Question

Give the oxidation numbers for the underlined atoms in the following molecules and ions: (a) \(\mathrm{Mg}_{3} \mathrm{~N}_{2},\) (b) \(\mathrm{Cs} \underline{\mathrm{O}}_{2},\) (c) \(\mathrm{Ca} \underline{\mathrm{C}}_{2}\) (d) \(\mathrm{CO}_{3}^{2-}\), (e) \(\underline{\mathrm{C}}_{2} \mathrm{O}_{4}^{2-}\) (f) \(\mathrm{ZnO}_{2}^{2-},(\mathrm{g}) \mathrm{Na} \underline{\mathrm{B}} \mathrm{H}_{4}\) (h) \(\underline{\mathrm{W}} \mathrm{O}_{4}^{2-}\)

Short answer

(b) O: -1/2, (c) C: -1, (e) C: +3, (g) B: -3, (h) W: +6.

Step-by-step solution

Oxidation state of O in \( \mathrm{Cs} \underline{\mathrm{O}}_{2} \)

In CsO\(_2\), oxygen exists in the form of superoxide \((\mathrm{O}_{2}^{-})\). Each oxygen generally has an oxidation state of -1/2 in superoxides. Since we want the oxidation state of the O atom, this is -1/2.

Oxidation state of C in \( \mathrm{Ca} \underline{\mathrm{C}}_{2} \)

In CaC\(_2\), carbon is in the acetylide ion \((\mathrm{C}_{2}^{2-})\). Each carbon in an acetylide ion has an oxidation state of -1.

Oxidation state of C in \( \underline{\mathrm{C}}_{2} \mathrm{O}_{4}^{2-} \)

In \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \) (oxalate ion), let the oxidation state of C be \( x \). The equation is \( 2x + 4(-2) = -2 \). Solving gives \( 2x - 8 = -2 \), or \( 2x = 6 \). So, \( x = +3 \). Each carbon is +3.

Oxidation state of B in \( \mathrm{Na} \underline{\mathrm{B}} \mathrm{H}_{4} \)

In NaBH\(_4\), boron typically has a -3 oxidation state as the complex is considered to be \( \mathrm{[BH}_{4}]^{-} \), due to the presence of an additional sodium cation maintaining charge neutrality.

Oxidation state of W in \( \underline{\mathrm{W}} \mathrm{O}_{4}^{2-} \)

In \( \mathrm{WO}_{4}^{2-} \), if we let the oxidation state of W be \( x \), then the equation is \( x + 4(-2) = -2 \). Solving gives \( x - 8 = -2 \) or \( x = +6 \). Hence, the oxidation state of tungsten (W) is +6.

Key concepts

Superoxide Ion

In chemistry, the superoxide ion is a fascinating species due to its unique structure and oxidation state. Composed of dioxygen carrying a single negative charge, \(\mathrm{O}_2^{-}\), superoxides are known for their electronic configuration which results from unpaired electrons.
In superoxides, the oxygen atom exhibits an unusual oxidation number of -1/2. This is because two oxygen atoms share a total oxidation charge of -1 in the superoxide ion. Practically, this shared charge divides evenly between the two oxygen atoms. To appreciate the role of superoxides in chemical reactions, it's vital to consider their strong oxidative nature. They are often found in various biochemical processes and industrial applications.
Understanding superoxide ions is particularly important in fields like biochemistry and environmental science, where their reactive properties are both a boon and a concern. Their oxidative reactions can generate energy and cause oxidative stress in biological systems.

Acetylide Ion

The acetylide ion, represented by the formula \(\mathrm{C}_2^{2-}\), is significant in organic and inorganic chemistry. It arises when an alkyne, such as acetylene, loses its proton due to strong base involvement, yielding the acetylide ion. This ion features a carbon-carbon triple bond, which is highly characteristic.
Each carbon atom in the acetylide ion exerts an oxidation state of -1. This comes from the total charge distribution of -2 across the two carbon atoms. Such chemistry is crucial as acetylides form essential intermediates in a wide range of synthetic procedures.
Acetylides are valuable in coupling reactions and are often utilized in the formation of complex molecular structures, particularly in organic syntheses and pharmaceuticals.

Oxalate Ion

The oxalate ion, known by the chemical formula \(\mathrm{C}_2\mathrm{O}_4^{2-}\), plays a pivotal role in various chemical contexts. It's a dicarboxylate ion, derived from oxalic acid by the loss of protons.
The oxidation state of carbon in the oxalate ion is determined by solving the equation \(2x + 4(-2) = -2\). Here, \(x\) represents the oxidation state of carbon, while \(-2\) is the common oxidation state for oxygen. Solving for \(x\) yields a value of +3 per carbon atom.
The oxalate ion is fundamental in coordination chemistry, forming stable chelates with various metal ions. It's evident in both biological systems and industrial applications, notably in the realm of metal extraction and processing. Furthermore, its study is essential in understanding redox reactions and electron transfer processes.

Acid-Base Chemistry

Understanding acid-base chemistry provides a foundation for grasping the broader chemical interactions that occur in different environments. An acid, according to the Brønsted-Lowry definition, donates a proton (H⁺), while a base accepts it.
Acetylide ions, for instance, form by deprotonating terminal alkynes in the presence of strong bases. This classic demonstration of acid-base interaction showcases how base strength influences the dislodgement of protons in less acidic hydrogen environments like alkynes.
With acids and bases also acting as catalysts or reactants in a myriad of industrial processes, comprehending their role is key to chemical engineering and synthesis. Studying these concepts allows for the creation of better materials, processes, and even the development of new reactions.

Redox Reactions

Redox reactions are chemical exchanges involving the transfer of electrons between species, thereby changing their oxidation states. Such reactions are foundational in disciplines like biochemistry, electrochemistry, and metallurgy.
In redox reactions, oxidizing agents accept electrons and become reduced, while reducing agents lose electrons and become oxidized. This electron exchange is pivotal in generating energy, especially in biological breathing cycles and in power generation through batteries.
A deep appreciation of redox reactions unveils the intricate balance of electron transfer in chemical systems, enabling scientists to harness these interactions for innovative applications. From extracting metals from ores to producing chemical energy, redox reactions are integral to numerous technological advancements.