Relative Atomic Mass ($A_r$) and Relative Formula Mass ($M_r$)
Why Do We Need Relative Masses in Chemistry?
- You are trying to weigh a single atom on a balance.
- It's impossible: atoms are so small that their masses are expressed in atomic mass units (amu), which are defined relative to the mass of a carbon-12 atom.
- Why carbon-12?
It serves as a universal reference: one atom of carbon-12 is assigned a mass of exactly 12 amu.
Relative Atomic Mass ($A_r$): A Comparison to Carbon-12
Definition
Relative atomic mass
The relative atomic mass of an element is a weighted average of the masses of its isotopes, based on their natural abundances, compared to 1/12th the mass of a carbon-12 atom. Since it is a ratio, $A_r$ has no units.
Key Points:
- Reference to Carbon-12: The mass of an atom is expressed relative to 1/12th the mass of a carbon-12 atom.
- Weighted Average: For elements with multiple isotopes, $A_r$ accounts for both the mass and natural abundance of each isotope.
- Data Booklet Values: $A_r$ values are provided in the IB Chemistry Data Booklet and are typically rounded to two decimal places.
- Chlorine has two isotopes:
- $^{35}\text{Cl}$, with a mass of 34.97 and an abundance of 75.78%.
- $^{37}\text{Cl}$, with a mass of 36.97 and an abundance of 24.22%.
- To calculate $A_r$:
$$A_r = \left(34.97 \times \frac{75.78}{100}\right) + \left(36.97 \times \frac{24.22}{100}\right)$$ $$A_r = 26.51 + 8.95 = 35.46$$ - Thus, the relative atomic mass of chlorine is approximately 35.46.
In exams, you’ll typically use the $A_r$ values provided in the data booklet rather than calculating them yourself.
Relative Formula Mass ($M_r$): Adding Up Atomic Masses
Definition
Relative formula mass
The relative formula mass ($M_r$) is the sum of the relative atomic masses ($A_r$) of all the atoms in a chemical formula.
It applies to both molecular compounds (like water) and ionic compounds (like sodium chloride).
Key Points:
- Molecular Compounds: For molecules, $M_r$ is the sum of the $A_r$ values of all atoms in the molecule.
