To determine how many moles of aluminum (Al) are present when there are 6.0 moles of sulfur (S) in a sample of aluminum sulfide (Al₂S₃), we need to use the molar ratio from the formula of aluminum sulfide.
Step-by-Step Solution:
1. Identify the chemical formula:
The chemical formula for aluminum sulfide is Al₂S₃. This tells us how many moles of each element are present in one mole of the compound.
2. Understand the molar ratio:
In one mole of Al₂S₃, there are:
- 2 moles of Al (aluminum)
- 3 moles of S (sulfur)
Thus, the molar ratio of Al to S in Al₂S₃ is 2:3.
3. Set up the ratio:
To find how many moles of Al correspond to 6.0 moles of S, we set up our ratio as follows:
[tex]\[
\frac{2 \text{ moles of Al}}{3 \text{ moles of S}} = \frac{x \text{ moles of Al}}{6.0 \text{ moles of S}}
\][/tex]
Here, [tex]\(x\)[/tex] represents the unknown number of moles of Al.
4. Solve for x:
We cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[
2 \times 6.0 = 3 \times x
\][/tex]
[tex]\[
12 = 3x
\][/tex]
[tex]\[
x = \frac{12}{3}
\][/tex]
[tex]\[
x = 4.0 \text{ moles of Al}
\][/tex]
So, when there are 6.0 moles of S, there are 4.0 moles of Al in the sample of Al₂S₃.
5. Determine the missing conversion factor:
The conversion factor from moles of S to moles of Al is the ratio [tex]\(\frac{2}{3}\)[/tex].
Therefore, the missing conversion factor is [tex]\(\frac{2}{3}\)[/tex].
Conclusion:
- The number of moles of Al present when there are 6.0 moles of S in a sample of Al₂S₃ is 4.0.
- The missing conversion factor is [tex]\(\frac{2}{3}\)[/tex].
