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?

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?
Transcript text: 20. Elemental analysis of an unknown mineral tells you that the mineral consists of $29.3 \% \mathrm{Al}, 20.6 \%$ $\mathrm{F}, 15.3 \% \mathrm{Si}$, and $34.8 \% \mathrm{O}$. What is the empirical formula of this mineral?
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Solution

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Solution Steps

Step 1: Convert Percentages to Grams

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
Step 2: Convert Grams to Moles

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

Moles of Al=29.3 g26.98 g/mol=1.0858 mol \text{Moles of Al} = \frac{29.3 \text{ g}}{26.98 \text{ g/mol}} = 1.0858 \text{ mol}

Moles of F=20.6 g18.998 g/mol=1.0843 mol \text{Moles of F} = \frac{20.6 \text{ g}}{18.998 \text{ g/mol}} = 1.0843 \text{ mol}

Moles of Si=15.3 g28.085 g/mol=0.5449 mol \text{Moles of Si} = \frac{15.3 \text{ g}}{28.085 \text{ g/mol}} = 0.5449 \text{ mol}

Moles of O=34.8 g16.00 g/mol=2.175 mol \text{Moles of O} = \frac{34.8 \text{ g}}{16.00 \text{ g/mol}} = 2.175 \text{ mol}

Step 3: Determine the Simplest Whole Number Ratio

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

1.08580.5449≈1.993≈2 \frac{1.0858}{0.5449} \approx 1.993 \approx 2

1.08430.5449≈1.990≈2 \frac{1.0843}{0.5449} \approx 1.990 \approx 2

0.54490.5449=1 \frac{0.5449}{0.5449} = 1

2.1750.5449≈3.992≈4 \frac{2.175}{0.5449} \approx 3.992 \approx 4

Final Answer

The empirical formula of the mineral is:

Al2F2SiO4 \boxed{\text{Al}_2\text{F}_2\text{SiO}_4}

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