Problem 50 - Chemistry The Central Science In Si Units

Question

Write the chemical formula for each of the following compounds, and indicate the oxidation state of nitrogen in each: (a) dinitrogen trioxide, (b) dinitrogen pentoxide, (c) hydrogen cyanide, \((\mathbf{d})\) ammonium nitrate, (e) iron(III) nitrite, \((\) f) nitrogen trichloride.

Step-by-Step Solution

Answer

Formulas: \(\text{N}_2\text{O}_3, \text{N}_2\text{O}_5, \text{HCN}, \text{NH}_4\text{NO}_3, \text{Fe(NO}_2)_3, \text{NCl}_3\) with N oxidation states: \(+3, +5, -3, -3/+5, +3, +3\).

Step 1: Determine the chemical formula for dinitrogen trioxide

Dinitrogen trioxide consists of two nitrogen atoms and three oxygen atoms. Its chemical formula is written as \( \text{N}_2\text{O}_3 \).

Step 2: Find the oxidation state of nitrogen in dinitrogen trioxide

In dinitrogen trioxide, each oxygen has an oxidation state of \(-2\). For three oxygens, this is \(-6\). There are two nitrogen atoms contributing to a total oxidation state of \(+6\) to balance the \(-6\) of the oxygens. Thus, each nitrogen in \( \text{N}_2\text{O}_3 \) has an oxidation state of \(+3\).

Step 3: Determine the chemical formula for dinitrogen pentoxide

Dinitrogen pentoxide is composed of two nitrogen atoms and five oxygen atoms. Its chemical formula is \( \text{N}_2\text{O}_5 \).

Step 4: Find the oxidation state of nitrogen in dinitrogen pentoxide

In \( \text{N}_2\text{O}_5 \), each oxygen has an oxidation state of \(-2\), totaling \(-10\) for five oxygens. To counter this, the two nitrogen atoms contribute a total of \(+10\), making each nitrogen atom have an oxidation state of \(+5\).

Step 5: Determine the chemical formula for hydrogen cyanide

Hydrogen cyanide is composed of one hydrogen atom, one carbon atom, and one nitrogen atom. The chemical formula is \( \text{HCN} \).

Step 6: Find the oxidation state of nitrogen in hydrogen cyanide

In \( \text{HCN} \), hydrogen has an oxidation state of \(+1\) and carbon \(0\). Therefore, nitrogen must balance this with an oxidation state of \(-3\).

Step 7: Determine the chemical formula for ammonium nitrate

Ammonium nitrate is composed of one ammonium ion \( \text{NH}_4^+ \) and one nitrate ion \( \text{NO}_3^- \). The chemical formula is \( \text{NH}_4\text{NO}_3 \).

Step 8: Find the oxidation state of nitrogen in ammonium nitrate

In \( \text{NH}_4^+ \), hydrogen has an oxidation state of \(+1\), summing to \(+4\); thus, nitrogen is \(-3\). In \( \text{NO}_3^- \), each oxygen is \(-2\) (total \(-6\)), so nitrogen must be \(+5\). Thus, in \( \text{NH}_4\text{NO}_3 \), nitrogen exhibits two oxidation states: \(-3\) and \(+5\).

Step 9: Determine the chemical formula for iron(III) nitrite

Iron(III) nitrite consists of iron with an oxidation state of \(+3\) combined with three nitrite ions \( \text{NO}_2^- \). The formula is \( \text{Fe(NO}_2)_3 \).

Step 10: Find the oxidation state of nitrogen in iron(III) nitrite

In the nitrite ion \( \text{NO}_2^- \), two oxygens total \(-4\), balanced by nitrogen as \(+3\) and \(-1\) net charge. Thus, nitrogen in \( \text{NO}_2^- \) is \(+3\).

Step 11: Determine the chemical formula for nitrogen trichloride

Nitrogen trichloride is composed of one nitrogen and three chlorine atoms. Its chemical formula is \( \text{NCl}_3 \).

Step 12: Find the oxidation state of nitrogen in nitrogen trichloride

In \( \text{NCl}_3 \), each chlorine has a state of \(-1\) (total \(-3\)). Hence, nitrogen is \(+3\).

Key Concepts

Dinitrogen Trioxide

Dinitrogen trioxide is a fascinating compound made up of nitrogen and oxygen. It is composed of 2 nitrogen atoms and 3 oxygen atoms, giving it the chemical formula \( \text{N}_2\text{O}_3 \). Understanding such a compound starts with knowing its structure.
Each molecule of dinitrogen trioxide contains:

• 2 nitrogen atoms
• 3 oxygen atoms

The oxidation state is an important concept here. Oxygen has a typical oxidation state of \(-2\). For three oxygen atoms, this results in a total of \(-6\). To balance this in the compound, the 2 nitrogen atoms must collectively provide a \(+6\) oxidation state, making each nitrogen atom \(+3\).
This careful balancing ensures the molecule is stable and neutral overall.

Chemical Formulas

Chemical formulas like \( \text{N}_2\text{O}_3 \) play a crucial role in chemistry. They represent the types and numbers of atoms in a compound. For instance, the formula \( \text{NH}_4\text{NO}_3 \) for ammonium nitrate shows:

• 1 ammonium ion \( \text{NH}_4^+ \)
• 1 nitrate ion \( \text{NO}_3^- \)

Writing chemical formulas is like writing the blueprint of a molecule.
Formulas not only tell you what's in a molecule but also how elements interact through charges. For ions like \( \text{NO}_2^- \), adjustments are made in the formula to express their net charge.
The structure of these formulas helps chemists quickly understand the composition and predicted behavior of compounds.

Nitrogen Oxidation State

Understanding the oxidation state of nitrogen is key in many chemical reactions. It's a way of indicating how much a specific atom can gain or lose electrons to become stable.
In ammonium nitrate \( \text{NH}_4\text{NO}_3 \), nitrogen exists in two distinct oxidation states:

• \(-3\) in the \( \text{NH}_4^+ \) ion, balancing the \(+4\) from hydrogen.
• \(+5\) in the \( \text{NO}_3^- \) ion, countering the \(-6\) from oxygen atoms.

This dual role is interesting because it highlights nitrogen's versatility. It reflects how the same element can play different roles depending on its surrounding environment in a compound.
Calculating oxidation states involves understanding these gains or losses of electron-like charges to maintain balance in the compound.

Ammonium Nitrate

Ammonium nitrate is widely known for both its uses in fertilizers and its explosive properties. It is composed of two ions: the ammonium ion \( \text{NH}_4^+ \) and the nitrate ion \( \text{NO}_3^- \), resulting in the chemical formula \( \text{NH}_4\text{NO}_3 \).
The nitrogen atoms in ammonium nitrate serve different functions:

• In the ammonium ion, nitrogen has an oxidation state of \(-3\), showing it gains electrons.
• In the nitrate ion, nitrogen has an oxidation state of \(+5\), indicating it loses electrons.

This dual nature allows ammonium nitrate to be a part of significant reactions, providing a great example of nitrogen's adaptability in chemistry.
Such characteristics make ammonium nitrate a compound of great interest in both industrial and environmental chemistry.

Iron(III) Nitrite

Iron(III) nitrite, represented by the formula \( \text{Fe(NO}_2)_3 \), combines iron ions with nitrite ions. In this compound, iron has an oxidation state of \(+3\) and is combined with three nitrite ions, each carrying a \(-1\) charge.
The breakdown is as follows:

• Each nitrite ion \( \text{NO}_2^- \) consists of nitrogen with an oxidation state of \(+3\).
• The compound ensures electrical neutrality by balancing iron's \(+3\) with the cumulative \(-3\) from three nitrite ions.

Understanding these interactions helps students grasp how metals like iron interact with non-metal ions, forming various complex ions and compounds.
Iron(III) nitrite demonstrates how transition metals can exhibit multiple oxidation states, influencing their bonding and properties.