Questions: Elemental analysis of an unknown mineral tells you that the mineral consists of 29.3% Al, 20.6% F, 15.3% Si, and 34.8% O. What is the empirical formula of this mineral?

Solution Steps

Assume we have 100 grams of the mineral. This simplifies the percentages directly to grams:

• Al: 29.3 grams
• F: 20.6 grams
• Si: 15.3 grams
• O: 34.8 grams

Use the molar masses of each element to convert grams to moles:

• Molar mass of Al: 26.98 g/mol
• Molar mass of F: 18.998 g/mol
• Molar mass of Si: 28.085 g/mol
• Molar mass of O: 16.00 g/mol

\[ \text{Moles of Al} = \frac{29.3 \text{ g}}{26.98 \text{ g/mol}} = 1.0858 \text{ mol} \]

\[ \text{Moles of F} = \frac{20.6 \text{ g}}{18.998 \text{ g/mol}} = 1.0843 \text{ mol} \]

\[ \text{Moles of Si} = \frac{15.3 \text{ g}}{28.085 \text{ g/mol}} = 0.5449 \text{ mol} \]

\[ \text{Moles of O} = \frac{34.8 \text{ g}}{16.00 \text{ g/mol}} = 2.175 \text{ mol} \]

Divide each mole value by the smallest number of moles calculated:

\[ \frac{1.0858}{0.5449} \approx 1.993 \approx 2 \]

\[ \frac{1.0843}{0.5449} \approx 1.990 \approx 2 \]

\[ \frac{0.5449}{0.5449} = 1 \]

\[ \frac{2.175}{0.5449} \approx 3.992 \approx 4 \]

Final Answer