Question

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?

Answer 1

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!