Molar mass of Fe: meaning and value
The molar mass of Fe is the mass of 1 mole of iron atoms. Numerically, an element’s molar mass in \(\mathrm{g/mol}\) matches its atomic mass from the periodic table.
Periodic-table value for iron: Fe has atomic mass \(\approx 55.845\ \mathrm{u}\), so the molar mass of Fe is \[ M(\mathrm{Fe}) = 55.845\ \mathrm{g/mol} \] (often rounded in coursework to \(55.85\ \mathrm{g/mol}\)).
How the molar mass of Fe is used in calculations
Molar mass links a measurable mass sample to the chemical amount (moles), and then Avogadro’s number links moles to a count of atoms.
\[ n = \frac{m}{M} \qquad\text{and}\qquad N = n \times N_A \] where \(m\) is mass, \(M\) is molar mass, \(n\) is moles, \(N\) is number of atoms, and \(N_A = 6.022 \times 10^{23}\ \mathrm{mol^{-1}}\).
Worked example: convert \(25.0\ \mathrm{g}\) Fe to moles and atoms
- Convert grams to moles using the molar mass of Fe. \[ n(\mathrm{Fe}) = \frac{25.0\ \mathrm{g}}{55.845\ \mathrm{g/mol}} = 0.4477\ \mathrm{mol} \approx 0.448\ \mathrm{mol} \] (3 significant figures, matching \(25.0\ \mathrm{g}\)).
- Convert moles to atoms using Avogadro’s number. \[ N(\mathrm{Fe\ atoms}) = (0.4477\ \mathrm{mol}) \times (6.022 \times 10^{23}\ \mathrm{mol^{-1}}) = 2.695 \times 10^{23} \approx 2.70 \times 10^{23}\ \text{atoms} \]
Quick reference table
| Quantity | Symbol | For iron (Fe) | Typical use |
|---|---|---|---|
| Molar mass | \(M(\mathrm{Fe})\) | \(55.845\ \mathrm{g/mol}\) (≈ \(55.85\ \mathrm{g/mol}\)) | Convert between mass and moles |
| Avogadro’s number | \(N_A\) | \(6.022 \times 10^{23}\ \mathrm{mol^{-1}}\) | Convert between moles and atoms |
| Mass–mole relation | \(n = m/M\) | \(n(\mathrm{Fe}) = m(\mathrm{Fe})/55.845\) | Stoichiometry setup |
Visualization: periodic-table tile to conversion map
Final results
The molar mass of Fe is \(55.845\ \mathrm{g/mol}\) (≈ \(55.85\ \mathrm{g/mol}\)); \(25.0\ \mathrm{g}\) Fe corresponds to \(0.448\ \mathrm{mol}\) and \(2.70 \times 10^{23}\) iron atoms.