Animated Solution for Chemistry - p-Block Elements: The oxidation states of nitrogen in $\text{NO}$, ${\text{NO}}_2$, ${\text{N}}_2\text{O}$ and ${\text{NO}}_3^{-}$ are in the order of

Understanding Oxidation States

Before we dive into the math, let's understand what an oxidation state actually represents. Imagine a tug-of-war for electrons between the atoms in a molecule. Because oxygen is highly electronegative (second only to fluorine), it almost always wins this tug-of-war against nitrogen.

In most of its compounds, oxygen pulls two electrons towards itself to complete its octet, effectively taking on an oxidation state of $-2$. Nitrogen, being the less electronegative atom in this pairing, is forced to give up its electron density, taking on a positive oxidation state.

The golden rule for calculating these states is beautifully simple: The sum of the oxidation states of all atoms in a molecule or ion must equal its net charge.

Let's start with the simplest molecule on our list: Nitric Oxide ($\text{NO}$).

This is a neutral molecule, meaning its net charge is zero. Let the oxidation state of nitrogen be $x$. We know oxygen is $-2$. Setting up our equation:

Solving this gives us:

So, in $\text{NO}$, nitrogen has an oxidation state of $+2$.

Next, we look at Nitrogen Dioxide (${\text{NO}}_2$), the reddish-brown gas responsible for the color of smog.

Again, it's a neutral molecule, but this time nitrogen is battling two oxygen atoms. Let's set up the equation:

With twice the oxygen pulling away electron density, nitrogen's oxidation state jumps to $+4$.

Nitrous Oxide (N2O)

Now, let's examine Nitrous Oxide (${\text{N}}_2\text{O}$), commonly known as laughing gas.

Here, the script is flipped. We have two nitrogen atoms sharing the burden of one oxygen atom. Let the oxidation state of each nitrogen be $x$. The equation becomes:

Because the two nitrogen atoms share the electron loss, each one only has an oxidation state of $+1$.

Finally, we tackle the Nitrate ion (${\text{NO}}_3^{-}$).

This is a polyatomic ion with a net charge of $-1$. Nitrogen is surrounded by three highly electronegative oxygen atoms. Let's see how high the oxidation state goes:

Surrounded by three oxygens, nitrogen is stripped of almost all its valence electron density, reaching its maximum possible oxidation state of $+5$.

Establishing the Order

Now that we have calculated the oxidation state of nitrogen in each species, let's line them up:

${\text{NO}}_3^{-}$ : $+5$ ${\text{NO}}_2$ : $+4$ $\text{NO}$ : $+2$ ${\text{N}}_2\text{O}$ : $+1$

Arranging these in decreasing order, we get:

A Quick Pro-Tip: You can often guess the relative oxidation states just by looking at the oxygen-to-nitrogen ratio. The more oxygen atoms attached to a single nitrogen atom, the higher the positive oxidation state of that nitrogen. ${\text{NO}}_3^{-}$ has 3 oxygens per nitrogen, ${\text{NO}}_2$ has 2, $\text{NO}$ has 1, and ${\text{N}}_2\text{O}$ has only 0.5 oxygens per nitrogen. The math perfectly aligns with this intuition!