Vanillin (used to flavour 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 gram per liter of air. If the current price of 50 g of vanillin is $112, determine the cost to supply enough vanillin so that the aroma could be detectable in a large aircraft hangar of volume 5.0 x 107 ft3.

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Question:

Vanillin (used to flavour 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 gram per liter of air. If the current price of 50 g of vanillin is $112, determine the cost to supply enough vanillin so that the aroma could be detectable in a large aircraft hangar of volume 5.0 x 107 ft3.

Answers

Answer:The cost is $0.063.Explanation:First, we need to express the volume of the hangar in liters. We know that 1 ft³ = 28.31 L, so using proportions:[tex]5.0 \times 10^{7} ft^{3} .\frac{28.31L}{1ft^{3} } =1.4 \times 10^{9} L[/tex]The amount of vanillin required would be:[tex]1.4 \times 10^{9} L.\frac{2.0\times 10^{-11}g }{1L} =0.028g[/tex]Finally, the price for such amount of vanillin is:[tex]0.028g.\frac{ \textdollar 112}{50g}=  \textdollar 0.063[/tex]

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