To calculate the amount of hydrogen cyanide (HCN) generated from the burning of one-third of the rug, we will follow these steps:
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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: \[ \text{Area in square yards} = \frac{180 , \text{ft}^2}{9 , \text{ft}^2/\text{yd}^2} = 20 , \text{yd}^2 \]
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Calculate the total mass of synthetic fiber in the rug:
- The rug contains 30 oz of synthetic fiber per square yard. Therefore: \[ \text{Total mass in oz} = 30 , \text{oz/yd}^2 \times 20 , \text{yd}^2 = 600 , \text{oz} \]
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Convert the mass of synthetic fiber from ounces to grams:
- There are approximately 28.3495 grams in an ounce, so: \[ \text{Total mass in grams} = 600 , \text{oz} \times 28.3495 , \text{g/oz} \approx 17009.7 , \text{g} \]
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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: \[ \text{Mass of HCN} = 5669.9 , \text{g} \times 0.509 \approx 2886.6 , \text{g} \]
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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.