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The \({\text{NO}}_2\) molecule is composed of one nitrogen atom and two oxygen atoms. To determine the oxidation numbers within this molecule, remember that oxygen typically has an oxidation number of \-2\. This is a helpful rule for many compounds containing oxygen. In the case of \({\text{NO}}_2\), assign the oxidation numbers as follows:

• The oxidation number of each oxygen atom is \-2\.
• The oxidation number of nitrogen is unknown, so let's call it \({x}\).

Since \({\text{NO}}_2\) is a neutral molecule, the sum of the oxidation numbers must equal zero:\[ x + 2(-2) = 0 \]This equation simplifies to \({x - 4 = 0}\), which further simplifies to \({x = +4}\).
Thus, within the \({\text{NO}}_2\) molecule:

• The oxidation number of the nitrogen atom is \(+4\).
• The oxidation number of each oxygen atom remains \(-2\).

Understanding how to assign these numbers is crucial as it helps in balancing chemical equations and in understanding redox reactions.

In the case of the \({\text{CrO}}_2^-\) ion, understanding the oxidation states helps in knowing how electrons are distributed. This ion contains one chromium atom and two oxygen atoms.

• Each oxygen atom has an oxidation number of \(-2\), which is common for oxygen.
• The oxidation number of chromium, which we need to find, is represented by \(y\).

Since the net charge of the ion is \-1\, the sum of oxidation numbers must equal \-1\:\[ y + 2(-2) = -1 \]This simplifies to \(y - 4 = -1\), leading to \(y = +3\).
Consequently, for \({\text{CrO}}_2^-\):

• The oxidation number of the chromium atom is \(+3\).
• Each oxygen atom carries the oxidation number \(-2\).

These values indicate how the electron distribution takes place in ions, which is fundamental for understanding reactivity and stability in compounds.

The compound \({\text{Co(NO}}_3)_3\) consists of a cobalt atom surrounded by three nitrate \((\text{NO}_3^-)\) ions. Assigning oxidation numbers in such compounds involves breaking them down into simpler components.First, assign oxidation numbers in the nitrate ion \((\text{NO}_3^-)\) itself:

• Oxygen in nitrate has an oxidation number of \(-2\).
• Let the oxidation number of nitrogen in nitrate be \(z\).

In the nitrate ion, the sum of oxidation numbers equals the ion's charge, \(-1\):\[ z + 3(-2) = -1 \]This gives \(z - 6 = -1\), leading to \(z = +5\).
Therefore, within each \({\text{NO}}_3^-\):

• The oxidation number of nitrogen is \(+5\).
• Each oxygen has \(-2\).

Now, consider the entire \({\text{Co(NO}}_3)_3\) compound:

• Three \({\text{NO}}_3^-\) ions give a total negative charge of \(-3\).
• To balance this, the oxidation number of cobalt must be \(+3\) to provide an overall charge of zero for the molecule.

Thus, for the whole \({\text{Co(NO}}_3)_3\) compound:

• Cobalt has an oxidation number of \(+3\).
• Each nitrogen within nitrate is \(+5\).
• Each oxygen remains \(-2\).

This understanding aids in predicting chemical behavior and in synthesizing compounds.