Defining Atomic Mass
The atomic mass of an element is the weighted average mass of the atoms of that element, based on the relative natural abundance of its isotopes. Because most elements exist in nature as a mixture of isotopes (atoms of the same element with different numbers of neutrons), the atomic mass listed on the periodic table is rarely a whole number. Instead, it reflects the "average" mass of all naturally occurring atoms of that element.
The Concept of Weighted Average
When calculating atomic mass, we cannot simply take a standard arithmetic average. We must account for the fact that some isotopes are more common than others. The formula used is:
$$\text{Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Relative Abundance})$$
Solving the Chlorine Problem
Problem Statement: Chlorine is naturally made up of 75% Cl-35 and 25% Cl-37. Calculate the atomic mass of chlorine.
Step-by-Step Calculation:
Identify the isotopes and their abundances:
- Isotope 1: Cl-35 (Mass = 35 u), Abundance = 75% or 0.75
- Isotope 2: Cl-37 (Mass = 37 u), Abundance = 25% or 0.25
Apply the formula: Multiply the mass of each isotope by its fractional abundance and sum the results:
$$\text{Atomic Mass} = (35 \times 0.75) + (37 \times 0.25)$$
Perform the arithmetic:
- $35 \times 0.75 = 26.25$
- $37 \times 0.25 = 9.25$
Find the final result: $$26.25 + 9.25 = 35.5$$
Conclusion: The calculated atomic mass of chlorine is 35.5 u (unified atomic mass units).
Why does this matter?
Understanding atomic mass is foundational for stoichiometry and chemical reactions. It allows chemists to determine the molar mass of compounds, enabling precise measurements in the lab. The value 35.5 for Chlorine, for instance, is why we use 35.5 g/mol when calculating the molar mass of substances like Sodium Chloride (NaCl).