Questions: An unknown compound has the following chemical formula: Fe(NO3)x where x stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 9.40 mol of nitrogen and 3.1 mol of iron. Write the complete chemical formula for the unknown compound.

An unknown compound has the following chemical formula:
Fe(NO3)x
where x stands for a whole number.
Measurements also show that a certain sample of the unknown compound contains 9.40 mol of nitrogen and 3.1 mol of iron. Write the complete chemical formula for the unknown compound.

Transcript text: An unknown compound has the following chemical formula: \[ \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{x} \] where $x$ stands for a whole number. Measurements also show that a certain sample of the unknown compound contains 9.40 mol of nitrogen and 3.1 mol of iron. Write the complete chemical formula for the unknown compound.

Solution

Solution Steps

Step 1: Determine the molar ratio of nitrogen to iron

To find the value of $ x $ in the chemical formula $\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{x}$, we need to determine the molar ratio of nitrogen to iron in the compound.

Given:

Moles of nitrogen ($\mathrm{N}$) = 9.40 mol
Moles of iron ($\mathrm{Fe}$) = 3.1 mol

Step 2: Calculate the ratio of nitrogen to iron

Each $\mathrm{NO}_{3}$ group contains 1 nitrogen atom. Therefore, the total number of nitrogen atoms in the compound is $ x $ times the number of $\mathrm{Fe}$ atoms.

The ratio of nitrogen to iron is: \[ \frac{\text{moles of nitrogen}}{\text{moles of iron}} = \frac{9.40}{3.1} \]

Step 3: Simplify the ratio

Simplify the ratio to find $ x $: \[ \frac{9.40}{3.1} = 3.0323 \approx 3 \]

Since $ x $ must be a whole number, we round 3.0323 to the nearest whole number, which is 3.