Final answer:
To calculate the volume of air needed to fill an underwater research station, considering the pressure difference at depth and the surface, use the Combined Gas Law. For a station volume of 2.00 x 10⁷ L at 27.0 atm of pressure, the volume needed at the surface at 1 atm is 5.40 x 10⁸ L.
Step-by-step explanation:
The student is asking about how to calculate the volume of air needed to fill an underwater research station, considering the difference in pressure at depth versus the surface. This is a typical application of the Combined Gas Law, which relates the pressure, volume, and temperature of a gas. To find the required volume of air to be delivered to the research station, we can set the product of pressure and volume at the surface equal to the product of pressure and volume at the depth, assuming that temperature remains constant (i.e., P1V1 = P2V2). Given that the pressure at the surface (P1) is 1 atm and the pressure at depth (P2) is 27.0 atm, and that the volume at depth (V2) is 2.00 x 10⁷ L, we can rearrange the Combined Gas Law to solve for V1, the volume at the surface:
V1 = (P2 x V2) / P1
Plugging in the values:
V1 = (27.0 atm x 2.00 x 10⁷ L) / 1 atm = 5.40 x 10⁸ L
Therefore, the volume of air that should be delivered at the surface to fill the underwater research station is 5.40 x 10⁸ L.