Imagine that you have a 7.00 L gas tank and a 3.50 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 125 atm , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time

We should fill the acetylene tank to a pressure of 100 atm

Explanation:

Step 1: Data given

Volume tank 1 = 7.00 L

Tank 1 is filled with oxygen and has a pressure of 125 atm

Volume tank 2 = 3.50 L

Step 2: The balanced equation

2 C2H2 + 5 O2 → 4 CO2 + 2 H2O

Step 3: Calculate the pressure of acetylene

p(oxygen) * V(Oxygen) = n(Oxygen) * R * T  

p(Acetylene) * V(Acetylene) = n(Acetylene) * R * T

We can assume both tanks are at the same temperature, so we can write this as followed:

p(Oxygen)* V(Oxygen) / p(Acetylene)*V(Acetylene) = n(Oxygen) / n(Acetylene)    

⇒with n(Oxygen) / n(Acetylene) = 5/2

⇒with p(Oxygen) = 125atm

⇒V(Oxygen) =7L

⇒V(Acetylene) = 3.5L

⇒ this gives us:   (125 * 7) / (P(Acetylene) * 3.5) = 5/2

p(Acetylene) = 100 atm

We should fill the acetylene tank to a pressure of 100 atm

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