Question

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 290 mg HCN per kilogram of air when formed during the burning of synthetic fibers containing Orlon® or Acrilan®. Acrilan® has an empirical formula of CH₂CHCN, with HCN comprising 50.9% of the formula by mass. A rug measures 14 × 17 ft and contains 30 oz of Acrilan® fibers per square yard of carpet. If the rug burns, will a lethal dose of HCN be generated in the room? Assume that the yield of HCN from the fibers is 20%, and that the carpet is 50% consumed.

a) Yes, a lethal dose of HCN will be generated in the room.
b) No, a lethal dose of HCN will not be generated in the room.
c) Insufficient information to determine.
d) The question cannot be answered based on the given data.

Answer 1

To determine if a lethal dose of HCN will be generated in the room, we need to calculate the amount of HCN that will be produced when the rug burns and compare it to the lethal dose. However, the question does not provide the volume of air in the room, so it is not possible to determine if a lethal dose of HCN will be generated.

Step-by-step explanation:

To determine if a lethal dose of HCN will be generated in the room, we need to calculate the amount of HCN that will be produced when the rug burns and compare it to the lethal dose.

1. First, calculate the amount of Acrilan® in the rug: 14 ft x 17 ft = 238 square feet. Since there are 30 oz of Acrilan® fibers per square yard, the total amount of Acrilan® fibers in the rug is 238 x 30 = 7140 oz.
2. To convert the amount of Acrilan® fibers to grams, use the conversion factor: 1 oz = 28.35 g. So, 7140 oz = 7140 x 28.35 g = 202,299 g.
3. From the empirical formula of Acrilan®, we know that HCN comprises 50.9% of the formula by mass. Therefore, the mass of HCN in 202,299 g of Acrilan® is 50.9% x 202,299 g = 102,938 g.
4. Since the yield of HCN from the fibers is 20%, the actual amount of HCN produced when the rug burns is 20% x 102,938 g = 20,588 g.
5. Finally, we need to consider that only 50% of the carpet is consumed. So, the amount of HCN that will be generated in the room is 50% x 20,588 g = 10,294 g.

The lethal dose of HCN is approximately 290 mg per kilogram of air. To determine if the room will have a lethal dose, we would need to know the volume of air in the room, which is not provided in the question. Therefore, the answer is: c) Insufficient information to determine.