Question 3.21: Calculating Percent Yield Problem Silicon carbide (SiC) is a......
Calculating Percent Yield
Problem Silicon carbide (SiC) is an important ceramic material made by reacting sand (silicon dioxide, SiO_2) with powdered carbon at a high temperature. Carbon monoxide is also formed. When 100.0 kg of sand is processed, 51.4 kg of SiC is recovered. What is the percent yield of SiC from this process?
Plan We are given the actual yield of SiC (51.4 kg), so we need the theoretical yield to calculate the percent yield. After writing the balanced equation, we convert the given mass of SiO_2 (100.0 kg) to amount (mol). We use the molar ratio to find the amount of SiC formed and convert it to mass (kg) to obtain the theoretical yield. Then, we use Equation 3.8 to find the percent yield (see the road map (Fig 3.21)).
\% \text{ yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100 (3.8)
Solution Writing the balanced equation:
SiO_2(s) + 3C(s) ⟶ SiC(s) + 2CO(g)Converting from mass (kg) of SiO_2 to amount (mol):
\text{Amount (mol) of }SiO_2 = 100.0 \cancel{kg SiO_2} \times \frac{1000 g}{1 \cancel{kg}} \times \frac{1 \text{mol} SiO_2}{60.09 \cancel{g SiO_2} } = 1664 \text{mol} SiO_2Converting from amount (mol) of SiO_2 to amount (mol) of SiC: The molar ratio is 1 mol SiC/1 mol SiO_2, so
\text{Amount (mol) of }SiO_2 = \text{moles of SiC = 1664 mol SiC}Converting from amount (mol) of SiC to mass (kg):
\text{Mass (kg) of SiC = 1664} \cancel{\text{mol} SiC} \times \frac{40.10 g SiC}{1 \cancel{\text{mol} SiC}} \times \frac{1 \text{kg}}{1000 g} = 66.73 \text{kg} SiCCalculating the percent yield:
\text{\% yield of SiC } = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100 = \frac{51.4 \cancel{\text{kg} SiC}}{66.73 \cancel{\text{kg} SiC}} \times 100 = 77.0\%Check Rounding shows that the mass of SiC seems correct: ∼1500 mol × 40 g/mol × 1 kg/1000 g = 60 kg. The molar ratio of SiC/SiO_2 is 1/1, and ℳ of SiC is about two-thirds (∼\frac{40}{ 60}) of ℳ of SiO_2, so 100 kg of SiO_2 should form about 66 kg of SiC.
