How is relative atomic mass calculated for elements on the periodic table?

Relative atomic mass is calculated as the weighted average of the masses of an element's isotopes, taking into account their natural abundance.

Here's a breakdown of the process:

1. Identify the Isotopes: Determine all the naturally occurring isotopes of the element. Isotopes are atoms of the same element that have different numbers of neutrons, and thus different mass numbers.

2. Determine Isotopic Masses: Find the mass of each isotope. This is usually expressed in atomic mass units (amu). These masses are very close to the mass number but not exactly equal due to the mass defect from nuclear binding energy.

3. Determine Natural Abundance: Find the natural abundance of each isotope. This is the percentage of atoms of that element that exist as a particular isotope. Abundances are usually expressed as percentages.

4. Calculate the Weighted Average: Multiply the mass of each isotope by its natural abundance (expressed as a decimal). Then, sum these values to obtain the relative atomic mass.

Formula:

Relative Atomic Mass = (Mass of Isotope 1 × Abundance of Isotope 1) + (Mass of Isotope 2 × Abundance of Isotope 2) + ... + (Mass of Isotope n × Abundance of Isotope n)

Example: Chlorine

Chlorine has two major isotopes:

• Chlorine-35 (³⁵Cl) with a mass of approximately 35 amu and an abundance of 75.76%.
• Chlorine-37 (³⁷Cl) with a mass of approximately 37 amu and an abundance of 24.24%.

Relative Atomic Mass of Chlorine = (35 amu × 0.7576) + (37 amu × 0.2424) = 26.516 amu + 8.9688 amu = 35.48 amu (approximately)

Therefore, the relative atomic mass of chlorine as shown on the periodic table is approximately 35.45 amu. The small difference compared to our calculated value is due to using approximate isotopic masses instead of more precise experimental values.

Key Points:

• Relative atomic mass is a weighted average. This means isotopes with higher abundance have a greater impact on the final value.
• The relative atomic mass is a dimensionless quantity, though it's often expressed with the unit "amu" (atomic mass units). However, the periodic table listings are generally considered unitless relative masses.
• The periodic table uses the term "relative atomic mass" (Ar). It is the weighted average mass of an atom relative to 1/12th of the mass of a carbon-12 atom.

In summary, the relative atomic mass represents the average mass of an element's atoms, considering the masses and abundances of all its naturally occurring isotopes. This weighted average is what you see listed on the periodic table.