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 2 × 107 L of gas at 22 atm? Assume that temperature remains constant.
Answer in units of L.
I understand that this is a typical P1V1=P2V2, however, I seem to be putting in all the wrong numbers because every time I get an answer it turns out to be wrong. Can someone please explain in better detail of what I am suppose to do?
Thanks in advance!
To solve this problem using the ideal gas law equation (PV = nRT), you need to consider the initial and final conditions of the gas.
Let's assign labels to the given values:
P1 = Initial pressure = 1 atm (surface pressure)
V1 = Initial volume = Unknown (what we need to find)
P2 = Final pressure = 22 atm (underwater pressure)
V2 = Final volume = 2 × 10^7 L (given)
T = Temperature (which remains constant)
Since the system is at STP (Standard Temperature and Pressure), we can assume that the temperature is 273.15 K (0 degrees Celsius) throughout this process.
Using the ideal gas law equation, we can write:
P1V1 / T = nR ----- (Equation 1)
P2V2 / T = nR ----- (Equation 2)
The ideal gas law states that the ratio of pressure, volume, and temperature (P1V1/T and P2V2/T) should remain constant as long as the number of moles (n) and the gas constant (R) stay the same.
Since the same gas is involved in both equations and the temperature remains constant, we can equate the two equations:
P1V1 / T = P2V2 / T
Canceling out the T terms and rearranging, we get:
(P1V1) / (P2) = V2
Substituting the known values, we can solve for V1:
(1 atm * V1) / (22 atm) = 2 × 10^7 L
Simplifying this equation, we find:
V1 = (22 atm * 2 × 10^7 L) / 1 atm
V1 = 44 × 10^7 L
V1 = 4.4 × 10^8 L
Thus, approximately 4.4 × 10^8 liters of gas at STP must be compressed on the surface to fill the underwater environment with 2 × 10^7 L of gas at 22 atm.
It's essential to carefully check the units and make sure they are consistent throughout the calculations to avoid errors.