A gas canister can tolerate internal pressures up to 210 atmospheres. If a 2.0 L canister holding 3.5 moles of gas is heated to 1350° C, will the canister explode?

1 Answer
Mar 5, 2016

Answer:

The canister will explode.

Explanation:

This appears to be an Ideal Gas Law problem.

The Ideal Gas Law is

#color(blue)(|bar(ul(PV = nRT)|)#,

where

  • #P# is the pressure
  • #V# is the volume
  • #n# is the number of moles
  • #R# is the Universal Gas Constant
  • #T# is the temperature

#V = "2.0 L"#
#n = "3.5 mol"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "(1350 + 273.15) K = 1623.15 K"#

We can rearrange the Ideal Gas Law to get

#P = (nRT)/V = (3.5 color(red)(cancel(color(black)("mol"))) × "0.082 06" color(red)(cancel(color(black)("L")))"·atm·"color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 1623.15 color(red)(cancel(color(black)("K"))))/(2.0 color(red)(cancel(color(black)("L")))) = "230 atm"#

This exceeds the burst pressure of the canister.

The canister will explode!