Chemistry Gas Law

Question

At a deep-sea station 200.m below the surface

of the Pacific Ocean, workers live in a highly

pressurized environment. How much gas at

STP must be compressed on the surface to fill

the underwater environment with 1 × 107 L

of gas at 16 atm? Assume that temperature

remains constant.

Answer in units of L.

Answer 1

This question can be solved by setting up a proportion equation using the ideal gas law (PV=nRT).  If we do that, we get:

 

P₁V₁ / n₁RT₁ = P₂V₂ / n₂RT₂

 

Now, lets see if we can simplify our expression.  We are not changing n (mol of gas) by moving from sea level to the deep-sea station, so n₁ = n₂, R is a constant, and the problem states that temperature remains constant, so T₁ = T₂.  Since n, R, and T are the same on each side of our proportion, we can cross them out, leaving:

 

P₁V₁ = P₂V₂ (note that this new equation is Boyle's law)

 

All that left is to plug and chug the answer.  Pressure at sea level is 1 atm, so P₁ = 1, pressure in the station is 16 atm, so P₂ = 16, and the volume of the station is 1 x 10⁷ L, so V₂ = 1 x 10⁷.

 

1 x V₁ = 16 x 1 x 10⁷, so V₁ = 16 x 10⁷ L, or 1.6 x 10⁸ L