Question

Naturally occurring lithium is a mixture of \(92.58 \% \mathrm{Li}-7\) with a mass of 7.016 amu and \(7.42 \%\) Li-6 with a mass of 6.015 amu. What is the atomic mass of lithium?

Short answer

The atomic mass of lithium is 6.941 amu.

Step-by-step solution

Understand the Objective

We need to calculate the atomic mass of lithium, given it is a mixture of two isotopes, namely Li-7 and Li-6. Each isotope has a different atomic mass and relative abundance.

Calculate Contribution of Li-7

The contribution of each isotope to the atomic mass is the product of its abundance and its atomic mass. For Li-7, this is calculated as follows:\[\text{Contribution of Li-7} = 0.9258 \times 7.016 = 6.4947 \text{ amu}\]

Calculate Contribution of Li-6

Similarly, calculate the contribution of Li-6 to the atomic mass:\[\text{Contribution of Li-6} = 0.0742 \times 6.015 = 0.4463 \text{ amu}\]

Sum the Contributions

The atomic mass of naturally occurring lithium is the sum of the contributions from Li-7 and Li-6:\[\text{Atomic mass of lithium} = 6.4947 + 0.4463 = 6.941 \text{ amu}\]

Key concepts

Isotopic abundance

Isotopic abundance is a key concept in understanding atomic mass calculation. It refers to the proportion, or percentage, of each isotope of an element present in a natural sample. In nature, most elements exist as a mixture of two or more isotopes. Each isotope has a different number of neutrons, and thus, a different atomic mass.
When calculating the atomic mass of an element, isotopic abundance becomes crucial. This calculation involves multiplying the mass of each isotope by its respective abundance, expressed as a fraction of 1 (i.e., converting the percentage into a decimal). Finally, by summing these weighted contributions, we obtain the average atomic mass. For lithium, the isotopic abundance of Li-7 is 92.58%, and that of Li-6 is 7.42%. This mixture gives rise to the average atomic mass of lithium, used in the periodic table.

Li-7 and Li-6 isotopes

Lithium is an interesting element because of its two main isotopes: Li-7 and Li-6. Isotopes are variants of the same chemical element, identical in the number of protons but differing in the number of neutrons.
- Li-7 has three protons and four neutrons, giving it a mass of 7.016 amu. - Li-6 has three protons and three neutrons, resulting in a mass of 6.015 amu.
In nature, lithium is predominantly found as the Li-7 isotope. The reason lies in its higher isotopic abundance of 92.58%. On the other hand, Li-6, with an abundance of just 7.42%, plays a smaller role. These abundances affect the elemental lithium's properties and its calculation for the atomic mass. Understanding this balance of isotopes is essential for tasks ranging from nuclear physics applications to manufacturing lithium batteries.

Atomic mass unit (amu)

The atomic mass unit (amu) is a standard unit of mass that represents atomic and molecular weights. It provides a convenient way to express and compare the mass of subatomic particles, atoms, and molecules.
An amu is defined precisely as one-twelfth of the mass of a carbon-12 atom, which is approximately 1.66053906660 x 10^-27 kilograms. This tiny unit simplifies the comparison of atomic masses and is essential for calculating the atomic mass of elements.
When dealing with isotopes, like Li-7 and Li-6, the amu allows us to express their masses (7.016 amu and 6.015 amu, respectively) in relatable terms. By applying this concept, we derive a single atomic mass value for an element considering its isotopic composition, as observed for naturally occurring lithium.