The mass of an atom is a fundamental property in chemistry and physics. Calculating atomic mass involves distinguishing between the mass of a single, specific atom and the average mass of an element as it exists in nature. The atomic mass unit (amu) is used to measure the exceedingly small mass of a single atom. The value found on the Periodic Table represents a weighted average, not the mass of any single atom.
Calculating Mass for a Specific Isotope
The mass of a specific, isolated atom, known as its isotopic mass, is determined by counting its constituent subatomic particles. The nucleus, containing protons and neutrons, holds almost all of the atom’s mass, while electrons contribute a negligible amount. The number of protons defines the element, and the sum of protons and neutrons is the mass number, which identifies the specific isotope.
To calculate the theoretical mass, the count of protons and neutrons is multiplied by their respective masses in atomic mass units. For basic calculations, both a proton and a neutron are approximated as having a mass of one amu. However, the total mass of the atom is not simply the sum of its parts.
A phenomenon called the nuclear binding energy causes the assembled nucleus’s mass to be slightly less than the total mass of the individual, unbound particles. This difference is the mass defect. Therefore, the most accurate isotopic mass must be measured experimentally using a mass spectrometer. Nonetheless, the theoretical calculation using the mass number provides a quick estimate in amu for any specific isotope.
Determining the Average Atomic Mass
The standard atomic mass listed on the Periodic Table is a weighted average that accounts for the natural occurrence of an element’s isotopes. Most elements exist in nature as a mixture of two or more isotopes, which are atoms of the same element containing different numbers of neutrons. The relative percentage of each isotope in a natural sample is called its natural abundance.
For example, chlorine has two main stable isotopes: Chlorine-35 and Chlorine-37. Approximately \(75.78\%\) of chlorine atoms are the lighter Chlorine-35 isotope, and \(24.22\%\) are the heavier Chlorine-37 isotope.
The weighted average is calculated by converting the natural abundance percentages into decimal fractions and multiplying each by its corresponding isotopic mass. For chlorine, this calculation is: \((0.7578 \times 34.96885 \text{ amu}) + (0.2422 \times 36.96590 \text{ amu})\). Summing these products yields the average atomic mass of approximately \(35.45\) amu, the value found on the Periodic Table. This reflects the blend of naturally occurring isotopes, explaining why atomic mass values are typically not whole numbers.
Converting Atomic Mass to Grams
The atomic mass unit (amu) is too small for practical laboratory use. To convert the microscopic mass of atoms into a macroscopic mass in grams, chemists use the concept of the mole. The mole is defined as the amount of substance containing \(6.02214076 \times 10^{23}\) elementary entities, known as Avogadro’s number.
The numerical value of an element’s average atomic mass in amu is exactly equal to its molar mass in grams per mole (\(\text{g/mol}\)). This provides a straightforward conversion factor. For example, the average atomic mass of chlorine is \(35.45\) amu, meaning one mole of chlorine atoms has a molar mass of \(35.45\) grams. This simple numerical equivalence is the most practical application of atomic mass calculations for scientists.