Think of an element as a basket of balls where each ball is an isotope.
The relative atomic mass is the average weight of all the balls in the basket, but measured against a special reference: 1/12 of a carbon‑12 atom.
Mathematically:
\$Ar = \frac{\sumi mi \cdot xi}{12}\$
where \$mi\$ = mass of isotope \$i\$, and \$xi\$ = its natural abundance (as a fraction).
⚡️ Analogy: Imagine you have a bag of marbles of different sizes. To find the average size, you add up all sizes and divide by the number of marbles. Here, the “size” is the mass of each isotope, and the “number” is the total number of atoms (scaled by 12 for carbon‑12).
Carbon‑12 is a standard because it’s easy to count: 12 carbon‑12 atoms weigh exactly 12 atomic mass units (amu).
By setting 1/12 of a carbon‑12 atom as the unit, all other atomic masses become dimensionless numbers that are easy to compare.
| Isotope | Mass (amu) | Abundance (%) |
|---|---|---|
| 12C | 12.0000 | 98.93 |
| 13C | 13.0034 | 1.07 |
| 14C | 14.0032 | 0.00 |
The molar mass of an element (in g mol⁻¹) is numerically equal to its relative atomic mass.
Example: Carbon’s molar mass = 12.011 g mol⁻¹.
For a compound, add the molar masses of all atoms.
Water (H₂O): 2 × 1.008 + 15.999 = 18.015 g mol⁻¹.
Tip 1: Always use the latest IUPAC values for relative atomic masses (they’re in the periodic table).
Tip 2: When calculating molar mass, round to the same number of significant figures as the given data.
Tip 3: Remember: Relative atomic mass = Molar mass (g mol⁻¹).
Tip 4: For isotopic mixtures, use the weighted average formula above.