Question

A rug made of synthetic fiber measures 12×15 ft rug. The rug contains 30 oz synthetic fiber Acrilan® per square yard.
Due to its composition, Acrilan® contains 50.9% of HCN by mass. If one third of the rug burns, how much HCN (in grams) will be generated?
Report 2 sig figs. in your answer.

Answer 1

To calculate the amount of hydrogen cyanide (HCN) generated from the burning of one-third of the rug, we will follow these steps:

1. **Calculate the area of the rug in square yards**:
- The dimensions of the rug are 12 ft × 15 ft.
- Convert the dimensions to square yards:
\[
\text{Area in square feet} = 12 \, \text{ft} \times 15 \, \text{ft} = 180 \, \text{ft}^2
\]
Since there are 9 square feet in a square yard:
\[
\text{Area in square yards} = \frac{180 \, \text{ft}^2}{9 \, \text{ft}^2/\text{yd}^2} = 20 \, \text{yd}^2
\]

2. **Calculate the total mass of synthetic fiber in the rug**:
- The rug contains 30 oz of synthetic fiber per square yard. Therefore:
\[
\text{Total mass in oz} = 30 \, \text{oz/yd}^2 \times 20 \, \text{yd}^2 = 600 \, \text{oz}
\]

3. **Convert the mass of synthetic fiber from ounces to grams**:
- There are approximately 28.3495 grams in an ounce, so:
\[
\text{Total mass in grams} = 600 \, \text{oz} \times 28.3495 \, \text{g/oz} \approx 17009.7 \, \text{g}
\]

4. **Calculate the mass of HCN produced when one-third of the rug burns**:
- First, determine the mass burned:
\[
\text{Mass burned (1/3 of total)} = \frac{1}{3} \times 17009.7 \, \text{g} \approx 5669.9 \, \text{g}
\]
- Now, calculate the mass of HCN generated. Since Acrilan® contains 50.9% HCN by mass:
\[
\text{Mass of HCN} = 5669.9 \, \text{g} \times 0.509 \approx 2886.6 \, \text{g}
\]

5. **Final result with 2 significant figures**:
- Rounding 2886.6 g to 2 significant figures, we get:
\[
\text{Mass of HCN} \approx 2900 \, \text{g}
\]

Thus, the amount of HCN generated is **2900 grams**.