Chlorine exists as two isotopes in nature, \({ }_{1} 5 \mathrm{Cl}\) (atomic mass \(34.969 \mathrm{amu}\), abundance \(75.77 \%\) ) and \({ }_{17}^{37} \mathrm{Cl}\) (atomic mass \(36.966\) amu). (a) What is the percent abundance of the \({ }_{1}^{37} \mathrm{Cl}\) isotope? (b) Calculate the weighted average of the atomic mass of naturally occurring chlorine. (c) How many times more massive is \({ }_{1}^{37} \mathrm{Cl}\) than \({ }_{17}^{35} \mathrm{Cl}\) ?

When we talk about the percent abundance of isotopes, we are referring to the proportion of each isotope present in a natural sample of an element. Since isotopes of an element have the same number of protons but a different number of neutrons, they can vary slightly in mass. The percent abundance is crucial for understanding the overall atomic mass of the element as found in nature. For example, in the case of chlorine, we have two stable isotopes: Chlorine-35 and Chlorine-37.

To find the percent abundance of Chlorine-37, we subtract the percent abundance of Chlorine-35 from 100%, assuming only these two isotopes exist. This is based on the principle that the sum of the percent abundances of all isotopes of an element must equal 100%. If Chlorine-35 has an abundance of 75.77%, then Chlorine-37, which makes up the remainder, has an abundance of 24.23%. Understanding this concept is critical when calculating the average atomic mass of an element.

Atomic mass calculation involves determining the mass of a single atom of an element. It's usually expressed in atomic mass units (amu), where one amu is defined as one twelfth the mass of a carbon-12 atom. For isotopes, these masses are measured using mass spectrometry and are crucial for scientific fields ranging from chemistry to geology. For instance, Chlorine-35 has an atomic mass of approximately 34.969 amu, and Chlorine-37 has a mass of approximately 36.966 amu. These values are constants for the isotopes and are used in calculations involving isotopic composition, such as computing the weighted average atomic mass.

The weighted average atomic mass of an element takes into account the masses of its isotopes and their percent abundances in nature. It's like the average grade in a class where some assignments count more towards the final grade than others. In this analogy, the 'grades' are the isotopic masses, and their 'weight' is the percent abundance of each isotope.

To calculate the weighted average atomic mass for chlorine, each isotope's mass is multiplied by its percent abundance, and the products are then summed up and divided by 100. This gives us the average mass of a chlorine atom as it typically occurs in nature, considering the relative abundance of Chlorine-35 and Chlorine-37. It's this weighted average that is listed on the periodic table for elements with naturally occurring isotopes.

The isotope mass ratio is a comparison of the masses of different isotopes of the same element. It informs us about the relative heaviness of isotopes compared to each other. This ratio is calculated by simply dividing the atomic mass of one isotope by the atomic mass of another. In our example, to find out how much heavier Chlorine-37 is compared to Chlorine-35, we divide the atomic mass of Chlorine-37 by that of Chlorine-35, yielding a ratio of 1.057.

This means that Chlorine-37 is approximately 1.057 times more massive than Chlorine-35. Knowing the isotope mass ratio is particularly useful in disciplines such as isotope geochemistry and radiometric dating, where isotopic differences play a significant role.