Question

used to flavor vanilla ice cream and other foods) is the substance whose aroma the human nose detects in the smallest amount. The threshold limit is 2.0 x 10-11 g per liter of air. If the current price of 50.0 g of vanillin is $104, determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.95 x 107 ft. Guided Solution

Answer 1

Answer:

The cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.95 x 10^7 ft^3 is $ 0.07.

Step-by-step explanation:

The volume of the hangar is

$V=5.95*10^7 \, ft^3$

The minimal amount of vainilla needed to be detected in the hangar is equivalent to the threshold multiplied by the volume of the hangar:

$Va=V*Th=5.95*10^7 \, ft^3*2.0*10^{-11}\,\frac{g}{L}*\frac{28.317L}{1ft^3}\\  \\Va=336.9723*10^{-4} \, g=0.0337\,g$

The cost of this amount of vainilla is

$Cost = Va*p=0.0337\,g*\frac{104\, usd}{50\, g} =0.07 \, usd$

The cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of 5.95 x 10^7 ft^3 is $ 0.07.