Problem 20 - Chemistry Principles and Practice

Question

Assign the oxidation numbers of all atoms in the following species. (a) \(\mathrm{NO}\) (b) \(\mathrm{BO}_{2}^{-}\) (c) \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{OH}\)

Step-by-Step Solution

Answer

(a) N: +2, O: -2; (b) B: +3, O: -2; (c) Cr: +3, N: +5, O: -2; (d) C: -2, H: +1, O: -2.

Step 1: Assigning Oxidation Numbers for NO

In the molecule \(\mathrm{NO}\), nitrogen and oxygen are bonded. Oxygen has a common oxidation number of \(-2\). Let the oxidation number of nitrogen be \(x\). The sum of oxidation numbers must equal 0 for neutral molecules. Hence, the equation is: \(x + (-2) = 0\). Solving gives \(x = +2\). Thus, nitrogen has oxidation number \(+2\) and oxygen has \(-2\).

Step 2: Assigning Oxidation Numbers for BO₂⁻

In the ion \(\mathrm{BO}_{2}^{-}\), we know there are two oxygens with oxidation numbers of \(-2\). Let the oxidation number of boron be \(x\). The sum of oxidation numbers should equal \(-1\), as indicated by the negative charge on the ion: \(x + 2(-2) = -1\). Solving gives \(x = +3\). Therefore, boron has an oxidation number of \(+3\) and each oxygen has \(-2\).

Step 3: Assigning Oxidation Numbers for Cr(NO₃)₃

In \(\mathrm{Cr(NO}_{3})_{3}\), start by analyzing the \(\mathrm{NO}_{3}^{-}\) ion. Each oxygen has \(-2\), and the nitrogen's oxidation number \(x\) must solve \(x + 3(-2) = -1\), yielding nitrogen’s oxidation number as \(+5\). The chromium oxidation \(y\) in the neutral complex must satisfy \(y + 3(-1) = 0\) because each \(\mathrm{NO}_{3}^{-}\) contributes \(-1\) charge. Thus, \(y = +3\). Chromium is \(+3\), nitrogen is \(+5\), and oxygen is \(-2\).

Step 4: Assigning Oxidation Numbers for CH₃OH

In \(\mathrm{CH}_{3}\mathrm{OH}\), carbon and hydrogen are bonded. Here, hydrogen has a \(+1\) oxidation number and oxygen is \(-2\). Let carbon's oxidation number be \(x\). The molecule is neutral, so \(x + 3(+1) + (-2) + (+1) = 0\). Solving yields \(x = -2\). Therefore, carbon is \(-2\), each hydrogen \(+1\), and oxygen \(-2\).

Key Concepts

Chemical Bonding

Chemical bonding is the process by which atoms combine to form molecules. These interactions are driven by the need to attain the stable electronic configuration of noble gases, often by sharing or transferring electrons. This can happen through different types of bonds:

• Ionic Bonds: This involves the complete transfer of electrons from one atom to another, usually between metals and non-metals. For example, in \[\text{NaCl}\], sodium donates an electron to chlorine.
• Covalent Bonds: Atoms share pairs of electrons to achieve stability. An example is \[\text{H}_2O\], where oxygen shares electrons with hydrogen atoms.
• Metallic Bonds: Electrons are free to move around, creating strong bonds between metal atoms. This type is common in metallic structures.

The type of bond affects the properties of the compound, such as melting point, electrical conductivity, and solubility. Understanding these bonds gives insights into the chemical behavior and reactivity of different species.

Oxidation State

Oxidation state, or oxidation number, is a concept that helps in understanding the electron transfer in chemical reactions. It describes the degree of oxidation of an atom in a chemical compound. To assign oxidation numbers, certain rules are followed:

• For an atom in its elemental form, the oxidation state is 0. For example, \[\text{O}_2\].
• In a neutral molecule, the sum of all oxidation numbers is 0; in ions, it equals the ion charge.
• Oxygen typically has an oxidation number of \[-2\], except in peroxides where it's \[-1\].
• Hydrogen generally is \[+1\], except when bonded to metals in hydrides, where it becomes \[-1\].

Using these rules, we can determine oxidation numbers easily, aiding in the analysis of chemical reactions.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, commonly referred to as redox reactions, are reactions where the electron transfer occurs. They involve an oxidizing agent and a reducing agent:

• Oxidization: Loss of electrons by a molecule, atom, or ion.\[\text{Example: Fe} \rightarrow \text{Fe}^{2+} + 2\text{e}^{-}\]
• Reduction: Gain of electrons.\[\text{Example: O}_2 + 4\text{e}^{-} \rightarrow 2\text{O}^{2-}\]
• The oxidizing agent is reduced by gaining electrons, while the reducing agent is oxidized, losing electrons.

Redox reactions are vital in energy production (e.g., respiration and combustion) and industrial processes like metal extraction.

Chemical Species Analysis

Chemical species analysis involves studying different ions, molecules, or atoms present in a sample. It helps in identifying the composition of a compound and understanding its chemical nature. Different methods can be employed:

• Spectroscopy: By studying the interaction of light with matter, we can infer the structure and composition.
• Titration: This quantitative method determines concentration through a reaction with a known reagent.
• Chromatography: Used for separating mixtures into their individual components.

Through chemical species analysis, we can assess the purity of compounds, determine metal ion concentration in solutions, and detect environmental pollutants. It supports accurate chemical reaction modeling and prediction.