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Chapter 3

Q. 3.16

Rechargeable lithium batteries are essential to portable electronic devices and are increasingly important to the automotive industry in gas–electric hybrid and all-electric vehicles (Figure 3.27). Analysis of the most common lithium-containing mineral,spodumene, shows it is composed of 3.73% Li, 14.50% Al, 30.18% Si, and 51.59% O. What is the empirical formula of spodumene?

Figure 3.27

Step-by-Step

Verified Solution

Collect and Organize We are given the percent composition by mass of spodumene and asked to determine the simplest whole-number ratio of the four elements (Li, Al, Si, and O), which defines the empirical formula of spodumene.

Analyze We follow the same steps as in Sample Exercise 3.15, except that here we must calculate more than one mole ratio.

Solve

1. Assuming an exactly 100 g sample of spodumene, we have 3.73 g of Li, 14.50 g of Al, 30.18 g of Si, and 51.59 g of O.

2. Converting the masses into moles, we have

3.73  \sout{g  Li} \times \frac{1  mol  Li}{6.941  \sout{g  Li}} =0.5374  mol  Li

14.50  \sout{g  Al} \times \frac{1  mol  Al}{26.98  \sout{g  Al}} =0.5374  mol  Al

30.18  \sout{g  Si} \times \frac{1  mol  Si}{28.09  \sout{g  Si}} =1.074  mol  Si

51.59  \sout{g  O} \times \frac{1  mol  O}{16.00  \sout{g  O}} =3.224  mol  O

3. We divide each mole value by the smallest value to obtain a simple ratio of the four elements:

\frac{0.5374  mol  Li}{0.5374}=1.000  or  1  mol  Li          \frac{0.5374  mol  Al}{0.5374}=1.000  or  1  mol  Al
\frac{1.074  mol  Si}{0.5374} =1.999  or  2  mol  Si                 \frac{3.224  mol  O}{0.5374}=5.999  or  6  mol  O

4. All these results are either whole numbers or very close to whole numbers, so no further simplification of terms is needed. Our mole ratio is Li:Al:Si:O = 1:1:2:6, which means the empirical formula of spodumene is LiAlSi_{2}O_{6}.

Think About It The sum of the mass percentages should be very close to 100%; in this case, 3.73% + 14.50% + 30.18% + 51.59% = 100.00%, so we know we have accounted for all the elements. Notice that lithium is present in the lowest percentage by mass of all four elements in spodumene. Nevertheless, spodumene remains the most commercially important source of lithium for batteries.