Ch.2 - Atoms & Elements

Problem 117

Chapter 2, Problem 117

Lithium has only two naturally occurring isotopes. The mass of lithium-6 is 6.01512 amu and the mass of lithium-7 is 7.01601 amu. Calculate the relative abundances of the two isotopes.

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Identify the given masses of the isotopes: lithium-6 has a mass of 6.01512 amu, and lithium-7 has a mass of 7.01601 amu.

Let the abundance of lithium-6 be represented as x, and the abundance of lithium-7 be represented as 1-x, since the total abundance must sum to 100%.

Use the average atomic mass of lithium from the periodic table, which is approximately 6.94 amu, to set up the equation: (6.01512 * x) + (7.01601 * (1-x)) = 6.94.

Solve the equation for x to find the abundance of lithium-6. This involves simplifying the equation and isolating x.

Substitute the value of x back into the expression for the abundance of lithium-7 (1-x) to find its abundance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For lithium, the two isotopes are lithium-6 and lithium-7, which have 3 protons each but differ in their neutron count (3 and 4, respectively). Understanding isotopes is crucial for calculations involving atomic mass and relative abundance.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a sample, usually expressed as a percentage. To calculate the relative abundances of isotopes, one can use the weighted average of their masses and the known average atomic mass of the element. This concept is essential for determining how much of each isotope contributes to the overall atomic mass.

Weighted Average

A weighted average is a mean that takes into account the relative importance or frequency of each value in a dataset. In the context of isotopes, the weighted average of the isotopes' masses is calculated using their relative abundances. This method allows for the determination of the average atomic mass of an element, which is critical for understanding its isotopic composition.

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