When 32.4 g of carbon is heated with silicon dioxide, 28.2 g of carbon monoxide is produced. Part A What is the percent yield of carbon monoxide for this reaction? $$ \mathrm{SiO}_{2}(\mathrm{~s})+3 \mathrm{C}(\mathrm{~s}) \rightarrow \mathrm{SiC}(\mathrm{~s})+2 \mathrm{CO}(\mathrm{~g}) $$ Express your answer with the appropriate units. The percent yield of CO $$ \square $$ Value Units Subint Requent Anower

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To calculate the percent yield of carbon monoxide (CO) in the reaction, we need to follow these steps:

1. **Determine the theoretical yield of CO** based on the amount of carbon used.
2. **Calculate the percent yield** using the actual yield and the theoretical yield.

### Step 1: Calculate the Theoretical Yield of CO

From the balanced chemical equation:
$$
\mathrm{SiO}_{2}(\mathrm{~s}) + 3 \mathrm{C}(\mathrm{~s}) \rightarrow \mathrm{SiC}(\mathrm{~s}) + 2 \mathrm{CO}(\mathrm{~g})
$$

This indicates that 3 moles of carbon produce 2 moles of carbon monoxide.

#### Molar Masses:
- Molar mass of Carbon (C) = 12.01 g/mol
- Molar mass of Carbon Monoxide (CO) = 28.01 g/mol

#### Calculate Moles of Carbon:
$$
\text{Moles of C} = \frac{\text{mass of C}}{\text{molar mass of C}} = \frac{32.4 \, \text{g}}{12.01 \, \text{g/mol}}
$$

#### Calculate Theoretical Yield of CO:
From the stoichiometry of the reaction, 3 moles of C produce 2 moles of CO. Therefore, the moles of CO produced from the moles of C can be calculated as follows:
$$
\text{Moles of CO} = \text{Moles of C} \times \frac{2 \, \text{moles of CO}}{3 \, \text{moles of C}}
$$

Now, we can convert the moles of CO to grams:
$$
\text{Mass of CO} = \text{Moles of CO} \times \text{molar mass of CO}
$$

### Step 2: Calculate Percent Yield
The percent yield is calculated using the formula:
$$
\text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100\%
$$

Where:
- Actual Yield = 28.2 g (given)
- Theoretical Yield = calculated from the previous step.

Now, let's perform the calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{32.4}{12.01}$$
- step1: Convert the expressions:
  $$\frac{\frac{162}{5}}{\frac{1201}{100}}$$
- step2: Multiply by the reciprocal:
  $$\frac{162}{5}\times \frac{100}{1201}$$
- step3: Reduce the numbers:
  $$162\times \frac{20}{1201}$$
- step4: Multiply:
  $$\frac{162\times 20}{1201}$$
- step5: Multiply:
  $$\frac{3240}{1201}$$
Calculate or simplify the expression $$ (32.4/12.01)*(2/3)*28.01 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{32.4}{12.01}\right)\times \frac{2}{3}\times 28.01$$
- step1: Divide the terms:
  $$\frac{3240}{1201}\times \frac{2}{3}\times 28.01$$
- step2: Multiply the terms:
  $$\frac{2160}{1201}\times 28.01$$
- step3: Convert the expressions:
  $$\frac{2160}{1201}\times \frac{2801}{100}$$
- step4: Multiply the fractions:
  $$\frac{2160\times 2801}{1201\times 100}$$
- step5: Multiply the terms:
  $$\frac{6050160}{1201\times 100}$$
- step6: Multiply the terms:
  $$\frac{6050160}{120100}$$
- step7: Reduce the fraction:
  $$\frac{302508}{6005}$$
Calculate or simplify the expression $$ (32.4/12.01)*(2/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{32.4}{12.01}\right)\times \frac{2}{3}$$
- step1: Divide the terms:
  $$\frac{3240}{1201}\times \frac{2}{3}$$
- step2: Reduce the numbers:
  $$\frac{1080}{1201}\times 2$$
- step3: Multiply:
  $$\frac{1080\times 2}{1201}$$
- step4: Multiply:
  $$\frac{2160}{1201}$$
### Step 1: Calculate Moles of Carbon
The moles of carbon (C) are calculated as follows:
$$
\text{Moles of C} \approx 2.70 \, \text{mol}
$$

### Step 2: Calculate Theoretical Yield of CO
Using the stoichiometry of the reaction:
$$
\text{Moles of CO} \approx 1.80 \, \text{mol}
$$

Now, converting moles of CO to grams:
$$
\text{Mass of CO} \approx 50.38 \, \text{g}
$$

### Step 3: Calculate Percent Yield
Now we can calculate the percent yield using the actual yield (28.2 g) and the theoretical yield (50.38 g):
$$
\text{Percent Yield} = \left( \frac{28.2 \, \text{g}}{50.38 \, \text{g}} \right) \times 100\%
$$

Let's perform this final calculation.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{28.2}{50.38}\right)\times 100$$
- step1: Divide the terms:
  $$\frac{1410}{2519}\times 100$$
- step2: Multiply:
  $$\frac{1410\times 100}{2519}$$
- step3: Multiply:
  $$\frac{141000}{2519}$$
The percent yield of carbon monoxide (CO) is calculated as follows:
$$
\text{Percent Yield} \approx 55.97\%
$$

### Final Answer
The percent yield of CO is approximately $$ 55.97\% $$.
The percent yield of CO is approximately 55.97%.

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