What is the volume of a scuba tank if it takes 2000 L of air collected at 1.00 atm to fill the tank to a pressure of 150 atm? T is constant.
P1V1 = P2V2
150*V1 = 1*2000
Solve for V1
13.3L
To find the volume of the scuba tank, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas
In this particular case, we are assuming T is constant, so we can simplify the equation to:
PV = constant
First, we need to convert the pressure of the air collected to the same units as the pressure to which the tank is filled (150 atm).
1 atm × (150 atm / 1 atm) = 150 atm
Now, we can set up the equation:
(P1)(V1) = (P2)(V2)
Where:
P1 = 1.00 atm (initial pressure of the air collected)
V1 = 2000 L (initial volume of the air collected)
P2 = 150 atm (final pressure when the tank is filled)
V2 = ?
Rearranging the equation to solve for V2:
V2 = (P1)(V1) / P2
Substituting the given values:
V2 = (1.00 atm)(2000 L) / 150 atm
Calculating:
V2 = 13.33 L
Therefore, the volume of the scuba tank is approximately 13.33 L.