To determine the empirical formula of a compound with given percentage compositions of aluminum and sulfur, follow these steps:
1. Convert the percentage to grams: Assume we have a 100-gram sample of the compound. This means:
- The sample has 35.94 grams of aluminum (Al).
- The sample has 64.06 grams of sulfur (S).
2. Calculate the number of moles of each element: Use the molar masses of aluminum and sulfur to convert grams to moles.
- The molar mass of aluminum (Al) is approximately 26.98 g/mol.
- The molar mass of sulfur (S) is approximately 32.06 g/mol.
Calculate the moles of aluminum:
[tex]\[
\text{Moles of Al} = \frac{35.94 \text{ grams}}{26.98 \text{ g/mol}} \approx 1.332
\][/tex]
Calculate the moles of sulfur:
[tex]\[
\text{Moles of S} = \frac{64.06 \text{ grams}}{32.06 \text{ g/mol}} \approx 1.998
\][/tex]
3. Determine the simplest mole ratio: Divide the number of moles of each element by the smallest number of moles calculated.
- The smallest number of moles is 1.332 (moles of Al).
Moles ratio of aluminum:
[tex]\[
\frac{1.332}{1.332} \approx 1
\][/tex]
Moles ratio of sulfur:
[tex]\[
\frac{1.998}{1.332} \approx 1.5
\][/tex]
4. Convert the mole ratio to the simplest whole number ratio: If necessary, multiply the ratios by the smallest number that converts all ratios to whole numbers.
- In this case, multiply by 2 to get approximate whole numbers:
[tex]\[
\left(1 \times 2\right) = 2 \quad \text{for aluminum (Al)}
\][/tex]
[tex]\[
\left(1.5 \times 2\right) = 3 \quad \text{for sulfur (S)}
\][/tex]
5. Write the empirical formula: Based on the whole number mole ratios, the empirical formula is:
[tex]\[
Al_2S_3
\][/tex]
So, the correct empirical formula of a compound with 35.94% aluminum and 64.06% sulfur is [tex]\(\boxed{Al_2S_3}\)[/tex]. Thus, the correct answer is Option D.
