Naturally occurring chlorine is \(75.53 \% \mathrm{Cl}^{35}\) which has an atomie mass of \(34.969 \mathrm{amu}\) and \(24.47 \% \mathrm{Cl}^{37}\), which has a mass of \(36.966\) amu. Calculate the average atomic mass of chlorine.

When we talk about the mass of atoms, we use the atomic mass unit (amu), which is a standardized unit of mass to express atomic and molecular weights. One atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom, which is approximately equal to the mass of one nucleon (either a proton or neutron). Why is this important? Because by using amu, scientists can convey very small mass values for atoms in a practical and understandable way.

Since atoms are incredibly tiny, their masses are almost insignificant in grams or kilograms. The amu provides a more feasible scale for measuring these particles. When working with isotopic abundances and calculating average atomic masses, amu is the unit we refer to for consistency and ease of understanding.

Isotopic abundance refers to the relative amount of each different isotope of an element that exists in a naturally occurring sample. Each element can have various isotopes, differing only in the number of neutrons within their nuclei. Importantly, the abundance is usually expressed as a percentage that represents how much of a given isotope contributes to the total amount of the element in nature.

The concept of isotopic abundance is essential in calculating the average atomic mass of an element. By knowing the abundance, we can better understand how the various isotopes of an element affect its average weight, and why the average atomic mass found on the periodic table may not match exactly with the mass of any single isotope.

The principle of calculating a weighted average is applied when different items have different levels of significance, which is similar to how the average atomic mass of an element is determined. It involves multiplying each quantity by its corresponding weight (in our case, the isotopic abundance) and adding these products together, then dividing by the sum of the weights, if they don't add up to 1 or 100%.

For example, if we are calculating grades in a class where homework counts for 40% and the final exam counts for 60%, a weighted average takes these percentages into account to weigh the contributions of both components accordingly. In the context of atomic masses, each isotope’s mass is 'weighted' by its abundance, reflecting its contribution to the overall average atomic mass of the element.

Chlorine has two stable isotopes, Cl-35 and Cl-37, and their atomic masses are distinct although their chemical properties are virtually the same. In the calculation provided, Cl-35 with an atomic mass of 34.969 amu is more abundant, accounting for 75.53% of naturally occurring chlorine, while Cl-37 with a slightly heavier atomic mass of 36.966 amu accounts for the remaining 24.47%.

These two isotopes, with their different masses and abundances, exemplify why understanding isotopic abundance and weighted averages is necessary. The 'average' atomic mass of chlorine found on the periodic table is derived from these isotopes and their respective contributions, leading to its value being a weighted average rather than just an arithmetic mean.