Problem 64 - General Chemistry: Principles and Modern Applications

Question

Write a formula for (a) an oxide of nitrogen with \(\mathrm{N}\) in the O.S. \(+5 ;\) (b) an oxoacid of nitrogen with \(\mathrm{N}\) in the O.S. \(+3 ;\) (c) an oxide of carbon in which the apparent O.S. of \(C\) is \(+4 / 3 ;\) (d) a sulfur- containing oxoanion in which the apparent O.S. of \(S\) is +2.5 and the ionic charge is \(2-\).

Step-by-Step Solution

Answer

The formula for: (a) an oxide of nitrogen is \(N_2O_5\); (b) an oxoacid of nitrogen is \(HNO_2\); (c) an oxide of carbon is \(C_3O_4\); (d) a sulfur-containing oxoanion is \(H_2S_2O_5^{2-}\).

Step 1: Determining the formula for an oxide of nitrogen

In an oxide of nitrogen where Nitrogen has an oxidation state (O.S) of +5, Nitrogen is bound to Oxygen which typically has an oxidation state of -2. In order for the total compound to be neutral, Nitrogen’s positive charge must be neutralized by Oxygen’s negative charge. Therefore, one Nitrogen atom with a +5 oxidation state will bind with 2.5 or, in whole numbers, 5 Oxygen atoms with a -2 oxidation state each. Therefore, the formula for the oxide will be \(N_2O_5\).

Step 2: Writing formula for an oxoacid of nitrogen

An oxoacid typically contains Hydrogen, Oxygen and another element. The other element in this case is Nitrogen which has an oxidation state of \(+3\), Oxygen has an oxidation state of \(-2\), and Hydrogen has an oxidation state of \(+1\). To keep the total charge neutral, 3 Hydrogen's can neutralize the -3 charge from Oxygen, and one Nitrogen with +3 charge can neutralize the remaining charge. So the formula for the oxoacid of Nitrogen will be \(HNO_2\).

Step 3: Determining the formula for an oxide of Carbon

In this case, Carbon has an oxidation state of \(+4/3\), which implies that to maintain charge balance with Oxygen (-2 oxidation state), three Carbon atoms are required against four Oxygen atoms. Therefore, the formula for the oxide of Carbon will be \(C_3O_4\).

Step 4: Writing the formula for a sulfur-containing oxoanion

In this case, Sulfur has an oxidation state of \(+2.5\) and the ionic charge is \(2-\). Therefore, to maintain the charge balance with Oxygen having an oxidation state of \(-2\), two Sulfur atoms are required against five Oxygen atoms. And, to neutralize the ionic charge, we need two Hydrogen atoms. Therefore, the formula for the sulfur-containing oxoanion will be \(H_2S_2O_5^{-2}\).

Key Concepts

Nitrogen Oxides

Nitrogen oxides are compounds formed by the combination of nitrogen and oxygen. These compounds are important in various chemical processes and have significant environmental impacts. The oxidation state (O.S.) of nitrogen in these oxides can vary, affecting the properties and reactivity of the compound. For example, in the oxide of nitrogen with nitrogen in the oxidation state of +5, such as in the compound \( N_2O_5 \), nitrogen achieves a high oxidation state resulting in the compound being more reactive.

• Nitrogen in Oxides: Different nitrogen oxides have different nitrogen oxidation states, influencing their stability and reactivity.
• Environmental Impact: Some nitrogen oxides contribute to air pollution and the formation of acid rain.
• Chemical Reactions: Nitrogen oxides are involved in important chemical reactions, including those in atmospheric chemistry.

Understanding these properties helps in predicting the behavior of nitrogen oxides in various environments.

Oxoacids

Oxoacids are a specific type of acid that contain oxygen, hydrogen, and another element, usually a non-metal. These acids aren't just important in chemistry, they play a crucial role in biological systems too. An example of a nitrogen-containing oxoacid is nitrous acid (\( HNO_2 \)), where nitrogen is in a +3 oxidation state. This particular oxidation state affects the acid’s strength and reactivity.

• Component Elements: Oxoacids are composed of hydrogen, oxygen, and a central non-metal element.
• Acid Strength: The oxidation state of the central element can influence the strength and reactivity of the acid.
• Applications: Used in chemical reactions, including as intermediates in some organic processes.

By understanding the composition and properties of oxoacids, you can predict their behavior in chemical reactions.

Carbon Oxides

Carbon oxides, primarily carbon monoxide (CO) and carbon dioxide (CO₂), are compounds formed between carbon and oxygen. They have distinct properties and occur naturally in the Earth's atmosphere. However, in the context of molecules like \( C_3O_4 \), where carbon has a fractional oxidation state of +4/3, these oxides take on different forms.

• Oxidation States: The unusual oxidation state of +4/3 indicates a mixed or intermediate composition.
• Structural Variations: Such compounds may have unique structural properties due to the sharing of electrons among carbon and oxygen.
• Relevance: Understanding carbon oxides or derivatives like \( C_3O_4 \) can help in studies involving catalysis and material science.

These derivatives, though less common, highlight the diverse chemistry of carbon and oxygen combinations beyond the more familiar forms.

Sulfur Oxyanions

Sulfur oxyanions are negatively charged ions that consist of sulfur and oxygen atoms. These oxyanions vary based on the oxidation state of sulfur, influencing their charge and resulting structure. For instance, in \( H_2S_2O_5^{2-} \), sulfur adopts an oxidation state of +2.5, which impacts the way sulfur atoms bond with oxygen.

• Oxidation State Impact: The oxidation state influences the stability, solubility, and reactivity of the oxyanion.
• Importance in Chemistry: These anions are often studied due to their presence in diverse chemical reactions and processes, including in industrial settings.
• Applications: Used in the production of chemicals and as intermediates in various chemical processes.

Recognizing the characteristics of sulfur oxyanions aids in predicting their role in chemical equations and environmental interactions.