Relative Atomic Mass (RAM) is the single number chemists use to represent an element’s mass on the periodic table. This standardized value allows scientists to accurately compare the masses of different elements. It is a fundamental concept that enables calculations in stoichiometry, the study of quantitative relationships in chemical reactions. The value itself is not a simple average but a weighted average that accounts for the natural variations of the element’s atoms.
The Role of Isotopes and Natural Abundance
The need to calculate relative atomic mass arises because not all atoms of a single element are identical in mass. Atoms of the same element have the same number of protons but can possess different numbers of neutrons; these variations are called isotopes. Since chemical reactions involve bulk amounts of an element, the mass used in calculations must reflect the mixed population of these isotopes.
The second piece of data required is the natural abundance of each isotope. Natural abundance refers to the percentage of each specific isotope found in a naturally occurring sample of the element. These percentages are determined experimentally using instruments like a mass spectrometer. The sum of the natural abundances for all isotopes must always total 100%. This abundance data provides the weight for the average, ensuring that the mass of a more common isotope contributes more significantly to the final relative mass value.
Defining the Standard: The Atomic Mass Unit
Measuring the mass of a single atom in standard units like grams is impractical. To create a manageable and universal scale for atomic masses, scientists established a relative standard called the Atomic Mass Unit (AMU). It is also referred to as the Dalton (Da) or the unified atomic mass unit (u).
The modern standard for the AMU is based on the most common isotope of carbon, Carbon-12 (C-12). One atomic mass unit is defined as exactly one-twelfth (1/12) of the mass of a single, neutral Carbon-12 atom. By setting the mass of the C-12 atom to precisely 12 AMU, all other atomic masses can be compared to this fixed reference point.
Calculating the Weighted Average
The final step in determining the relative atomic mass is combining the isotopic masses and their natural abundances into a single, representative value. This process is known as calculating the weighted average. The weighted average ensures that the more plentiful isotopes have a proportionally greater influence on the final result.
The general formula involves multiplying the mass of each isotope by its fractional abundance and then summing the results for all isotopes. Fractional abundance is the percentage abundance converted to a decimal by dividing by 100. The calculation is represented mathematically as: Relative Atomic Mass = (Mass Isotope 1 x Fractional Abundance 1) + (Mass Isotope 2 x Fractional Abundance 2) + …
Example: Chlorine
Consider the element Chlorine, which has two primary naturally occurring isotopes: Chlorine-35 and Chlorine-37. Chlorine-35 has a mass of approximately 34.969 AMU and a natural abundance of 75.77%. The heavier isotope, Chlorine-37, has a mass of about 36.966 AMU and an abundance of 24.23%.
To calculate the weighted average, the percentage abundances are first converted to their fractional form: 0.7577 for Cl-35 and 0.2423 for Cl-37. The calculation then proceeds by multiplying each isotopic mass by its fractional abundance: (34.969 AMU x 0.7577) + (36.966 AMU x 0.2423).
Summing these products yields the final relative atomic mass: 26.495 AMU + 8.956 AMU = 35.451 AMU. This result, 35.451 AMU, is the value printed on the periodic table for Chlorine. This calculated average is closer to 35 AMU than 37 AMU because the Cl-35 isotope is significantly more abundant.