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## 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?

## 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.