Relative Atomic Mass and Relative Molecular Mass

Full Notes

The background theory and more detail on relative atomic mass can be found here.

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Understanding Relative Atomic Mass (A_r)

The relative atomic mass (A_r) of an element is the weighted average mass of its isotopes compared to 1/12th of the mass of a carbon-12 atom.

• A_r has no units (it is a relative measure).
• It considers the percentage abundance of each isotope.
• For elements with one isotope (e.g. fluorine-19), the A_r equals mass number.
• For elements with multiple isotopes, the A_r is calculated using isotope abundances.

Example: A_r of chlorine (³⁵Cl and ³⁷Cl):

As a result, the periodic table lists chlorine with an atomic mass of 35.5.

Relative Molecular Mass (M_r)

The relative molecular mass (M_r) is the sum of the relative atomic masses of all atoms in a molecule.

Example:M_r of water (H₂O) :

• Hydrogen A_r = 1.0
• Oxygen A_r = 16.0
• M_r = (2 × 1.0) + (1 × 16.0) = 18.0

Relative Formula Mass (M_r) of Ionic Compounds

For ionic compounds, the term relative formula mass is used instead of molecular mass. It is the sum of the A_r values of the ions in the empirical formula.

Example:M_r of NaCl:

• Sodium A_r = 23.0
• Chlorine A_r = 35.5
• M_r = 23.0 + 35.5 = 58.5

Importance of A_r and M_r in Chemistry

• Essential for mole calculations (next topic).
• Used in balanced chemical equations and stoichiometry.
• Helps determine reacting masses and empirical formulas.

Summary

• A_r: Weighted average of isotopes relative to carbon-12.
• A_r = (Σ (isotopic mass × % abundance)) ÷ 100.
• M_r (molecules): Sum of A_r values of atoms in a molecule.
• M_r (ionic compounds): Sum of A_r values of ions in empirical formula.
• M_r = total A_r values of all atoms/ions.
• Both A_r and M_r are essential for mole calculations and stoichiometry.