Question

4.8g of sulfur and 5.4g of aluminum react to form aluminum sulfide (AI2S3). If 4.5g of aluminum sulfide are recovered, determine the percent yield. (Molar mass of S = 32.06 g/mol, molar mass of Al = 26.98 g/mol)

Answer 1

To calculate the percent yield, we need to compare the actual yield (what was obtained in the experiment) with the theoretical yield (what could be obtained based on stoichiometry). The percent yield, we need to compare the actual yield is 45.52%.

Step-by-step explanation:

To calculate the percent yield, we need to compare the actual yield (what was obtained in the experiment) with the theoretical yield (what could be obtained based on stoichiometry).

1. Determine moles of sulfur (S) and aluminum (Al):

moles of S =
`\frac{\text{mass of S}}{\text{molar mass of S}}`

moles of Al =
`\frac{\text{mass of Al}}{\text{molar mass of Al}}`

moles of S =
`\frac{4.8 \, \text{g}}{32.06 \, \text{g/mol}}`

≈ 0.15 mol

moles of Al =
`\frac{5.4 \, \text{g}}{26.98 \, \text{g/mol}}`

≈ 0.20 mol

2. Determine the limiting reactant:

The limiting reactant is the one that forms fewer moles of the product. From the balanced equation 3 S + 2 Al → Al₂S₃, we see that 3 moles of sulfur react with 2 moles of aluminum to form 1 mole of aluminum sulfide.

For sulfur:
`\(\frac{0.15 \, \text{mol}}{3}` = 0.05 mol Al₂S₃

For aluminum:
`\(\frac{0.20 \, \text{mol}}{2}` = 0.10 mol Al₂S₃

The limiting reactant is sulfur.

3. Calculate the theoretical yield of aluminum sulfide (Al₂S₃):

moles Al₂S₃ =
`\frac{\text{moles of S}}{3}`

moles Al₂S₃ =
`\frac{0.15 \, \text{mol}}{3}` = 0.05 mol

Theoretical yield = moles Al₂S₃ × molar mass of Al₂S₃

Theoretical yield = 0.05 mol × (2 × 26.98 g/mol + 3 × 32.06 g/mol)

4. Calculate the percent yield:

Percent yield =
`\left( \frac{\text{Actual yield}}{\text{Theoretical yield}} \right) * 100`

Percent yield =
`\left( \frac{4.5 \, \text{g}}{0.05 \, \text{mol} * \left( 2 * 26.98 \, \text{g/mol} + 3 * 32.06 \, \text{g/mol} \right)} \right) * 100`

Percent yield = 45.52

So, the percent yield, we need to compare the actual yield is 45.52%.