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Chapter 3: Problem 6

The atomic masses of \({ }_{3}^{6} \mathrm{Li}\) and \({ }_{3}^{7} \mathrm{Li}\) are \(6.0151 \mathrm{amu}\) and 7.0160 amu, respectively. Calculate the natural abundances of these two isotopes. The average atomic mass of \(\mathrm{Li}\) is \(6.941 \mathrm{amu}\).

Short Answer

Expert verified
The natural abundances of \({ }_{3}^{6}\mathrm{Li}\) and \({ }_{3}^{7}\mathrm{Li}\) are approximately 7.54% and 92.46%, respectively.

Step by step solution

01

Define Variables

Let's denote the abundance of \({ }_{3}^{6}\mathrm{Li}\) as \(x\) and the abundance of \({ }_{3}^{7}\mathrm{Li}\) as \(1 - x\) because the total natural abundance must equal 1 or 100%.
02

Set Up Equations

The atomic mass of lithium is \(6.941 \mathrm{amu}\), which is calculated by the formula: \(x \cdot 6.015 \mathrm{amu} + (1 - x) \cdot 7.016 \mathrm{amu} = 6.941 \mathrm{amu}\). This equation represents the contribution from both isotopes to the average atomic mass.
03

Solve for \(x\)

Now, we need to solve the equation for \(x\). Rearranging the equation gives us \(x = \frac{7.016 \mathrm{amu} - 6.941 \mathrm{amu}}{7.016 \mathrm{amu} - 6.015 \mathrm{amu}}\), which equals 0.075421.
04

Calculate Abundances

The abundance of \({ }_{3}^{6}\mathrm{Li}\) is \(x \cdot 100\% = 7.5421\%\). Subtracting this from 100% gives us the abundance of \({ }_{3}^{7}\mathrm{Li}\), which is \(100\% - 7.5421\% = 92.4579\%\).

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Most popular questions from this chapter

What mole ratio of molecular chlorine \(\left(\mathrm{Cl}_{2}\right)\) to molecular oxygen \(\left(\mathrm{O}_{2}\right)\) would result from the breakup of the compound \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) into its constituent elements?

Which of the following substances contains the greatest mass of chlorine? (a) \(5.0 \mathrm{~g} \mathrm{Cl}_{2},\) (b) \(60.0 \mathrm{~g}\mathrm{NaClO}_{3}\) (c) \(0.10 \mathrm{~mol} \mathrm{KCl}\), (d) \(30.0 \mathrm{~g} \mathrm{MgCl}_{2}\), (e) \(0.50 \mathrm{~mol} \mathrm{Cl}_{2}\).

Ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right),\) an important industrial organic chemical, can be prepared by heating hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\) at \(800^{\circ} \mathrm{C}:$$$\mathrm{C}_{6} \mathrm{H}_{14} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}+\text { other products }$$ If the yield of ethylene production is 42.5 percent, what mass of hexane must be reacted to produce \)481 \mathrm{~g}$ of ethylene?

limestone \(\left(\mathrm{CaCO}_{3}\right)\) is decomposed by heating to quicklime \((\mathrm{CaO})\) and carbon dioxide. Calculate how many grams of quicklime can be produced from \(1.0 \mathrm{~kg}\) of limestone.

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