I do not understand how my math is incorrect. Can someone please help me with my math component?

I had to watch these two videos:

http://www.youtube.com/watch?v=TerZPj1a1D4

https://www.youtube.com/watch?v=c5_ho2sc0fc

Could you please explain, using physics arguments, what is happeningwith the barrel in this video ? (Hint: Implosion).

This is what I put:

The math model is useful because it provides the experimenter the ability to observe the physical changes the drum undergoes. The ideal gas law is PV=nrT, where P= Pressure (atm), V= volume (L), and n=moles, R=gas constant=8.314 J mol^-1 K ^-1 = 0.821atm*L/ mol*K, and T=temperature (Kelvin). Typically, in ideal gas laws, one is solving for the new variables of "P","V", "T", or"n". In this case, one is solving for pressure because:

1. When the drum is heated, the water turns to steam [phase change]

2. While there is steam in the drum, its pressure is equal to the air pressure outside so no net force

3. When the drum cools, steam condenses very rapidly leaving nothing to support the drum from the inside, so air pressure (P) crushes the drum.

Now, one can re-arrange the ideal gas law, and the new ewuation is P=nRT/V. Conceptually, increasing the temperature (T) adds energy to the gas molecules, thus increasing collisions.

To solve qunatitatively, one must label the givens:

1. n= grams of a gass/ molar mass

2. R= 0.0826 L*atm/mol*k

3. T= 375 K at 100 degrees Celsius

4. V = 55L of the galloon drum

However, one is not given the n, number of moles so one can assume 1 mole because one is not given the exact name of the chemical nonmenclature.

Thus,

P= (1 mole) (0.08206 L*atm/ mol*k) (375K) / 55L

P= 0.5595 atm