Chemistry Help

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 is an application of Boyle's Law:

 

P₁V₁ = P₂V₂

 

Initial pressure P₁ = 1 atmosphere, since you've been told it's STP (standard temperature and pressure). Initial volume is unknown. Final pressure P₂ = 16, and final volume V₂ = 1 × 10⁷. Plug in the values and solve for the unknown, V₁.

 

-------------------------------------

 

Hi Teresa,

 

Here's a more thorough explanation. This problem uses a formula called Boyle's Law, which says that if you've got a gas in some contained area, then (as long as you don't change the gas's temperature or add more gas to the contained area) volume and pressure are related. Let's say you make some change to the gas's pressure or volume without changing anything else. The gas initially had pressure P₁ and volume V₁. After the change, it has final pressure P₂, and final volume V₂. Knowing any three of those values, you can find the other one using Boyle's Law:

 

P₁V₁ = P₂V₂

 

This problem is one of those situations. We're not changing number of molecules or temperature, just volume and pressure. Initially, the gas is at the surface at STP, which is "Standard Temperature and Pressure." Standard pressure is 1 atmosphere, so P₁ = 1. Initially, we don't know the volume V₁. That's what the problem asks you to find. After the gas is brought down to the underwater environment, pressure is 16 atmospheres, so P₂ = 16. Volume in the environment is 10⁷ liters (I assume you meant for that to be an exponent), so V₂ = 10⁷. Plug those values into Boyle's Law:

 

P₁V₁ = P₂V₂

(1)V₁ = (16)(10⁷)

V₁ = 16 × 10⁷

V₁ = 1.6 × 10⁸    (proper scientific notation)

 

So, the initial volume of gas you need is 1.6 × 10⁸ L.

 

Does that make sense?