The atomic masses of \({ }_{17}^{35} \mathrm{Cl}(75.53\) percent \()\) and \({ }_{17}^{37} \mathrm{Cl}\) (24.47 percent) are 34.968 amu and 36.956 amu, respectively. Calculate the average atomic mass of chlorine. The percentages in parentheses denote the relative abundances.

Isotopes are variants of a particular chemical element that share the same number of protons but differ in the number of neutrons they contain in their nuclei. This means that while they have the same atomic number, each isotope has a different mass number.

For example, chlorine has two stable isotopes, \( ^{35}Cl \) and \( ^{37}Cl \) which are represented as \( _{17}^{35}Cl \) and \( _{17}^{37}Cl \) respectively. These isotopes of chlorine have the same number of protons (17), but different numbers of neutrons, resulting in different atomic masses.

Understanding isotopes is essential because their abundances and masses are used to determine the average atomic mass of the elements as found on the periodic table.

The atomic mass unit (amu) is a standard unit of mass that quantifies the mass of an atom or molecule. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 at its nuclear and electronic ground state.

One amu is approximately equal to \(1.66 \times 10^{-24}\text{grams}\). This very small unit of mass allows chemists and physicists to compare the masses of different atoms and molecules on a scale suitable for small particles. For instance, as given in the exercise, the atomic mass of \( _{17}^{35}Cl \) is 34.968 amu, and that of \( _{17}^{37}Cl \) is 36.956 amu. These values are specific to the isotopes of chlorine and are used in calculating their average atomic mass.

Relative abundance refers to the proportion of a particular isotope present compared to the total amount of all isotopes of that element in a given sample. It is usually expressed as a percentage.

To use the relative abundance for calculations such as determining the average atomic mass, it is often converted to a decimal form by dividing the percentage value by 100. In our exercise, we see that \( _{17}^{35}Cl \) has a relative abundance of 75.53%, which converts to 0.7553 in decimal form. Similarly, \( _{17}^{37}Cl \) has a relative abundance of 24.47%, or 0.2447 in decimal form. These figures are crucial in accurately calculating an element's average atomic mass.

The atomic mass of chlorine, like that of any element with multiple stable isotopes, is not a whole number because it is calculated as a weighted average of the atomic masses of its naturally occurring isotopes. This takes into account both the mass and the relative abundance of each isotope.

In the case of chlorine, to find its average atomic mass, we utilize the atomic masses and relative abundances of its isotopes \( _{17}^{35}Cl \) and \( _{17}^{37}Cl \). The previously outlined steps demonstrate how to equate each mass with its decimal relative abundance and then add the products together. This calculation provides us with the average atomic mass for chlorine, which is an essential data point for various applications in chemistry such as stoichiometry and is commonly found on the periodic table.