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

Dec 29, 2016

The volume is 30 L.

Explanation:

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

The Ideal Gas Law is:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

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

$V = \frac{n R T}{P}$

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

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)