Question

Assign oxidation numbers to each element in the following ions: (a) \(\mathrm{ClO}_{3}\) (b) \(\mathrm{SO}_{3}^{2-}\) (c) \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) (d) \(\mathrm{NO}_{2}^{-}\) (e) \(\mathrm{BrO}^{-}\) (f) \(\mathrm{AsO}_{4}{ }^{3-}\)

Short answer

(a) +5, (b) +4, (c) +3, (d) +3, (e) +1, (f) +5.

Step-by-step solution

Understand the Rules for Assigning Oxidation Numbers

1. The oxidation number of any free element is zero. 2. The oxidation number of a monoatomic ion is equal to its charge. 3. Oxygen usually has an oxidation number of -2. 4. Hydrogen usually has an oxidation number of +1. 5. The sum of oxidation numbers in a compound must equal the overall charge of the compound.

Assign Oxidation Numbers in \(\mathrm{ClO}_3^-\)

- Let \(x\) be the oxidation number of \(\mathrm{Cl}\).- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -1. Hence, the equation is: \[ x + 3(-2) = -1 \]- Simplifying gives: \[ x - 6 = -1 \]- Solving for \(x\): \[ x = +5 \]- Therefore, \(\mathrm{Cl}\) has an oxidation number of +5.

Assign Oxidation Numbers in \(\mathrm{SO}_3^{2-}\)

- Let \(x\) be the oxidation number of \(\mathrm{S}\).- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -2. Hence, the equation is: \[ x + 3(-2) = -2 \]- Simplifying gives: \[ x - 6 = -2 \]- Solving for \(x\): \[ x = +4 \]- Therefore, \(\mathrm{S}\) has an oxidation number of +4.

Assign Oxidation Numbers in \(\mathrm{C}_2\mathrm{O}_4^{2-}\)

- Let \(x\) be the oxidation number of \(\mathrm{C}\). Note that there are two carbon atoms.- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -2. Hence, the equation is: \[ 2x + 4(-2) = -2 \]- Simplifying gives: \[ 2x - 8 = -2 \]- Solving for \(x\): \[ 2x = 6 \ x = +3 \]- Therefore, \(\mathrm{C}\) has an oxidation number of +3.

Assign Oxidation Numbers in \(\mathrm{NO}_2^-\)

- Let \(x\) be the oxidation number of \(\mathrm{N}\).- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -1. Hence, the equation is: \[ x + 2(-2) = -1 \]- Simplifying gives: \[ x - 4 = -1 \]- Solving for \(x\): \[ x = +3 \]- Therefore, \(\mathrm{N}\) has an oxidation number of +3.

Assign Oxidation Numbers in \(\mathrm{BrO}^-\)

- Let \(x\) be the oxidation number of \(\mathrm{Br}\).- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -1. Hence, the equation is: \[ x + (-2) = -1 \]- Simplifying gives: \[ x - 2 = -1 \]- Solving for \(x\): \[ x = +1 \]- Therefore, \(\mathrm{Br}\) has an oxidation number of +1.

Assign Oxidation Numbers in \(\mathrm{AsO}_4^{3-}\)

- Let \(x\) be the oxidation number of \(\mathrm{As}\).- Since \(\mathrm{O}\) is oxygen, it has an oxidation number of -2.- The charge of the ion is -3. Hence, the equation is: \[ x + 4(-2) = -3 \]- Simplifying gives: \[ x - 8 = -3 \]- Solving for \(x\): \[ x = +5 \]- Therefore, \(\mathrm{As}\) has an oxidation number of +5.

Key concepts

Assigning Oxidation Numbers

Assigning oxidation numbers is a fundamental task in chemistry, particularly when analyzing redox reactions. An oxidation number is a theoretical charge that an atom would have if all bonds to atoms of different elements were fully ionic.
These numbers help us keep track of how electrons are shared. They are not actual charges, but rather a tool for electron bookkeeping. To assign oxidation numbers correctly:

• Identify the compound or ion you are working with.
• Apply the rules for assigning oxidation numbers systematically.
• Use the known oxidation numbers of other elements in the compound to calculate the unknown.

Understanding how to assign oxidation numbers accurately allows chemists to predict the course of reactions and identify which elements are being oxidized or reduced.

Rules for Oxidation Numbers

The assignment of oxidation numbers follows a systematic set of rules that help maintain consistency. Here are the most important rules to remember:

• Any free element, meaning it is not combined with different elements, has an oxidation number of zero. For example, \( ext{O}_2\) or \( ext{N}_2\).
• A monoatomic ion, one that is composed only of a single atom, will have an oxidation number equal to its ionic charge. For instance, the oxidation number of Cl in \( ext{Cl}^-\) is -1.
• Oxygen in most compounds has an oxidation number of -2. Exceptions exist, such as when it is part of peroxides.
• Hydrogen usually has an oxidation number of +1 when bonded to non-metals, but it can be -1 in metal hydrides.
• The sum of the oxidation numbers for a neutral compound must be zero, while it should equal the charge for a polyatomic ion.

Applying these rules assures you can systematically assign the right oxidation numbers.

Oxidation States

Oxidation states provide insight into the electron distribution in molecules and ions. The concept helps to identify which atoms gain or lose electrons during chemical reactions. Understanding oxidation states is crucial for:

• Determining if a redox reaction is occurring.
• Predicting products and balancing redox reaction equations.
• Identifying oxidizing and reducing agents in a given reaction.

Oxidation states are essentially the bookkeeper's tools in chemistry. It allows chemists to visualize and quantify the shift in electrons that occur in reactions, providing a way to predict and explain reaction mechanisms.

Chemical Ion Analysis

Chemical ion analysis involves studying the composition and behavior of ions in chemical reactions. It often means determining the oxidation states, among other properties, which plays a crucial role in many processes such as:

• Environmental testing to determine pollutant levels.
• Quality control in manufacturing chemicals and pharmaceuticals.
• Research in developing new chemical compounds and reactions.

By understanding the oxidation numbers of ions, chemists can infer chemical properties, behavior, and potential reaction pathways. This analysis is vital for designing experiments and understanding complex biochemical and industrial processes.