Problem 73 - Chemistry Matter and Change

Question

Determine the oxidation number of the boldface element in each of the following. a. \(\mathrm{OF}_{2}\) b. \(\mathrm{UO}_{2}^{2+}\) c. \(\mathrm{RuO}_{4}\) d. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\)

Step-by-Step Solution

Answer

a. Oxygen: +2; b. Uranium: +6; c. Ruthenium: +8; d. Iron: +3.

Step 1: Determine Oxidation Number for Oxygen in OF2

In compounds, oxygen typically has an oxidation state of -2. However, in fluorine compounds like \(OF_2\), oxygen takes a positive oxidation state, since fluorine is more electronegative. Fluorine always has an oxidation state of -1. In \(OF_2\), the compound must be balanced at 0. Therefore, if each fluorine is -1, two fluorines contribute -2 overall to the compound. Oxygen must therefore be +2 to balance this out. Thus, the oxidation number of oxygen in \(\mathrm{OF}_{2}\) is +2.

Step 2: Calculate Uranium's Oxidation Number in UO2^2+

Assuming the typical oxidation number of oxygen as -2, and given \( UO_2^{2+} \) indicates the complex as a whole has a charge of +2, we first add the oxidation contributions of the two oxygen atoms, which total -4. Using the overall charge, we solve for uranium: \( x + 2(-2) = +2 \rightarrow x - 4 = +2 \rightarrow x = +6 \). Therefore, uranium in \(UO_2^{2+} \) has an oxidation number of +6.

Step 3: Determine Oxidation Number for Ruthenium in RuO4

\(RuO_4\) includes four oxygen atoms, each with a conventional oxidation number of -2, amounting to -8 in total. As \( Ru's\) oxide has to balance this to zero: \( x + 4(-2) = 0 \rightarrow x - 8 = 0 \rightarrow x = +8 \). Thus, ruthenium in \(RuO_4\) has an oxidation number of +8.

Step 4: Determine Iron's Oxidation Number in Fe2O3

Oxygen, with its usual oxidation number of -2, in \( Fe_2O_3\) contributes -6 in total. With iron's contribution, the equation is \(2x + 3(-2) = 0\). Solving \(2x - 6 = 0\rightarrow 2x = 6\rightarrow x = +3\), indicates each iron atom has an oxidation number of +3 in \( Fe_2O_3\).

Key Concepts

Understanding Oxidation States

Oxidation states, also known as oxidation numbers, are incredibly important in understanding chemical reactions, especially those involving electron transfer. They serve as a bookkeeping tool that helps chemists track electron movement. Here are the crucial points about oxidation states:

• Oxidation states indicate the charge that an atom would have if all bonds were ionic.
• They are helpful in identifying which atoms have gained or lost electrons in a reaction.
• Usually, oxidation states are whole numbers, but fractions can appear in specific conditions.

Let's consider oxygen, which typically has an oxidation state of -2. This is true for most compounds, except in cases like peroxides or when bonded to more electronegative elements like fluorine. This exception is seen in the compound \(OF_2\), where oxygen adopts a +2 oxidation state because fluorine, the most electronegative element, dominates in electron attraction. By keeping track of these states, chemists can deduce the number of electrons involved in bond-making and breaking processes, a crucial aspect for understanding complex reactions.

Chemistry Education and Oxidation Numbers

Learning about oxidation numbers is an integral part of chemistry education. It might seem a bit challenging at first due to the different rules and exceptions that apply. However, understanding oxidation numbers is fundamental to mastering topics such as redox reactions and balancing chemical equations. Here's why learning oxidation numbers is beneficial:

• They simplify the classification of reactions, particularly redox reactions, by indicating which elements undergo oxidation or reduction.
• They help predict the outcomes of chemical reactions and the stability of compounds.
• They form a foundation for learning about electron configurations and bonding models.

Educational approaches often include exercises with multiple choice questions, lab experiments, and computational simulations to help students grasp these concepts. By moving beyond memorization and understanding the 'why' behind oxidation state changes, students can appreciate the underlying principles that drive chemical behavior.

The Role of Redox Reactions

Redox reactions are a fascinating category of chemical reactions involving the transfer of electrons between two species. The term "redox" is a combination of the words "reduction" (gain of electrons) and "oxidation" (loss of electrons).Understanding these reactions involves several key points:

• An element is oxidized in a redox reaction if its oxidation number increases.
• Conversely, an element is reduced if its oxidation number decreases.
• The concept of oxidation states helps in writing balanced redox equations, ensuring that the number of electrons lost equals the number of electrons gained.

In redox reactions, substances that provide electrons are known as reducing agents, while those that accept electrons are called oxidizing agents. For example, in the compound \(Fe_2O_3\), each iron atom is oxidized during the process when it goes from an oxidation state of +3 to 0 when forming pure iron, while oxygen is reduced from -2 to 0.Redox reactions are pivotal not just in industrial processes, such as metal extraction and combustion, but also in biological systems, where they are crucial for processes like cellular respiration.