Imagine that you have a 6.00 L
gas tank and a 4.50 L
gas tank. You need to fill one tank with oxygen and the other with acetylene to use in conjunction with your welding torch. If you fill the larger tank with oxygen to a pressure of 135 atm
, to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behavior for all gases.
To determine the pressure that the acetylene tank should be filled to in order to run out of each gas at the same time, we can use the ideal gas law.
First, let's calculate the number of moles of oxygen in the 6.00 L tank when it is filled to 135 atm:
PV = nRT
(135 atm) (6.00 L) = n (0.0821 L atm/mol K) (298 K)
810 = n (24.4858)
n = 33.2 moles
Next, we need to determine the volume of the acetylene tank that would contain an equivalent number of moles of acetylene to the oxygen tank. Since the acetylene tank has a volume of 4.50 L, the pressure required to reach the same number of moles as the oxygen tank can be calculated as follows:
PV = nRT
P (4.50 L) = (33.2 moles) (0.0821 L atm/mol K) (298 K)
4.50P = 33.2 (24.4858)
4.50P = 813.3
P = 180 atm
Therefore, the acetylene tank should be filled to a pressure of 180 atm to ensure that you run out of oxygen and acetylene at the same time.