# 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?

Mar 5, 2016

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

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

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!