Problem 122 - Chemistry The Molecular Science

Question

Lithium has two stable isotopes, \({ }^{6} \mathrm{Li}\) and \({ }^{7} \mathrm{Li}\). The atomic weight of lithium is 6.941 . Without doing a calculation, explain which is the more abundant isotope.

Step-by-Step Solution

Answer

The isotope \\({ }^{7} \mathrm{Li}\\) is more abundant.

Step 1: Understanding Atomic Weight

The atomic weight of an element is the weighted average of the atomic masses of its isotopes, based on their natural abundance.

Step 2: Identify the Isotopes and Their Masses

Lithium has two isotopes: - \({ }^{6} \mathrm{Li}\) with a mass of 6 - \({ }^{7} \mathrm{Li}\) with a mass of 7.

Step 3: Isotopic Abundance and Atomic Weight

The average atomic weight, 6.941, is closer to 7 than to 6. This suggests that the heavier isotope, \({ }^{7} \mathrm{Li}\), is more abundant.

Key Concepts

Atomic weight

The concept of atomic weight involves understanding how the average mass of atoms in an element is calculated. Atomic weight is essentially a weighted average of all the naturally occurring isotopes of an element. To picture this, imagine a class where students' grades are averaged to get a class average. However, unlike the class average where each student contributes equally, in atomic weight, each isotope contributes to the average based on how common it is (its abundance) in nature.

Some important points to remember about atomic weight:

• It is measured in atomic mass units (amu), a standard that allows us to easily compare the weights of different atoms.
• It often does not equate to a whole number, reflecting the fact that it is an average of isotopes with different masses.
• The atomic weight given on the periodic table represents the weighted average of isotopes present on Earth, not just a simple arithmetic mean.

This is why, in the case of lithium with isotopes ^{6}Li and ^{7}Li, the atomic weight of 6.941 is a blended average reflecting the available quantities of these isotopes.

Isotopic abundance

Isotopic abundance refers to how common or rare a specific isotope of an element is in nature. When an element has multiple isotopes, isotopic abundance determines how much each isotope contributes to the atomic weight.

To understand how isotopes affect atomic weight, consider:

• The contribution of each isotope is equal to the product of its abundance and its atomic mass.
• If an isotope is more abundant, it influences the atomic weight more significantly.
• For lithium, the closer the atomic weight to a particular isotope's mass, the more abundant that isotope is.

Using lithium as an example, the atomic weight value of 6.941, being closer to 7, indicates that ^{7}Li is the more abundant isotope. This means that, in nature, ^{7}Li is found in greater quantities than ^{6}Li.

Atomic mass

Atomic mass is the mass of an individual atom, generally expressed in atomic mass units (amu). Each isotope of an element has a distinct atomic mass due to differences in the number of neutrons.

Here's what you should know about atomic mass:

• It accounts for the total number of protons and neutrons in an atom's nucleus.
• For isotopes of the same element, the atomic number (protons) remains the same, while the atomic mass varies due to differing neutron counts.
• Individual atomic masses contribute to the overall atomic weight of the element based on isotopic abundance.

In the lithium isotope example:
- ^{6}Li has an atomic mass of 6 amu.
- ^{7}Li has an atomic mass of 7 amu.
These values are instrumental in calculating atomic weight, where the more abundant ^{7}Li isotope pushes the atomic weight of lithium closer to its mass, as evidenced by the atomic weight of 6.941.