral molecule must equal zero.

Oxidation numbers provide a bookkeeping system to keep track of electron movements in chemical reactions, ensuring that all charges balance out for neutrality. In the solution, the compound \(\mathrm{BaTiO}_{3}\) maintains neutrality by the oxidation states of barium (+2), titanium (to be determined), and oxygen (-2) summing to zero.

Understanding this principle emphasizes the importance of charge balance in compounds, which is fundamental in predicting the composition of compounds, their formation, and the chemical reactions they undergo.