Question

A snorkeler takes a syringe filled with 16.0 mL of air from the surface, where the pressure is 1.00 atm to an unknown depth. The volume of the air in the syringe at this depth is 7.5 mL. What is the pressure at this depth? If the pressure increases by 1 atm for every 10.0 m of depth, how deep is the snorkeler?

a) 5.0 m
b) 10.0 m
c) 15.0 m
d) 20.0 m

Answer 1

The pressure at the snorkeler's depth is determined to be 2.13 atm using Boyle's Law. By accounting for pressure change per depth, the snorkeler is determined to be approximately 10.0 m deep, which is option (b).

Step-by-step explanation:

To determine the pressure at the unknown depth where the snorkeler is swimming, we can use Boyle's Law, which states that the product of the pressure and volume of a gas is constant if the temperature remains unchanged (P1V1 = P2V2). From the surface to the unknown depth, the volume changes from 16.0 mL to 7.5 mL, and the pressure increases correspondingly.

Using Boyle’s Law:

• P1 = 1.00 atm (at the surface)
• V1 = 16.0 mL
• V2 = 7.5 mL
• P2 = P1 * (V1/V2) = 1.00 atm * (16.0 mL / 7.5 mL) = 2.13 atm

Pressure at depth is 2.13 atm. Since each 10 m of depth adds 1 atm of pressure, and we know the surface pressure is 1 atm, we can find the depth by subtracting the surface pressure and multiplying the remainder by 10 m/atm.

Depth = (P2 - 1 atm) * (10 m/atm) = (2.13 atm - 1 atm) * (10 m/atm) = 11.3 m

Given the possible answers, the snorkeler is approximately 10.0 m underwater, because the pressure rounds to about 2 atm and there would be an additional 1 atm from the atmosphere.