Determining the Relative Atomic Mass of a Molecule from the Isotopic Abundance Percentage

To determine the relative atomic mass of a molecule from the isotopic abundance percentage, you need to follow these steps:

1. Identify the Isotopes: Determine which isotopes of each element are present in the molecule. For example, hydrogen has isotopes ${\text{H}}^1$ (protium), ${\text{H}}^2$ (deuterium), and ${\text{H}}^3$ (tritium).

2. Find the Atomic Masses: Look up the atomic masses of each isotope. These can be found in the periodic table. For example, the atomic masses of hydrogen isotopes are approximately 1.008 u, 2.014 u, and 3.016 u for protium, deuterium, and tritium, respectively.

3. Determine the Isotopic Abundance: Given the isotopic abundance percentage of each isotope, convert these percentages into decimal fractions. For example, if the abundance of ${\text{H}}^1$ is 99.985% and ${\text{H}}^2$ is 0.015%, then in decimal form, these would be $0.99985$ and $0.00015$, respectively.

4. Calculate the Weighted Average: Multiply each isotope's atomic mass by its isotopic abundance fraction, and then sum these products for all isotopes of each element present in the molecule. This gives you the weighted average atomic mass for each element in the molecule.

5. Sum the Weighted Averages: Add up the weighted average atomic masses for all elements present in the molecule. This gives you the relative molecular mass (or relative formula mass) of the molecule.

6. Optional Step for Molecules: If you want to find the relative atomic mass of a specific atom within the molecule, you can calculate its contribution to the overall mass by considering its atomic mass and the number of atoms of that element in the molecule.

Let's illustrate this with an example:

Consider the molecule water (${\text{H}}_2\text{O}$):

• Hydrogen has two isotopes: protium (${\text{H}}^1$) and deuterium (${\text{H}}^2$).
• Oxygen has three isotopes: ${\text{O}}^{16}$, ${\text{O}}^{17}$, and ${\text{O}}^{18}$.

Given the isotopic abundances and atomic masses, you can calculate the relative atomic mass of water.