Question

Chlorine exists mainly as two isotopes, \({ }^{37} \mathrm{Cl}\) and \({ }^{35} \mathrm{Cl}\). Which is more abundant? How do you know?

Short answer

The \({ }^{35}\mathrm{Cl}\) isotope is more abundant than the \({ }^{37}\mathrm{Cl}\) isotope. By considering the atomic mass of chlorine from the periodic table (35.5 amu) and the masses of its two isotopes, we can calculate their relative abundances (A for \({ }^{37}\mathrm{Cl}\) and B for \({ }^{35}\mathrm{Cl}\)). Solving the equation, we find that A = 0.25 and B = 0.75, which indicates that \({ }^{35}\mathrm{Cl}\) is more abundant (0.75 > 0.25).

Step-by-step solution

Find the atomic mass of chlorine from the periodic table

Look for chlorine on the periodic table and find its atomic mass, which is around 35.5 amu (atomic mass units).

Consider the atomic masses of the two isotopes and their relative abundances

The two isotopes are \({ }^{37}\mathrm{Cl}\), with a mass of 37 amu, and \({ }^{35}\mathrm{Cl}\), with a mass of 35 amu. Let's assume that \({ }^{37}\mathrm{Cl}\) has an abundance of A, while \({ }^{35}\mathrm{Cl}\) has an abundance of B. Since only these two isotopes contribute to the atomic mass, their relative abundance sum is 1: A+B = 1

Calculate the weighted sum of the isotopic masses

To get the atomic mass from the isotopes, we need to multiply the isotopic mass by its abundance and sum it up to compare it to the atomic mass found on the periodic table. The weighted sum is: \[(37 \times A) + (35 \times B) = 35.5\]

Solve for the relative abundances

We can substitute the sum from step 2 into the weighted sum (step 3) and solve for the relative abundances of the isotopes: \[(37 \times A) + (35 \times (1 - A)) = 35.5\] Expanding and rearranging, we get: \[2A = 0.5\] Solving for A, we find: \[A = 0.25\] From this, we can calculate B: \[B = 1 - A = 1 - 0.25 = 0.75\]

Compare the relative abundances

Since the relative abundance of \({ }^{35}\mathrm{Cl}\) (represented by B) is greater than the relative abundance of \({ }^{37}\mathrm{Cl}\) (represented by A): B > A or 0.75 > 0.25 Therefore, the \({ }^{35}\mathrm{Cl}\) isotope is more abundant than the \({ }^{37}\mathrm{Cl}\) isotope.

Key concepts

Atomic Mass

Atomic mass is a fundamental concept when discussing the properties of elements on the periodic table. It is a weighted average of all the isotopes of an element, measured in atomic mass units (amu). For example, chlorine has an atomic mass of approximately 35.5 amu. This value helps us understand the average mass of chlorine atoms, taking into account the mass and abundance of its isotopes. Since the atomic mass is not always a whole number, it reflects the presence of isotopes in different amounts. This is crucial for elements like chlorine, where multiple isotopes contribute to its atomic mass.

Isotope Abundance

Isotope abundance refers to the relative amount of each isotope present in a naturally occurring sample of an element. Each isotope of an element has the same number of protons but a different number of neutrons, resulting in different atomic masses.

In chlorine's case,

• extsuperscript{35}Cl has a mass of 35 amu
• extsuperscript{37}Cl has a mass of 37 amu
• The abundance of extsuperscript{35}Cl is about 75%
• The abundance of extsuperscript{37}Cl is about 25%

These abundances explain why the average atomic mass of chlorine is closer to 35. Isotope abundance is essential for calculating the weighted average atomic mass for any element.

Periodic Table

The periodic table is a systematic arrangement of elements showcasing periodic trends and elemental properties. Each element is listed with its atomic number and atomic mass, helping chemists and students quickly gather information.

For chlorine, the periodic table shows its atomic mass around 35.5 amu, hinting at its isotopic composition. Students can use this information to infer which isotope is more abundant by comparing the atomic mass with the mass of known isotopes.

The periodic table not only organizes elements by atomic structure but also serves as a valuable tool for understanding chemical behavior and reactivity, making it indispensable in education and research.

Weighted Average

A weighted average is a calculation used to take into account the varying contributions of different values. For isotopes, this means considering both their mass and abundance to find the atomic mass listed on the periodic table.

For chlorine, the equation for weighted average is set as:\[(37 \times A) + (35 \times B) = 35.5\]Where:

• \(A\) is the abundance of \textsuperscript{37}Cl
• \(B\) is the abundance of \textsuperscript{35}Cl

Since the sum of \(A\) and \(B\) is 1, the weighted average gives us the atomic mass when calculated accurately. Understanding weighted averages is crucial in chemistry for interpreting data related to isotopic composition and other applications involving varying contributions.