Question Video: Calculating the Relative Atomic Mass of Chlorine from Isotopic Abundances Chemistry

Chlorine has two stable isotopes, chlorine-35 and chlorine-37. A sample of chlorine was analyzed using a mass spectrometer, and the following isotopic abundances were calculated. What is the relative atomic mass of chlorine in the sample?

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Video Transcript

Chlorine has two stable isotopes, chlorine-35 and chlorine-37. A sample of chlorine was analyzed using a mass spectrometer, and the following isotopic abundances were calculated. What is the relative atomic mass of chlorine in the sample?

Isotopes are atoms of the same element that have a different mass. This sample contains two isotopes of chlorine, chlorine-35 and chlorine-37. The number which appears after the hyphen is the mass number, the sum of the number of protons and neutrons in the nucleus of all atoms of that isotope. The mass number is approximately the same as the exact mass of an atom of that isotope in unified atomic mass units. The relative atomic mass is the weighted average of the isotopic masses.

When looking at a cell on the periodic table, the relative atomic mass is reported for all elements that have naturally occurring stable isotopes. We can calculate the relative atomic mass by multiplying the isotope abundance times the isotope mass number for each isotope and summing the resulting values. The abundance is the relative amount of each isotope in a sample. Abundances are reported as percentages but must be converted into decimal notation before we can use the value in the relative atomic mass equation. As the term percent means per 100, we can convert a percentage into decimal notation by dividing by 100.

We can then substitute the abundance in decimal notation and the mass number for each isotope into the relative atomic mass equation. We perform the calculation and determine the relative atomic mass of the chlorine in this sample to be 35.484. As abundance and mass number are unitless values, the relative atomic mass is also a unitless value. As the abundances in the question were given to one decimal place, let’s also report our answer to one decimal place.

Thus, our final answer for the relative atomic mass is 35.5.

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