Percent abundance is a concept in chemistry related to isotopes, which are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count results in varying atomic masses for the element. Percent abundance represents the relative amount of a particular isotope found naturally in a sample. The atomic weight listed on the periodic table is a weighted average that accounts for the natural prevalence of each isotope.
Calculating Average Atomic Mass from Known Isotopic Abundances
The atomic mass listed for an element on the periodic table is calculated by taking a weighted average of the masses of its naturally occurring isotopes. This calculation uses the precise mass of each isotope and its fractional abundance, which is the percent abundance converted into a decimal by dividing by 100. To find the average atomic mass, you multiply the mass of each isotope by its fractional abundance.
For example, if an element has two isotopes, the calculation is structured as: (Isotope Mass 1 \(\times\) Fractional Abundance 1) + (Isotope Mass 2 \(\times\) Fractional Abundance 2). The products of these multiplications are then added together to yield the weighted average atomic mass. The resulting average atomic mass is then typically expressed in atomic mass units (amu).
Determining Unknown Isotopic Abundances
A more complex calculation involves determining the unknown percent abundances of two isotopes when the element’s average atomic mass is already known from the periodic table. This problem requires setting up and solving an algebraic system of equations. The first equation is the weighted average formula, where the fractional abundances of the two isotopes are represented by a variable, \(x\), and its complement, \((1-x)\).
The second equation is the constraint that the sum of the two fractional abundances must equal \(1\), or \(100\%\), since they are the only two isotopes being considered. Substituting \((1-x)\) for the second isotope’s fractional abundance into the weighted average formula allows the entire expression to be solved for a single variable, \(x\). The equation becomes: (Mass 1 \(\cdot\) x) + (Mass 2 \(\cdot\) (1-x)) = Average Atomic Mass. Solving for \(x\) yields the fractional abundance of the first isotope, and subtracting that value from \(1\) gives the fractional abundance of the second isotope. The final result is converted to percent abundance by multiplying by \(100\).
Calculating Elemental Percent Composition in a Compound
Elemental percent composition determines the mass percentage of a specific element within a larger compound. This calculation is based on the compound’s molar mass, which is the sum of the atomic masses of all atoms present in the chemical formula. The formula for this percentage is determined by dividing the total mass contributed by the element in the compound by the total molar mass of the compound, and then multiplying by \(100\).
For example, to find the percent mass of oxygen in water (\(\text{H}_2\text{O}\)), the total mass of oxygen in one mole of water is divided by the molar mass of the entire \(\text{H}_2\text{O}\) molecule. The sum of the percent compositions for all elements in the compound must always add up to \(100\%\). This percentage by mass helps chemists understand the make-up of a substance.