At a deep-sea station 200.m below the surface
of the Pacific Ocean, workers live in a highlypressurized 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 temperatureremains constant.
Answer in units of L.
P1V1 = P2V2
To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to convert the given pressure of 16 atm into the unit of pressure used in the ideal gas law, which is in terms of Pascals (Pa). Since 1 atm is equal to 101,325 Pa, we can convert 16 atm as follows:
16 atm x 101,325 Pa/atm = 1,620,400 Pa
Next, we convert the volume of gas at the deep-sea station. We are given that the volume is 1 × 10^7 L.
Now, let's assume that the temperature remains constant. Therefore, the temperature can be canceled out from both sides of the equation.
Rearranging the ideal gas law equation, we get: n = PV / RT.
Since we want to find the number of moles of gas (n) required to fill the underwater environment, we need to find the term PV. Rearranging the equation once again, we get: PV = nRT.
Substituting the given values into the equation:
PV = (1,620,400 Pa) x (1 × 10^7 L)
Now, we can solve for the number of moles (n) using this equation. However, we need to know the value of the ideal gas constant (R). The value of R depends on the units used. In this case, we need to use R with units to match the given pressure and volume units.
For pressure in Pascals (Pa) and volume in liters (L), the value of R is 0.0821 L·atm/(mol·K).
Substituting the given values:
PV = (1,620,400 Pa) x (1 × 10^7 L)
nRT = (1,620,400 Pa) x (1 × 10^7 L) x (0.0821 L·atm/(mol·K))
Now, the units of pressure (Pa) and volume (L) will cancel out, leaving us with the units of moles (mol):
n = (1,620,400 Pa) x (1 × 10^7 L) x (0.0821 L·atm/(mol·K))
Calculating this equation will give us the number of moles of gas required to fill the underwater environment.