Q. We compute \(n^2 + 3h^2 \to 2nh^3\).

We are given the chemical reaction:

Unbalanced equation:

\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]

We must determine whether this equation is balanced, and (if needed) balance it.

## Step 1: Interpret the reactants and products

The reactants are:

• \(\text{N}_2\): nitrogen molecules
• \(3\text{H}_2\): three hydrogen molecules worth of hydrogen

The product is:

• \(2\text{NH}_3\): two ammonia molecules

## Step 2: Count nitrogen atoms

On the left (reactant side):

• \(\text{N}_2\) contains 2 nitrogen atoms

So total nitrogen on the left is:

\[ 2 \]

On the right (product side):

• \(\text{NH}_3\) contains 1 nitrogen atom per molecule
• There are \(2\text{NH}_3\) molecules, so total nitrogen is \(2 \times 1 = 2\)

So nitrogen on the right is:

\[ 2 \]

✅ Nitrogen atoms balance.

## Step 3: Count hydrogen atoms

On the left (reactant side):

• \(\text{H}_2\) contains 2 hydrogen atoms per molecule
• There are \(3\text{H}_2\) molecules, so total hydrogen is \(3 \times 2 = 6\)

So total hydrogen on the left is:

\[ 6 \]

On the right (product side):

• \(\text{NH}_3\) contains 3 hydrogen atoms per molecule
• There are \(2\text{NH}_3\) molecules, so total hydrogen is \(2 \times 3 = 6\)

So hydrogen on the right is:

\[ 6 \]

✅ Hydrogen atoms balance.

## Step 4: Conclude whether the equation is balanced

Since both nitrogen and hydrogen atoms match on both sides, the given equation is already balanced.

## Final balanced equation

\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]