#
**Problem**: Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 310 mg HCN per kilogram of air when inhaled.HCN forms when synthetic fibers containing Orlon® or Acrilan® burn. Acrilan® has an empirical formula of CH2CHCN, so HCN is 50.9% of the formula by mass. A rug measures 13 x 17 ft and contains 30 oz of HCN 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.

###### FREE Expert Solution

###### FREE Expert Solution

Calculate the area of the rug in square yard (yd^{2}):

1 yd = 3 ft

$\overline{)\mathbf{A}\mathbf{=}\mathbf{l}\mathbf{\times}\mathbf{w}}\phantom{\rule{0ex}{0ex}}\mathbf{A}\mathbf{=}\mathbf{13}\mathbf{}\mathbf{ft}\mathbf{\times}\mathbf{17}\mathbf{}\mathbf{ft}\phantom{\rule{0ex}{0ex}}\mathbf{A}\mathbf{=}\mathbf{221}\mathbf{}{\mathbf{ft}}^{\mathbf{2}}\mathbf{\times}{\mathbf{\left(}\frac{\mathbf{1}\mathbf{}\mathbf{yd}}{\mathbf{3}\mathbf{}\mathbf{ft}}\mathbf{\right)}}^{\mathbf{2}}\phantom{\rule{0ex}{0ex}}\mathbf{A}\mathbf{=}\mathbf{221}\mathbf{}\overline{){\mathbf{ft}}^{\mathbf{2}}}\mathbf{\times}\frac{\mathbf{1}\mathbf{}{\mathbf{yd}}^{\mathbf{2}}}{\mathbf{9}\mathbf{}\overline{){\mathbf{ft}}^{\mathbf{2}}}}$

A = 24.5555 yd^{2}

Calculate the mass of Acrilan® in the rug:

1 oz = 28.3495 g

$\mathbf{mass}\mathbf{}\mathbf{Acrilan}\mathbf{\circledR}\mathbf{=}\mathbf{24}\mathbf{.}\mathbf{5555}\mathbf{}\overline{){\mathbf{yd}}^{\mathbf{2}}}\mathbf{\times}\frac{\mathbf{30}\mathbf{}\overline{)\mathbf{oz}}}{\mathbf{1}\mathbf{}\overline{){\mathbf{yd}}^{\mathbf{2}}}}\mathbf{\times}\frac{\mathbf{28}\mathbf{.}\mathbf{3495}\mathbf{}\mathbf{g}}{\mathbf{1}\mathbf{}\overline{)\mathbf{oz}}}$

mass Acrilan® = 20884.1 g

Calculate the mass of HCN:

###### Problem Details

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 310 mg HCN per kilogram of air when inhaled.

HCN forms when synthetic fibers containing Orlon^{®} or Acrilan^{®} burn. Acrilan^{®} has an empirical formula of CH_{2}CHCN, so HCN is 50.9% of the formula by mass. A rug measures 13 x 17 ft and contains 30 oz of HCN 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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Dimensional Analysis concept. You can view video lessons to learn Dimensional Analysis Or if you need more Dimensional Analysis practice, you can also practice Dimensional Analysis practice problems .

How long does this problem take to solve?

Our expert Chemistry tutor, Dayana took 7 minutes to solve this problem. You can follow their steps in the video explanation above.