gas ideal laws and which equation to us

Question

gas storage cylinder for nitrogen, N2(g), is filled with 25,000 g of gas and has a volume of 25.0 L. It is designed to withstand pressures up to 1,000 atmospheres. If this cylinder is left out in the sun, where the temperature could reach up to 50.◦C, is there a danger of it exploding?

Answer 1

Hello, Alyssa,

We'll use the gas law PV=nRT, where

P = pressure in atmospheres (atm)

V = Volume in liters

n = moles of gas

R = the gas constant. I'll use 0.08206 L-atm/mol-⁰K, since it has the units we want.

T = the temperature in ⁰K

We need the moles of N₂. We have 25,000 of N₂ gas and the molar mass of N₂ is 28 g/mole. Divide the mass by the molar mass to obtain the moles N₂. 25,000g/(28 g N₂/mole N₂). I get 893 moles (3 sig figs, for now, although we only have, at most, 2 going in).

Put everything into the gas law equation and solve for P. Remember that T must be in ⁰K.

PV=nRT

P = [(893 moles)(0.08206 L-atm/mol-⁰K)(50 + 273⁰K)]/(25.0 L)

moles and ⁰K cancel out, leaving just atm, which is what we want.

P = 947 atm

We are under 1,000 atm, but I'm moving my desk. A 25L metal cylinder at 1,000 atm would create a bang, plus a fast moving cylinder. Consider moving it to Nate's room. He's the one who left it in the sun. The question simply asks "are we in danger?" I'd say yes, although we are under the design pressure, we don't know where it's been and if it has any cracks that would weaken the tank. Just my opinion. The sought answer is possibly "no danger."

Bob