Video: Calculating the Average Atomic Mass of a Lithium Sample from the Isotopes' Atomic Masses and Their Percentages in the Sample

A sample of lithium contains a mixture of ⁶Li and ⁷Li isotopes with atomic masses 6.01512 u and 7.01600 u respectively. The sample is 4.21% ⁶Li by moles. (a) Calculate, to 3 significant figures, the average atomic mass of the sample. (b) A second sample of lithium also contains a mixture of ⁶Li and ⁷Li but displays a higher abundance of ⁶Li. How does the average atomic mass of this sample compare with that of the first?

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Video Transcript

A sample of lithium contains a mixture of lithium-6 and lithium-7 isotopes with atomic masses 6.01512 u and 7.01600 u, respectively. The sample is 4.21 percent lithium-6 by moles. Calculate, to three significant figures, the average atomic mass of the sample.

Lithium is a relatively light element to be found in the alkali metals on the periodic table. Lithium-6 and lithium-7 are commonly found isotopes of lithium. Each atom of lithium-6 has three protons and three neutrons in its nucleus. And each atom of lithium-7 has three protons and four neutrons in its nucleus. In this context, the atomic masses refer to the mass of a single atom of that isotope. So an atom of lithium-6 has a mass of 6.01512 unified atomic mass units, while an atom of lithium-7 has a mass of 7.01600 unified atomic mass units. One unified atomic mass unit is the equivalent of one twelfth of the mass of a carbon-12 atom. You might see atomic mass units written amu instead of unified atomic mass units.

The question tells us that the sample is 4.21 percent lithium-6 by moles. This means that 4.21 percent of all of the lithium atoms are lithium-6 atoms. The only other isotope this sample of lithium contains is lithium-7. So the rest of the atoms are lithium-7 atoms. We can calculate the percentage of lithium-7 atoms by taking 4.21 percent away from 100 percent. This means that 95.79 percent of all the atoms in our lithium sample are lithium-7 atoms. Our job is to calculate the average mass for one atom for this sample.

Let’s look quickly at what this average lithium atom would look like. It would have definitely three protons because lithium-6 and lithium-7 both have three protons. If it’s neutral, it would also have three electrons. But how many neutrons would it have? The average lithium atom would have more than six neutrons because we have some lithium-7 in there, which has seven neutrons, which would raise the average. But it would also have less than seven neutrons because there’s some lithium-6 in there, reducing the average. So our average lithium atom would have between six and seven neutrons.

However, you can’t add a fraction of a neutron to an individual atom. So this average lithium atom is an idea, not something that’s physically possible. However, we can use this perspective to help us calculate the average mass. We can think about the mass of the average atom like a circle. A fraction of this circle will be because of lithium-6. And the rest of it will be because of lithium-7. 4.21 percent of this average lithium atom is represented by lithium-6. So the mass of that section is 4.21 percent multiplied by the atomic mass of lithium-6.

The remaining 95.79 percent of this lithium atom will be represented by lithium-7. So the mass of this section is equal to 95.79 percent multiplied by the atomic mass of lithium-7, 7.01600 u. So the average atomic mass is simply the sum of these two contributions. So the bit of the average atom that comes from lithium-6 has a mass of 0.253237 unified atomic mass units. And the bit that comes from lithium-7 has a mass of 6.72063 unified atomic mass units, giving us the average atomic mass for this sample of 6.97386 u. We’ve been asked to give our answer to three significant figures. So our final answer for the average atomic mass for this sample is 6.97 unified atomic mass units.

A second sample of lithium also contains a mixture of lithium-6 and lithium-7 but displays a higher proportion of lithium-6. How does the average atomic mass of this sample compare with that of the first?

So just to review, we have sample one where 4.21 percent of all the atoms are lithium-6 atoms and the rest are lithium-7 atoms. And we have sample two, where we again have a mixture of lithium-6 and lithium-7 atoms. But more than 4.21 percent of those atoms are lithium-6. Sample one has more of the heavier lithium-7 atoms. And sample two has more of the light lithium-6 atoms. So sample one would have a higher average atomic mass. And sample two would have a lower average atomic mass.

So the answer to how does the average atomic mass of the second sample compare with that of the first is that it is lower.

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