Vanillin (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 i \( 2.0 \times 10^{-11} \mathrm{~g} \) per liter of air. If the current price of 50.0 g of vanillin is \( \$ 108 \), determine the cost to supply enough vanillin so that the aroma could be detected in a large aircraft hangar with a volume of \( 4.95 \times 10^{7} \mathrm{ft}^{3} \). Note that \( 1 \mathrm{ft}^{3} \) contains 28.317 L . Round your answer to 2 significant digits.

To determine the cost of supplying enough vanillin for the aroma to be detected in the hangar, we first need to convert the hangar volume from cubic feet to liters. 1. **Convert volume:** \[ \text{Volume in liters} = 4.95 \times 10^{7} \text{ft}^3 \times 28.317 \text{L/ft}^3 \approx 1.404 \times 10^{9} \text{L} \] 2. **Calculate the amount of vanillin needed:** The threshold limit of vanillin is \( 2.0 \times 10^{-11} \mathrm{~g} \) per liter of air, so for our volume: \[ \text{Mass of vanillin} = 1.404 \times 10^{9} \text{L} \times 2.0 \times 10^{-11} \mathrm{~g/L} \approx 0.029 \text{g} \] 3. **Determine the cost of vanillin:** First, we need to calculate the cost per gram of vanillin: \[ \text{Cost per gram} = \frac{\$108}{50.0 \text{g}} = \$2.16 \text{ per gram} \] Then, calculate the total cost for 0.029 g: \[ \text{Total cost} = 0.029 \text{g} \times \$2.16/\text{g} \approx \$0.0632 \] 4. **Round the answer to two significant digits:** The total cost is therefore approximately: \[ \boxed{0.063} \] So, the cost to supply enough vanillin for the aroma to be detected in the aircraft hangar is approximately 0.063 dollars.