The relative molecular mass (Mr) is calculated by adding up the relative atomic masses (Ar) of all the atoms present in a molecule.
Here's a breakdown of the process:
1. Understand the Basics
- Relative Atomic Mass (Ar): This is the weighted average mass of an atom of an element compared to 1/12th the mass of a carbon-12 atom. You can find Ar values on the periodic table.
- Relative Molecular Mass (Mr): This is the mass of a molecule relative to 1/12th the mass of a carbon-12 atom. It's a dimensionless quantity.
2. Identify the Chemical Formula
You need to know the chemical formula of the molecule. This tells you which elements are present and how many atoms of each element there are.
3. Find the Relative Atomic Masses (Ar)
Look up the Ar values for each element in the molecule on the periodic table.
4. Multiply and Add
For each element, multiply its Ar value by the number of atoms of that element present in the molecule (as indicated by the chemical formula). Then, add up all these values to get the Mr.
Formula:
Mr = (Number of atoms of element 1 x Ar of element 1) + (Number of atoms of element 2 x Ar of element 2) + ...
Example 1: Water (H₂O)
- Hydrogen (H): Ar = 1.008 (approximately 1)
- Oxygen (O): Ar = 16.00 (approximately 16)
Mr (H₂O) = (2 x 1) + (1 x 16) = 2 + 16 = 18
Example 2: Carbon Dioxide (CO₂)
- Carbon (C): Ar = 12.01 (approximately 12)
- Oxygen (O): Ar = 16.00 (approximately 16)
Mr (CO₂) = (1 x 12) + (2 x 16) = 12 + 32 = 44
Example 3: Methane (CH₄)
- Carbon (C): Ar = 12.01 (approximately 12)
- Hydrogen (H): Ar = 1.008 (approximately 1)
Mr (CH₄) = (1 x 12) + (4 x 1) = 12 + 4 = 16
Alternative Method: Mass Spectrometry
While the calculation method is the most common way to determine relative molecular mass, it can also be experimentally determined using a mass spectrometer. The molecule is ionized, and the instrument measures the mass-to-charge ratio (m/z) of the molecular ion. This value directly corresponds to the Mr of the molecule.
In summary, calculating relative molecular mass involves identifying the chemical formula, obtaining the relative atomic masses of each element from the periodic table, multiplying each atomic mass by the number of atoms of that element in the molecule, and then summing these values.
