Question

What is the volume in the liters occupied by 4 moles of `SO_2` at 6 atmospheres and 270°C?

Answer 1

The volume is 30 L.

Explanation:

We can use the Ideal Gas Law to calculate the volume.

The Ideal Gas Law is:

`color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "`

where

• `P` is the pressure
• `V` is the volume
• `n` is the number of moles
• `R` is the gas constant
• `T` is the temperature

We can rearrange the Ideal Gas Law to get

`V = (nRT)/P`

`n = "4 mol"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "(270 + 273.15) K" = "543.15 K"`
`P = "6 atm"`

`V = (nRT)/P = (4 color(red)(cancel(color(black)("mol"))) × "0.082 06 L"· color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1"))) × 543.15 color(red)(cancel(color(black)("K"))))/(6 color(red)(cancel(color(black)("atm")))) = "30 L"`
(1 significant figure)